## 统计代写|决策与风险作业代写decision and risk代考|Output Analysis for Transient Simulations

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|决策与风险作业代写decision and risk代考|A Simple Inventory Model

The simple model that we introduce below is based on the model proposed in Muñoz and Muñoz (2011) to forecast the demand of items with sporadic demand, and is inspired in the ideas of Kalchsmidth et al. (2006), where they suggest the use of forecasting techniques that take into account not only the time series, but also the structure of the process that generates the demand (non-systematic variability). In what follows we will refer to this model as Model $1 .$

Let us suppose that a seller uses a $(Q, R$ ) policy (see, e.g., Nahmias 2013 ) to order the supply of a certain product, i.e., when the inventory level reaches the reorder point $(R)$, a quantity $Q$ is ordered. If an order is placed at time $t=0$ and $L$ is the delay, then the demand for the product during the delay is
$$W_{1}=\left{\begin{array}{cc} \sum_{i=1}^{N(L)} U_{i}, & N(L)>0 \ 0, & \text { otherwise } \end{array}\right.$$
where, for $t \geq 0, N(t)$ is the number of clients that arrived up to time t, and for $i=1,2, \ldots, U_{i}$ is the demand for client $i$. We assume that $U_{1}, U_{2}, \ldots$ are i.i.d. random variables and are also independent of the stochastic process ${N(t): t \geq 0}$. In order to obtain analytical results for some of our performance measures, we also assume that ${N(t): t \geq 0}$ is a Poisson process with rate $\Theta_{0}$.

Under our assumptions, we can define the following parameters that represent important properties for the policy $(Q, R)$ (for details on the derivation of the analytical expressions see Muñoz et al. 2013).

The expected demand is an important measure to forecast demand $W_{1}$, and is defined by
$$\mu_{W}=E\left[W_{1}\right]=\Theta_{0} L \mu_{U}$$
where $E[X]$ denotes the expected value of a random variable $X$, and $\mu_{U}=E\left[U_{1}\right]$.
The variance of demand $W_{1}$ is an important measure for the magnitude of the uncertainty on the forecast of demand $W_{1}$, and is defined by
$$\sigma_{W}^{2}=E\left[W_{1}^{2}\right]-E\left[W_{1}\right]^{2}=\Theta_{0} L\left(\mu_{U}^{2}+\sigma_{U}^{2}\right)$$
where $\mu_{U}^{2}=E\left[U_{1}\right]^{2}, \sigma_{U}^{2}=E\left[U_{1}^{2}\right]-\mu_{U^{*}}^{2}$
Given a value $R$ for the reorder point, an important risk measure is the probability of no stockout (called type-l service level), and is defined by
$$\alpha_{1}(R)=P\left[W_{1} \leq R\right]=E\left[I\left(W_{1} \leq R\right)\right]$$
where, for any event $A, I(A)$ denotes the indicator random variable that takes a value of 1 if event $A$ occurs and zero otherwise.

Given a value $0<\alpha<1$, the type-1 reorder point is a value for the reorder point that provides an approximate type-1 service level of $\alpha$, and is defined by
$$r_{1}(\alpha)=\inf \left{R \geq 0: \alpha_{1}(R) \geq \alpha\right}$$
where $\alpha_{1}(R)$ is defined in (6.5).
Similarly, given a value $R$ for the reorder point, another important risk measure is the proportion of demand that is met from stock (called type-2 service level or fill

rate), and is defined by
$$\alpha_{2}(R)=1-\frac{E\left[\left(W_{1}-R\right) I\left(W_{1}>R\right)\right]}{Q}$$
and given a value $0<\alpha<1$, the type-2 reorder point is a value for the reorder point that provides an approximate type- 2 service level of $\alpha$, and is defined by
$$r_{2}(\alpha)=\inf \left{R \geq 0: \alpha_{2}(R) \geq \alpha\right}$$
where $\alpha_{2}(R)$ is defined in $(6.7)$.
In the next sections, we show how to estimate the measures of risk defined by Eqs. (6.3) through (6.6) from the output of a simulation, and remark that Model 1 , as defined in (6.1), is a very simple model just to verify (using simulation) that we are proposing valid estimation procedures that may be applied to a complex model, for which we would not have analytical solutions.

## 统计代写|决策与风险作业代写decision and risk代考|Properties of a Good Estimator

In order to discuss the main properties that a good simulation-based estimator must satisfy, we use the concept of weak converge of random variables. We say that a sequence of random variables $X_{1}, X_{2}, \ldots$ converge weakly to a random variable $X$ (and denote $X_{m} \Rightarrow X$, as $m \rightarrow \infty$ ), if $\lim {m \rightarrow \infty} F{X_{m}}(x)=F_{X}(x)$, at any point $x$ where $F$ is continuous, where $F_{X_{m}}$ and $F_{X}$ denote the c.d.f. of $X_{m}$ and $X$, respectively (see, e.g., Chung 2000 ). Note that $X$ can also be a constant $(M)$, on which case $X$ is simply the random variable that takes the value of $M$ with probability 1 .

A first property that a good estimator must satisfy is consistency. We say that the estimator $T\left(F_{m}\right)$, where $F_{m}$ is defined in (6.1) is consistent if
$$T\left(F_{m}\right) \Rightarrow T(F)$$
as $m \rightarrow \infty$. Note that consistency means that the estimator $T\left(F_{m}\right)$ approaches the parameter $T(F)$ as the sample size $m$ increases, and this is a required property since we do not want the estimator to converge to a different value (or not to converge at all).

In order to assess the accuracy of a consistent estimator $T\left(F_{m}\right)$, we usually verify if a Central Limit Theorem (CLT) in the form of
$$\frac{\sqrt{m}\left(T\left(F_{m}\right)-T(F)\right)}{\sigma_{T}} \Rightarrow N(0,1)$$
as $m \rightarrow \infty$ is satisfied, on which case we may also look for a consistent estimator $\hat{\sigma}^{2}(m)$ for the asymptotic variance $\sigma_{T}^{2}$, so that if follows from $(6.10)$ and standard

properties of weak convergence (see, e.g., Serfling 2009) that
$$\frac{\sqrt{m}\left(T\left(F_{m}\right)-T(F)\right)}{\hat{\sigma}(m)} \Rightarrow N(0,1),$$
as $m \rightarrow \infty$, where $N(0,1)$ denotes a random variable distributed as Normal with mean 0 and variance 1 . It is worth mentioning that the CLT of (6.10) implies consistency of $T\left(F_{m}\right)$, as defined in (6.9).

A CLT in the form of $(6.11)$ is sufficient to assess the accuracy of the point estimator $T\left(F_{m}\right)$, since (6.11) implies that
$$\lim {m \rightarrow \infty} P\left[\left|T\left(F{m}\right)-T(F)\right| \leq z_{\beta} \frac{\hat{\sigma}(m)}{\sqrt{m}}\right]=1-\beta$$
where $z_{\beta}$ denotes the $(1-\beta / 2)$-quantile of a $N(0,1)$, which is sufficient to establish an asymptotically valid $(1-\beta) 100 \%$ confidence interval (CI) for $T(F)$ with halfwidth
$$H W_{T}=\frac{t_{(m-1, \beta)} \hat{\sigma}(m)}{\sqrt{m}}$$
where $t_{(m-1, \beta)}$ denotes the $(1-\beta / 2)$-quantile of a Student-t distribution with $(\mathrm{m}-$ 1) degrees of freedom. A halfwidth in the form of $(6.12)$ is the typical measure used in simulation software to assess the accuracy of $T\left(F_{m}\right)$ for the estimation of a parameter $T(F)$. Note that we are using a Student-t distribution to have a wider CI when the value of $m$ is small, and the CI is still asymptotically valid since $t_{(m-1, \beta)} \rightarrow z_{\beta}$, as $m \rightarrow \infty$. Note also from (6.12) that, to lower the value of a halfwidth (i.e., improve the accuracy of $T\left(F_{m}\right)$ ), we need to increase the sample size $m$, so that the halfwidth will be reduced approximately by half if we multiply the sample size $m$ by 4 .

## 统计代写|决策与风险作业代写decision and risk代考|Estimation of Expected Values

For the estimation of the expected value $T(F)=E\left[W_{1}\right]$, the point estimator $T\left(F_{m}\right)$ becomes the sample average
$$\bar{W}(m)=\frac{\sum_{i=1}^{m} W_{i}}{m},$$
and it is well-known from the classical CLT that the CLT (6.10) is satisfied for $T\left(F_{m}\right)=\bar{W}(m)$, and $\sigma_{T}^{2}=E\left[W_{1}^{2}\right]-E\left[W_{1}\right]^{2}$. Moreover, since $W_{1}, W_{2}, \ldots, W_{m}$ are i.i.d., it is well known that a consistent (and unbiased) estimator for $\sigma_{T}^{2}$ is

$$S_{W}^{2}(m)=\frac{\sum_{i=1}^{m}\left(W_{i}-\bar{W}(m)\right)^{2}}{m-1}$$
so that, it follows from (6.11) that an asymptotically valid $(1-\beta) 100 \%$ halfwidth for the expected value $\mu_{W}=E\left[W_{1}\right]$ is given by
$$H W_{\mu_{W}}=\frac{t_{(m-1 . \beta)} S_{W}(m)}{\sqrt{m}},$$
where $S_{W}(m)$ is defined in (6.14).
Thus, Eq. (6.13) can be used to compute a point estimator for the expected value in a transient simulation, and Eq. (6.15) allows us to compute an assessment of the accuracy of the point estimator. Note that Eqs. (6.13) and (6.15) can be applied not only to the estimation of the expected demand (6.3) in Model 1 but also for the estimation of a type-1 service level defined in (6.5) or a type- 2 service level defined in (6.7), since the service levels are also expectations, to be more precise, we can take $W_{1 i}=I\left[W_{i} \leq R\right]$ for parameter $(6.5)$ and $W_{2 i}=1-\left(W_{i}-R\right) I\left[W_{i}>R\right] / Q$ for parameter $(6.7), i=1, \ldots, m$. A $\mathrm{C}++$ code for the estimation of these risk measures using simulation output was compiled to produce a library and below we report numerical examples using this code.

## 统计代写|决策与风险作业代写decision and risk代考|A Simple Inventory Model

$$W_{1}=\left{∑一世=1ñ(大号)ü一世,ñ(大号)>0 0, 除此以外 \对。$$

μ在=和[在1]=θ0大号μü

σ在2=和[在12]−和[在1]2=θ0大号(μü2+σü2)

r_{1}(\alpha)=\inf \left{R \geq 0: \alpha_{1}(R) \geq \alpha\right}r_{1}(\alpha)=\inf \left{R \geq 0: \alpha_{1}(R) \geq \alpha\right}

r_{2}(\alpha)=\inf \left{R \geq 0: \alpha_{2}(R) \geq \alpha\right}r_{2}(\alpha)=\inf \left{R \geq 0: \alpha_{2}(R) \geq \alpha\right}

## 统计代写|决策与风险作业代写decision and risk代考|Properties of a Good Estimator

H在吨=吨(米−1,b)σ^(米)米

## 统计代写|决策与风险作业代写decision and risk代考|Estimation of Expected Values

H在μ在=吨(米−1.b)小号在(米)米,

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|决策与风险作业代写decision and risk代考|Simulation Output Analysis for Risk

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|决策与风险作业代写decision and risk代考|Assessment and Mitigation

According to Aven (2016), the area of risk assessment and management has evolved considerably since its beginnings in the $1970 \mathrm{~s}$, and there have been developed a wide variety of methods and applications in most societal sectors. As evidence of this evolution, we can observe the variety of research groups of the Society for Risk Analysis, among which we can mention: Dose Response, Ecological Risk Assessment, Emerging Nanoscale Materials, Engineering and Infrastructure, Exposure Assessment, Microbial Risk Analysis, Occupational Health and Safety, Risk Policy and Law, and Security and Defense.

Aven (2016) also mentions that the area of risk assessment and management has two fundamental tasks: (i) to use risk assessments and management to study and treat the risk caused by the execution of specific activities (for example, the operation of an offshore facility or investment), and (ii) conduct research and development (in

general) on risk, developing concepts, theories, frameworks, approaches, principles, methods and models to understand, evaluate, characterize, communicate and (in a broad sense) manage and mitigate risk.

Parallel to the development of the area of risk assessment and mitigation, concepts, techniques and available tools (software) have been developed for systems simulation and, in particular, for stochastic simulation, which is the type of simulation that allows us to include uncertainty and risk components in a model. In practice, a model for risk management can become complex, in the sense that we cannot obtain analytical expressions for the risk measures that are relevant to the problem under study and, in such circumstances, stochastic simulation has particular relevance for the estimation (from the output of simulation experiments) of the risk measures to be mitigated.
The objective of this Chapter is to present a review of the techniques that have been proposed to analyze the output of simulation experiments, in order to estimate performance measures that are important to conduct a risk assessment and mitigation study, when a simulation model is used to imitate the evolution of a system.

The Chapter is organized as follows. After this introduction, we present a brief literature review on the relevant applications of systems simulation for risk assessment and mitigation. In the next section, we present an overview of the necessary concepts and tools available to conduct simulation experiments. The following section discusses the most important techniques for estimating risk measures in transient simulations, including the estimation of expectations, variances and risk measures based on quantiles and M estimators. In this Section, we also present a Bayesian framework to incorporate parameter uncertainty in the process of estimating risk measures. Finally, the last section discusses the techniques available to estimate risk measures in steady-state simulations, considering again the estimation of expectations, variances, and quantile-based risk measures. In the last section we also discuss the initial transient problem and how can it be mitigated.

## 统计代写|决策与风险作业代写decision and risk代考|Literature Review

In this section we present a brief review on the main literature related to simulation applications that have been successfully applied for risk assessment and mitigation in different areas. The literature on the applications of risk assessment and mitigation is abundant, and this is only a very brief review on the applications of simulation in this area, for a more detailed review on the applications of risk assessment and mitigation, the reader is referred to Aven (2016).

According to Aven (2016), an important step in the process of making informed decisions for risk management corresponds to risk assessment, which consists of the analysis of the knowledge base to have an understanding about the risks and the uncertainties related to the case under study. As explained in Aven (2012), although it is true that the criteria for evaluating risks are usually based on the estimation of expected values (e.g., the cost of a negative event) or probabilities (of a negative event), we can find arguments for the use of other measures for risk assessment.

For example, in the area of finance, risk measures have been proposed based not only on the estimation of expected losses, but also on quantile-based measures, such as the Value at Risk (VaR) or the Conditional Value at Risk (CVar), see e.g., Natarajan et al. (2009). Because of these reasons, in addition to the techniques for estimating expectations and probabilities from the output of simulation experiments, in this Chapter we will also deal with the estimation of other risk measures, such as the variance and risk measures based on quantiles and $\mathrm{M}$ estimators, recognizing that some other measures for risk management and mitigation could be proposed in addition to the ones discussed in this Chapter.

Stochastic simulation has been widely used for risk assessment in various areas, for example, in supply chain management, where risk measures are mainly related to shortages, the occurrence of catastrophes and the costs incurred (see, e.g., Wu and Olson 2008; Wu et al. 2012; Chen et al. 2013; Hamdi et al. 2018; Oliveira et al. 2019 ; and their references). Stochastic simulation has also been used extensively in the areas related to production planning to design products with high reliability, for example, for water distribution (see, e.g., Wagner et al. 1988; Ostfeld et al. 2002), for the design of integrated circuits (see, e.g., Hu 1992; Wang et al. 2007; Li et al. 2008), or for the design of highly reliable products (see, e.g., Heidelberger 1995; Juneja and Shahabuddin 2006; Bucklew 2013). One area of production planning where stochastic simulation is particularly important for risk mitigation is operations scheduling, where the achievement of programs that meet delivery dates is very important (see, e.g., Pegden 2017; Smith et al. 2019).

In areas related to health care, stochastic simulation experiments have also been successfully conducted, for example, to design spaces for medical care with a low risk of experiencing long waiting times (see, e.g., Fone et al. 2003), to improve the understanding and mitigation of epidemics (see, e.g., Salathe et al. 2012), to make economic evaluations of diseases and their treatments (see, e.g., Cooper et al. 2006). A more complete review of the applications of simulation for health care can be found in Mielczarek and Uziałko-Mydlikowska (2012).

Simulation has been successfully applied in the areas of waste treatment and energy recovery (see, e.g., Ren et al. 2010; Ren 2018; Liang et al. 2020; Yang et al. 2020), and to mitigate the risk of the occurrence of landslides (see, e.g., Dai et al. 2002; Fell et al. 2005), or to quantify the resilience of power systems (see, e.g., Pantelli et al. 2017) or urban infrastructure (see e.g., Ouyang and Duenas-Osorio 2012).

## 统计代写|决策与风险作业代写decision and risk代考|Systems Simulation

The term system is used in various disciplines to identify the elements and dynamics of a phenomenon that is intended to be understood, analyzed and/or designed from the point of view of the corresponding discipline. According to Schmidt and Taylor (1970), a system is a collection of entities that interact to achieve a goal. For example, in Industrial Engineering we study industrial systems (supply chains, service centers, manufacturing plants, etc.) that consist of raw materials, human resources and capital, organized to efficiently produce and distribute manufactures and/or services. In the same way, systems can be studied in Economics from the point of view of the welfare of the agents involved in the economic phenomenon and, similarly, each discipline study systems from its analytical perspective.

Without a doubt, humanity has studied systems from very ancient times. Initially, an attempt was made to understand natural systems through experimentation with the real system. The search for knowledge led to the development, first of physical models of systems (prototypes, scale models, etc.) that allowed them to carry out controlled experiments, and later, theories and mathematical models that could explain and predict the behavior of systems, both existing ones and those that were developed. A physical model is an imitation, generally simpler, of a real system, whose experimentation (under controlled conditions) allows us to study the behavior of the system in a natural way, as it would happen with the real system. A mathematical model, on the other hand, represents the system to be studied by means of mathematical relationships; therefore, by experimenting with it, we can predict the behavior of the relevant variables of the system and imagine the main behavior of the system, even if it is not physically reproduced.

One of the purposes of a mathematical model is to predict the behavior of one or more characteristics of the system (known as response variables) based on other variables (called control variables). A mathematical model in which, through a set of equations, the response variables are expressed as a (explicit) function of the control variables is very convenient to predict the behavior of a system, and we say that the model has an analytical solution when this set of equations exists.

However, when we want to study a system in great detail, we must consider variables whose relationships are not easy to solve to find an analytical solution. Nonetheless, the model can still be useful to analyze the system, since for this purpose numerical methods have been developed. Given particular values for the control variables, numerical methods allow us to calculate, by using a computer, the value of the response variables.

Among the numerical methods used to study a system (see Fig. 6.1), simulation has the fundamental characteristic that the model tries to imitate the behavior of the system under study, in order to calculate, with the help of a computer, the value of the system’s response variables. For the purposes of this Chapter, we will recognize by simulation the computer imitation of the behavior of a system, using a (mathematical) model to explain its relevant characteristics, in order to numerically evaluate the performance measures of the system.

## 统计代写|决策与风险作业代写decision and risk代考|Assessment and Mitigation

Aven（2016）还提到风险评估和管理领域有两个基本任务：（i）使用风险评估和管理来研究和处理由执行特定活动（例如，离岸设施或投资），以及（ii）进行研究和开发（在

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|决策与风险作业代写decision and risk代考|Application for Mining Activities

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|决策与风险作业代写decision and risk代考|Ulas Cinar, Omer Faruk Ugurlu, and Selcuk Cebi

The current novel coronavirus (COVID-19) is a global pandemic that has caused infections and deaths all over the globe. People with weakened immune systems and over 40 are more vulnerable. The risk of serious illness increases with age and chronic diseases such as diabetes, heart, and lung diseases (WHO 2020a). The places where the virus has transmitted most are the workplaces. Therefore, personal hygiene and social distancing are the two key parameters to avoid COVID-19 transmission, particularly in the workplace (WHO $2020 \mathrm{~b}$ ).

This unpredicted and unprecedented outbreak has not only affected human lives, but has also wrecked the global economy (Ahamed and Samad 2004). The economy of many developed and developing countries directly depends on the activities in the mining sector. Therefore, mining activities must inevitably continue to keep the supply chain intact in the industry. However, the outbreak has a profound impact on the mining activities which are essential services. According to Fernandes (2020a), the mining sector has fallen by more than $30 \%$. The demand for metals and minerals has decreased immensely. The reduction has caused extensive falls in the mineral prices and the production rate in the short term. These falls have been most dramatic for aluminum and copper (Laing 2019). The medium and long-term effects are highly uncertain (Baker et al. 2020); therefore, the risk assessment of virus transmission is vital to ensure that the mining sector can continue the operations.

The risk of transmission of the COVID-19 virus and its effects have only just begun to be understood, and the virus is still unknown. There have been a lot of studies conducted to explore the transmission characteristic of the virus (Hassen et al. 2020). COVID-19 often spreads by the droplets of infected fluids of someone who has coughed or even exhaled (Chen 2020 ). Meteorological conditions such as temperature, humidity, and ventilation speed have a crucial impact on the effect of the virus (Rosario et al. 2020). Touching contaminated surfaces and objects is one of the main reasons for the transmission of the virus (WHO 2019). Another reason is standing within a meter with an infected person (WHO 2020a). Mines are one of the environments with a high risk of COVID-19 transmission because mining activities often require large numbers of workers working, eating, sleeping, and bathing together in confined spaces. Social distancing is difficult and nearly impossible to practice in those conditions, contributing to increased risks of transmission. There is nothing more important than the safety and health of the workforce. Therefore, companies must adhere to strict preventive measures. While different companies have different measures and guidelines in place for businesses to operate through the pandemic such as reducing the production and workforce, social distancing measures, workplace hygiene policy, and temperature checks at the operations must be implemented (WHO 2020a).

## 统计代写|决策与风险作业代写decision and risk代考|Literature Review

COVID-19 is a new phenomenon around the globe. There is a lot of research that has been carried out and most of them have been going on. It is expected to have accurate results in the near future. In this section, some researches related to the risk analysis and the fuzzy inference system are examined to show the eligibility of the method in order to measure the risk of COVID-19 transmission.

Rezaee et al. (2020) presented a hybrid approach based on the Linguistic FMEA, Fuzzy Inference System (FIS), and Fuzzy Data Envelopment Analysis (DEA) model to calculate a novel score for covering shortcomings and the prioritization of health, safety, and environmental risk factors in the chemical industry. The task of the fuzzy inference mechanism in this model is to remove the ambiguity in linguistic expressions and to transform complex data into meaningful outputs. Jamshidi et al. (2013) developed an application to assess pipeline risk using the Mamdani Fuzzy Inference System in engineering problems. The researchers aimed to integrate Relative Risk Score (RRS) methodology depending on the Mamdani algorithm with experts’ knowledge. When compared with the evaluations made with classical methods, it has been observed that the proposed method gives more accurate and precise results.
Kim et al. (2016) conducted a study to provide valuable information regarding worker safety represented by a numerical accident analysis in dynamic environments such as construction sites. Firstly, computer vision was used to monitor a construction site and extract spatial information for each entity (workers and equipment). Then, a fuzzy inference system was used to assess the proper safety levels of each entity using spatial information. It was aimed to represent a safety level that shows the potential hazard or the integrating danger in the working environment.

A hybrid method including Fuzzy Inference System, Fuzzy AHP, and Fine Kinney methods was proposed by Ilbahar et al. (2018). Occupational health and safety risks were evaluated using the hybrid method. An application has been implemented in the construction industry using the Fuzzy Inference System to transform linguistic expressions into analytical data. It was aimed to provide a more accurate risk assessment in dynamic environments such as construction sites. The hybrid method and other methods were compared and the results showed that the hybrid method produced reliable and informative outcomes to represent better vagueness of the decision-making process. Similarly, Debnath et al. (2016) formulated a model to consider the risk factors and controlling factors for accidental injuries in construction sites. The Takagi-Sugeno Fuzzy Inference System was applied to the occupational health and safety risk assessment study recommended for the construction industry. In the model formulation process, the risk factors and controlling factors for accidental injuries were considered as input parameters. The applicability of the model was tested in the selected construction sites to validate the approach. Another study was conducted about the risk assessment of a construction project by using fuzzy systems (Ebrat and Ghodsi 2014). The authors designed to evaluate the risk of construction projects using the neuro-fuzzy inference system. The results of the study show that the model gives satisfactory information to practitioners.

## 统计代写|决策与风险作业代写decision and risk代考|Methods

In the proposed method, the parameters affecting COVID-19 transmission risk in mining activities are determined as the number of employees, co-working time, co-working distance, and working environment for the production techniques. The literature studies about the COVID-19 were taken into consideration in determining the parameters and establishing the rule base for the mining activities (Liu et al. 2020 ). Each mining activity is weighted using the parameters by the Mamdani fuzzy inference system. The model characterizes a rule-based system, and the general

structure of the system used in the model is given in Eq. (5.1) (Mamdani and Assilian 1999; Mamdani 1977).
if $x_{1}=Z_{i 1}$ and $x_{2}=Z_{i 2}$ and $x_{3}=Z_{i 3}$ and $\ldots x_{n}=Z_{\text {in }}$ then $y=P_{i} . i=1,2,3, \ldots, k$
where $x_{n}\left(n=1,2,3, \ldots m\right.$ ) represents the input dataset, $Z_{i}$ and $P_{i}$ are linguistic expressions of membership function, $y$ is the output value, and $k$ is the number of rules in the rule base. If multiple discrete rules existing in the system are activated simultaneously, the result is usually obtained by using the max-min operator which is given in Eq. (5.2) (Mamdani and Assilian 1999; Mamdani 1977).
$$\mu_{P k}(y)=\operatorname{maks}\left[\min \left[\mu_{Z 1 k}\left(x_{1}\right), \mu_{Z 2 k}\left(x_{2}\right)\right]\right], \quad k=1,2,3, \ldots, n$$
The $\mu_{p k}, \mu_{Z l k}$, and $\mu_{Z 2 k}$ given in the equation are the membership degrees of the $y$, $x_{1}$, and $x_{2}$, respectively. If there are more than one evaluator, the output value which is obtained as a fuzzy value from the model should be clarified. The centroid of area (also called center of gravity) method is used for the clarifying process which is given in Eqs. (5.3) and (5.4) (Mamdani and Assilian 1999; Mamdani 1977).
$$\begin{gathered} Z_{\mathrm{COZ}}^{}=\frac{\int_{Z}^{x} \mu_{X}(x) x d x}{\int_{Z}^{x} \mu_{Z}(x) d x} \ Z_{C O Z}^{}=\frac{\sum_{i}^{q} \mu_{Z}\left(x_{i}\right) x_{i}}{\sum_{i}^{q} \mu_{A}\left(x_{i}\right)} i=1,2,3, \ldots, q \end{gathered}$$
where $Z_{C O z}^{*}$ is the exact value obtained from the system. More information about the Mamdani fuzzy inference system can be found in Ilbahar et al. (2018), Cinar and Cebi (2019), and Karasan et al. (2018).

## 统计代写|决策与风险作业代写decision and risk代考|Ulas Cinar, Omer Faruk Ugurlu, and Selcuk Cebi

COVID-19 病毒的传播风险及其影响才刚刚开始被了解，该病毒仍然未知。已经进行了大量研究来探索病毒的传播特征（Hassen et al. 2020）。COVID-19 通常通过咳嗽甚至呼出的人的感染液体飞沫传播（Chen 2020）。温度、湿度和通风速度等气象条件对病毒的影响具有至关重要的影响（Rosario et al. 2020）。接触受污染的表面和物体是病毒传播的主要原因之一（WHO 2019）。另一个原因是与感染者站在一米以内（WHO 2020a）。矿山是 COVID-19 传播风险高的环境之一，因为采矿活动通常需要大量工人在密闭空间中一起工作、吃饭、睡觉和洗澡。在这种情况下，保持社交距离是困难的，而且几乎是不可能的，从而增加了传播的风险。没有什么比劳动力的安全和健康更重要的了。因此，企业必须坚持严格的预防措施。尽管不同的公司为企业在大流行期间运营制定了不同的措施和指导方针，例如减少生产和劳动力，但必须实施社会疏离措施、工作场所卫生政策和运营中的温度检查（WHO 2020a）。在这种情况下，保持社交距离是困难的，而且几乎是不可能的，从而增加了传播的风险。没有什么比劳动力的安全和健康更重要的了。因此，企业必须坚持严格的预防措施。尽管不同的公司为企业在大流行期间运营制定了不同的措施和指导方针，例如减少生产和劳动力，但必须实施社会疏离措施、工作场所卫生政策和运营中的温度检查（WHO 2020a）。在这种情况下，保持社交距离是困难的，而且几乎是不可能的，从而增加了传播的风险。没有什么比劳动力的安全和健康更重要的了。因此，企业必须坚持严格的预防措施。尽管不同的公司为企业在大流行期间运营制定了不同的措施和指导方针，例如减少生产和劳动力，但必须实施社会疏离措施、工作场所卫生政策和运营中的温度检查（WHO 2020a）。

## 统计代写|决策与风险作业代写decision and risk代考|Literature Review

COVID-19 是全球范围内的一种新现象。已经进行了很多研究，其中大多数一直在进行。预计在不久的将来会有准确的结果。在本节中，检查了一些与风险分析和模糊推理系统相关的研究，以显示该方法的适用性，以衡量 COVID-19 传播的风险。

Ilbahar 等人提出了一种混合方法，包括模糊推理系统、模糊层次分析法和精细 Kinney 方法。（2018 年）。使用混合方法评估职业健康和安全风险。使用模糊推理系统将语言表达转换为分析数据的应用程序已在建筑行业实施。它旨在在建筑工地等动态环境中提供更准确的风险评估。将混合方法与其他方法进行了比较，结果表明混合方法产生了可靠且信息丰富的结果，以更好地代表决策过程的模糊性。同样，Debnath 等人。（2016）建立了一个模型来考虑建筑工地意外伤害的风险因素和控制因素。Takagi-Sugeno 模糊推理系统应用于推荐给建筑业的职业健康和安全风险评估研究。在模型制定过程中，将意外伤害的危险因素和控制因素作为输入参数。该模型的适用性在选定的建筑工地进行了测试，以验证该方法。另一项关于使用模糊系统对建设项目进行风险评估的研究（Ebrat 和 Ghodsi 2014）。作者旨在使用神经模糊推理系统评估建设项目的风险。研究结果表明，该模型为从业者提供了令人满意的信息。在模型制定过程中，将意外伤害的危险因素和控制因素作为输入参数。该模型的适用性在选定的建筑工地进行了测试，以验证该方法。另一项关于使用模糊系统对建设项目进行风险评估的研究（Ebrat 和 Ghodsi 2014）。作者旨在使用神经模糊推理系统评估建设项目的风险。研究结果表明，该模型为从业者提供了令人满意的信息。在模型制定过程中，将意外伤害的危险因素和控制因素作为输入参数。该模型的适用性在选定的建筑工地进行了测试，以验证该方法。另一项关于使用模糊系统对建设项目进行风险评估的研究（Ebrat 和 Ghodsi 2014）。作者旨在使用神经模糊推理系统评估建设项目的风险。研究结果表明，该模型为从业者提供了令人满意的信息。另一项关于使用模糊系统对建设项目进行风险评估的研究（Ebrat 和 Ghodsi 2014）。作者旨在使用神经模糊推理系统评估建设项目的风险。研究结果表明，该模型为从业者提供了令人满意的信息。另一项关于使用模糊系统对建设项目进行风险评估的研究（Ebrat 和 Ghodsi 2014）。作者旨在使用神经模糊推理系统评估建设项目的风险。研究结果表明，该模型为从业者提供了令人满意的信息。

## 统计代写|决策与风险作业代写decision and risk代考|Methods

μ磷到(是)=最大限度⁡[分钟[μ从1到(X1),μ从2到(X2)]],到=1,2,3,…,n

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|决策与风险作业代写decision and risk代考|Theoretical Validation

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|决策与风险作业代写decision and risk代考|Theoretical Validation

In this section, the proposed novel fuzzy risk assessment method based on Z-grey numbers is theoretically validated based on ranking fuzzy quantity (Bakar and Gegov 2015; Baker et al. 2019, 2020). This validation serves as the generic analysis for risk assessment evaluations made by the proposed method in distinguishing which risk is riskier than other risks under consideration. Details on the validation are given as follows.

Let $Z_{A}$ and $Z_{B}$ be risk $A$ and risk $B$, respectively, in the form of Z-grey numbers. Meanwhile, $A_{Z_{A}}$ and $A_{Z_{B}}$ be the risk assessment evaluation for risk $A$ and risk $B$, respectively, using the proposed novel fuzzy risk assessment method based on Z-grey numbers.
Property 1 If $Z_{A} \succcurlyeq Z_{B}$ and $Z_{B} \succcurlyeq Z_{A}$, then $Z_{A} \approx Z_{B}$.
Proof $Z_{A} \succcurlyeq Z_{B}$ implies that $A_{Z_{A}} \geq A_{Z_{B}}$ and $Z_{B} \succcurlyeq Z_{A}$ implies that $A_{Z_{B}} \geq A_{Z_{A}}$, thus $A_{Z_{A}}=A_{Z_{B}}$ which is $Z_{A} \approx Z_{B}$.
Property 2 If $Z_{A} \succcurlyeq Z_{B}$ and $Z_{B} \succcurlyeq Z_{C}$, then $Z_{A} \succcurlyeq Z_{C}$.
Proof $Z_{A} \succcurlyeq Z_{B}$ implies that $A_{Z_{A}} \geq A_{Z_{B}}$ and $Z_{B} \succcurlyeq Z_{C}$ implies that $A_{Z_{B}} \geq A_{Z_{C}}$, thus $A_{Z_{A}} \geq A_{Z_{C}}$ which is $Z_{A} \succcurlyeq Z_{C}$.

Property 3 If $Z_{A} \cap Z_{B}=\varphi$ and $Z_{A}$ is on the right side of $Z_{B}$, then $Z_{A} \succcurlyeq Z_{B}$.
Proof $Z_{A} \cap Z_{B}=\varphi$ and $Z_{A}$ is on the right side of $Z_{B}$ implies that $A_{Z_{A}} \geq A_{Z_{B}}$, thus $Z_{A} \succcurlyeq Z_{B}$.

Property 4 The order of $Z_{A}$ and $Z_{B}$ are not affected by other $Z-$ grey numbers under comparison.

Proof The ordering of $Z_{A}$ and $Z_{B}$ are completely determined by $A_{Z_{A}}$ and $A_{Z_{B}}$ respectively, thus the ordering of $Z_{A}$ and $Z_{B}$ are not affected by other $Z$-grey numbers under comparison.

## 统计代写|决策与风险作业代写decision and risk代考|Fuzzy Risk Assessment in Electrical Arc Welding

Consider the following real-world risk assessment problem experienced by a welding factory, which is the electrical arc welding. In the factory, risk assessment has become one of the most crucial aspects considering the presence of multiple types of hazards that may affect the safety of the workers during the operation of the electrical arc welding. Among the hazardous situations that involve in the electrical arc welding operations are exposure towards flammable substances, welding on wet floor, inhales

toxic welding fumes and least protection towards extreme bright flash. To ensure that the safety of the factory workers is well-supervised, the risks of all of the mentioned hazardous situations have to be assessed. The following are the hazardous situations that involve in the electrical arc welding operations and their descriptions.

1. Injury-Radiation that burn the workers’ skin; extremely bright flash that damages the workers’ eyes.
2. Fire and Electrical Shock-Exposure towards flammable substances (paper and thinner) when the welding process is carried out; exposure towards electrical shock when the floor is wet.
3. Fumes-Workers inhale toxic welding fumes created from the electrical arc process.

Based on these details, the structure of risk assessment for the electrical arc welding operations is illustrated as Fig. 4.3.

In the following, the proposed fuzzy risk assessment method based on Z-grey numbers that is developed in Sect. $4.3$ is applied to assess the correct risk ordering for all hazardous situations under consideration, such that the ordering result is consistent with the actual risk evaluation on the level of hazards in the electrical arc welding operations. The actual risk information of by each risk analyst in the form Z-grey numbers is given in Table 4.2, while details on the proposed fuzzy risk assessment method based on Z-grey numbers are presented as follows.

## 统计代写|决策与风险作业代写decision and risk代考|Discussion

In order to validate the novelty and feasibility of the proposed novel fuzzy risk assessment method based on Z-grey numbers, this study analyses the risk assessment evaluation rating results obtained with the actual risk evaluation on the level of hazards in the electrical arc welding operations. It is worth mentioning that, the

actual risk evaluations are obtained from the factory risk assessment as shown in the following Table $4.8$.

From the actual factory risk evaluations on all of the hazardous situations in Table $4.8, F_{2}$ is considered as the most hazardous situation as it is the most likely to occur as compared to $F_{1}$ and $F_{3}$. Furthermore, the level of severity for $F_{2}$ is the highest from all of the hazardous situations under consideration. The company grades $F_{2}$ as high level of hazard but the most hazardous situation among those under consideration in this case. For $F_{1}$, the chance for the hazard to occur is moderate, meanwhile $F_{3}$ is unlikely to occur. With respect to levels of severity for $F_{1}$ and $F_{3}$, they are moderate and low, respectively. Thus, the company grades the level of hazard for all of the hazardous situations under consideration as $F_{2}>F_{1}>F_{3}$.

## 统计代写|决策与风险作业代写decision and risk代考|Fuzzy Risk Assessment in Electrical Arc Welding

1. 伤害——灼伤工人皮肤的辐射；极其明亮的闪光会伤害工人的眼睛。
2. 进行焊接过程时，火灾和电击暴露于易燃物质（纸和稀释剂）；地板潮湿时接触电击。
3. 烟雾——工人吸入由电弧过程产生的有毒焊接烟雾。

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|决策与风险作业代写decision and risk代考|Method

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|决策与风险作业代写decision and risk代考|Consensus Reaching

In this phase, fuzzy risk assessment involving the presence of uncertainty in the heterogeneous preferences elicited by the risk analysts is defined in the form of $Z$ grey numbers. As both restriction of the preferences elicited by the risk analysts and the reliability of the restriction are grey numbers, the fuzzy risk assessment representations can exist in the form of white numbers (for completely known risk analysts’ preferences elicitation), black numbers (completely unknown risk analysts’ preferences elicitation) and grey numbers (partially known/unknown risk analysts’ preferences elicitation). Since, the grey numbers forms are distinct from one to another (as in Table 4.1), a novel fuzzy agreement relation approach is developed for the first time to define fuzzy risk assessment representations involving the presence of uncertainty for each heterogeneous form of preferences elicited by the risk analysts as a

single common form. The approach involves the transformation of Z-grey number into Z-number, where the transformation is given as follows.

Let $P_{S, t}^{\prime}$ and $Q_{S, t}^{\prime}$ be the probability of failure and the severity of loss, respectively, in the form of Z-grey numbers define as $P_{S_{i, k}}^{\prime}=\left[H_{P_{s_{i, k}}^{G}}^{G}, L_{P_{s, t, k}^{\prime}}^{G}\right]$ and $Q_{S_{i, k}}^{\prime}=\left[H_{Q_{s_{i, k}}^{G}}^{G}, L_{Q_{s_{i, k}}^{G}}^{G}\right]$, where $H_{P_{s_{s, k}}^{G}}^{G}$ and $H_{Q_{s_{i, k}}^{G}}^{G}$ are the restriction of the preferences elicited by the risk analysts for $P_{S_{i, k}^{\prime}}^{\prime}$ and $Q_{S_{i, t}}^{\prime}$ respectively, while $L_{P_{S_{,}, k}^{\prime}}^{G}$ and $L_{Q_{s, t, k}^{\prime}}^{G}$ are the reliability of the restriction for $P_{S_{i, k}^{\prime}}^{\prime}$ and $Q_{S_{i, k}}^{\prime}$, respectively.

1. If $P_{S, k}^{\prime} \in[0,1]$ and $Q_{S_{i, k}}^{\prime} \in[0,1]$ are $Z$-grey numbers that represent the preferences elicited by the risk analysts that are completely known, then $P_{S_{i, k}}^{\prime}$ and $Q_{S_{i, k}}^{\prime}$ are transformed into Z-numbers, $P_{S_{i, k}}^{}$ and $Q_{S_{i, k}}^{}$, respectively using the transformation function, $T_{\sigma}, \sigma=P_{S_{i, k},}^{\prime}, Q_{S_{i, i}}^{\prime}$, given as the following Eqs. (4.2) and (4.3).
$$T_{P_{c_{i, k}}^{\prime}}:[0,1] \rightarrow P_{S_{i, k}^{}}^{}=\left[H_{P_{s_{, k}}^{}}^{G}, L_{P_{s_{i, k}}^{}}^{G}\right]$$
and
$$T_{Q_{c_{i k}}^{\prime}}:[0,1] \rightarrow Q_{S_{i, k}}^{*}=\left[H_{Q_{s_{i, k}}^{G}}^{G}, L_{Q_{s_{i, k}}^{G}}^{G}\right]$$
2. If $P_{S_{i, k}}^{\prime} \in[0,1]$ and $Q_{S_{i, k}}^{\prime} \in[0,1]$ are Z-grey numbers that represent the preferences elicited by the risk analysts that are completely unknown, then $P_{S_{i, k}}^{\prime}$ and $Q_{S_{i, k}}^{\prime}$ are transformed into Z-numbers, $P_{S_{j, k}}$ and $Q_{S_{i, i}}^{}$, respectively using the transformation function, $T_{v}, v=P_{S_{i, k}}^{\prime}, Q_{S_{i, k}}^{\prime}$, given as the following Eqs. (4.4) and (4.5). $$T_{P_{c_{i, k}^{\prime}}}:[0,1] \rightarrow P_{S_{i, k}^{}}^{}=\left[H_{P_{s_{i, k}}^{G}}^{G}, L_{P_{s_{i, k}}^{g}}^{G}\right]$$ and $$T_{Q_{C_{i, t}}^{\prime}}:[0,1] \rightarrow Q_{S_{i, k}}^{}=\left[H_{Q_{s_{i, k}}^{\xi}}^{G}, L_{Q_{s_{i, k}}^{G}}^{G}\right]$$

## 统计代写|决策与风险作业代写decision and risk代考|Conversion

Note that from Phase 1, the current form for the fuzzy risk assessment representations involving the presence of uncertainty in the heterogeneous preferences elicited by the risk analysts is a single consensus form, which is the Z-numbers. The representation of the obtained single consensus form, however, is too complex in nature (Bakar and Gegov 2015; Kang et al. 2012; Zadeh 2011). Thus in this phase, this study converts the obtained single consensus form into a much simpler consensus form, which is the Z-fuzzy number. The conversion which involves incorporation of defuzzified value of the risk reliability into the risk restriction component, converts the obtained single consensus form (Z-numbers) $P_{S_{i, k}^{}}^{}$ and $Q_{S_{i, t}}^{*}$ into the reduced consensus form (Z-fuzzy numbers), $P_{S_{i, k}}^{o}$ and $Q_{S_{i, k}}^{o}$, respectively (Bakar and Gegov 2015; Kang et al. 2012). Details on the conversion are given by the following procedures (Bakar and Gegov 2015; Kang et al. 2012).

Step 1: Obtain the defuzzified value, $T_{n}$, of $L_{P_{S_{i}^{}, k}^{G}}^{G}$ and $L_{Q_{\dot{\xi}, k}^{}}^{G}$ for both $P_{S_{i, k}^{}}^{}$ and $Q_{S_{i, k}^{}}^{}$, respectively, using the following Eq. (4.8).
$$T_{n}=\frac{1}{3}\left[b_{n 1}+b_{n 2}+b_{n 3}+b_{n 4}-\frac{b_{n 3} b_{n 4}-b_{n 1} b_{n 2}}{\left(b_{n 3}+b_{n 4}\right)-\left(b_{n 1}+b_{n 2}\right)}\right]$$
where $n=L_{P_{s_{i, k}^{}}^{G}}^{G}, L_{Q_{s_{i, k}^{}}^{G}}^{G}$.
Step 2: Incorporate $T_{n}$ into $H_{P_{S_{i, k}^{}}^{G}}^{G}$ and $H_{Q_{s_{i, k}}^{}}^{G}$ for both $P_{S_{i, k}^{}}^{}$ and $Q_{S_{i, k}^{}}^{}$, respectively, using the following Eq. (4.9).
$$X_{m}=\left[T_{n} * a_{m 1}, T_{n} * a_{m 2}, T_{n} * a_{m 3}, T_{n} * a_{m 4} ; 1\right]=\left[\bar{a}{m 1}, \bar{a}{m 2}, \bar{a}{m 3}, \bar{a}{m 4} ; 1\right]$$
where $X=P_{S_{i, k}}^{o}, Q_{S_{i, k}}^{o}$ and $m=H_{P_{S_{i, k}^{}}^{G}}^{G}, H_{Q_{s_{i, k}}^{}}^{G}$.

## 统计代写|决策与风险作业代写decision and risk代考|Risk Assessment Evaluation

In phase 2 , fuzzy risk assessment representations involving the presence of uncertainty in the heterogeneous preferences elicited by the risk analysts in the form of

Z-grey number, has successfully converted into the reduced consensus forms (Zfuzzy numbers). This reduced consensus forms are then aggregated using a novel fuzzy risk evaluation rating method to assess the correct level of risks, such that the assessments are consistent with the presence of uncertainty in the heterogeneous preferences elicited by the risk analysts. Steps provided in this phase are similar to established methods (Bakar and Gegov 2014, 2015; Baker et al. 2019, 2020), only that the proposed novel method uses Z-grey numbers. Details on the proposed novel fuzzy risk evaluation rating method are given as the following.

Step I: Evaluate the interaction score, $S_{i}$, between $P_{S_{i, t}}^{o}$ and $Q_{S_{i, t}}^{o}$ for each risk under consideration as
$$S_{i}=\frac{\sum_{i, k=1}^{n}\left(P_{S_{i, k}}^{o} \times Q_{S_{i, k}}^{o}\right)}{\sum_{i, k=1}^{n}\left(Q_{S_{i, k}}^{o}\right)}$$
Step 2: Compute the centroid- $x$ component value for $S_{i}$ as
$$x_{S_{i}}=\frac{1}{3}\left[a_{1 S_{i}}+a_{2 S_{i}}+a_{3 S_{i}}+a_{4 S_{i}}-\frac{a_{3 S_{i}} a_{4 S_{i}}-a_{1 S_{i}} a_{2 S_{i}}}{\left(a_{3 S_{i}}+a_{4 S_{i}}\right)-\left(a_{1 S_{i}}+a_{2 S_{i}}\right)}\right]$$
and the centroid- $y$ component value for $S_{i}$ as
$$y_{S_{i}}=\frac{w_{S_{i}}}{3}\left[1+\frac{a_{3 S_{i}} a_{4 S_{i}}-a_{1 S_{i}} a_{2 S_{i}}}{\left(a_{3 S_{i}}+a_{4 S_{i}}\right)-\left(a_{1 S_{i}}+a_{2 S_{i}}\right)}\right]$$
where $x_{S_{i}} \in[0,1]$ and $y_{S_{i}} \in[0,1]$.
Step 3: Obtain the deviation of centroid component value for $S_{i}$ as
$$\psi_{S_{i}}=\left|a_{4 S_{i}}-a_{1 S_{i}}\right| \times y_{S_{i}}$$

## 统计代写|决策与风险作业代写decision and risk代考|Consensus Reaching

1. 如果磷小号,到′∈[0,1]和问小号一世,到′∈[0,1]是从- 灰色数字，代表完全已知的风险分析师引发的偏好，然后磷小号一世,到′和问小号一世,到′转换为 Z 数，磷小号一世,到和问小号一世,到，分别使用变换函数，吨σ,σ=磷小号一世,到,′,问小号一世,一世′，给出如下等式。(4.2) 和 (4.3)。
吨磷C一世,到′:[0,1]→磷小号一世,到=[H磷s,到G,大号磷s一世,到G]

吨问C一世到′:[0,1]→问小号一世,到∗=[H问s一世,到GG,大号问s一世,到GG]
2. 如果磷小号一世,到′∈[0,1]和问小号一世,到′∈[0,1]是 Z 灰色数字，代表完全未知的风险分析师引发的偏好，然后磷小号一世,到′和问小号一世,到′转换为 Z 数，磷小号j,到和问小号一世,一世，分别使用变换函数，吨v,v=磷小号一世,到′,问小号一世,到′，给出如下等式。(4.4) 和 (4.5)。吨磷C一世,到′:[0,1]→磷小号一世,到=[H磷s一世,到GG,大号磷s一世,到GG]和吨问C一世,吨′:[0,1]→问小号一世,到=[H问s一世,到XG,大号问s一世,到GG]

## 统计代写|决策与风险作业代写decision and risk代考|Conversion

Step 1：获取去模糊化后的值，吨n， 的大号磷小号一世,到GG和大号问X˙,到G对彼此而言磷小号一世,到和问小号一世,到，分别使用以下等式。(4.8)。

X米=[吨n∗一种米1,吨n∗一种米2,吨n∗一种米3,吨n∗一种米4;1]=[一种¯米1,一种¯米2,一种¯米3,一种¯米4;1]

## 统计代写|决策与风险作业代写decision and risk代考|Risk Assessment Evaluation

Z-灰色数，已成功转换为简化共识形式（Zfuzzy numbers）。然后使用一种新的模糊风险评估评级方法汇总这种简化的共识表格，以评估正确的风险水平，以便评估与风险分析师引发的异质偏好中存在的不确定性一致。此阶段提供的步骤类似于已建立的方法（Bakar and Gegov 2014, 2015; Baker et al. 2019, 2020），只是所提出的新方法使用 Z-grey 数。所提出的新型模糊风险评估评级方法的详细信息如下。

X小号一世=13[一种1小号一世+一种2小号一世+一种3小号一世+一种4小号一世−一种3小号一世一种4小号一世−一种1小号一世一种2小号一世(一种3小号一世+一种4小号一世)−(一种1小号一世+一种2小号一世)]

ψ小号一世=|一种4小号一世−一种1小号一世|×是小号一世

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|决策与风险作业代写decision and risk代考|Assessment in the Presence

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|决策与风险作业代写decision and risk代考|Preferences Elicitation and Reliability

Fuzzy risk assessment methods are developed to handle risks that involve uncertainty. One of the established fuzzy concepts that concerns with the uncertainty is the Znumbers (Bakar and Gegov 2015; Kang et al. 2012; Zadeh 2011; Allahviranloo and Ezadi 2019). Established fuzzy risk assessment methods based on Z-numbers often describe each risk under consideration as an ordered pair of restriction of the preferences elicited by the risk analyst’s and the reliability of the restriction (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018). In the literature on fuzzy risk assessment, incorporation of the pair (restriction and reliability components) has complemented established fuzzy risk assessment methods to successfully resolve numerous risk assessment problems such as risk assessment evaluations in failure mode of rotor blades of an aircraft turbine (Jiang et al. 2017), investigation on risk components in manufacturing and medical industries (Wu et al. 2018) and assessment of risk in food security (Abiyev et al. 2018). In order to define risks, established fuzzy risk assessment methods based on Z-numbers evaluate each risk under consideration based on two common risk factors, namely, the risk severity of loss and the risk probability of failure (Bakar et al. 2020; Zhao et al. 2020; Natha Reddy and Gokulachandran 2020 ; Chukwuma et al. 2020). Each of these factors that are usually expressed based on the preferences elicited by the risk analysts, is in this case represented by their own ordered pair of restriction and reliability (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018).

The literature on established fuzzy risk assessment methods based on Z-numbers signify that they possess great capability to deal with the presence of uncertainty (Marhamati et al. 2018; Peng et al. 2019; Hendiani et al. 2020; Azadeh and Kokabi 2016). However, their acknowledgement in terms of the presence of uncertainty on each risk under consideration is graded as partially complete. This is because established fuzzy risk assessment methods based on Z-numbers take into account only the presence of uncertainty when preferences elicited by the risk analysts are partially known (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018). Nonetheless, the presence of uncertainty can also happen when preferences elicited by the risk analysts are completely known, completely unknown and partially unknown (Bakar et al. 2020; Yang and John 2012; Huang et al. 2008). This points out that established fuzzy risk assessment methods based on Z-numbers do not have the holistic feature as they restrict the presence of uncertainty in the preferences elicited by the risk analysts to be homogeneous (partially known only), even if the presence of uncertainty is actually heterogeneous in nature (Bakar et al. 2020). Apart from that, the interactions between the common and uncommon heterogeneous preferences elicited by the risk analysts also indicate that the established fuzzy risk assessment methods based on Z-numbers are unable to holistically track the performance of risks in the presence of uncertainty. The above-mentioned inefficiencies of the established fuzzy risk assessment methods based on Z-numbers point out the motivations for this study.

## 统计代写|决策与风险作业代写decision and risk代考|Z-Number

As overcoming the uncertainty in human decision making is crucial, the concept of Z-numbers (Zadeh 2011) is introduced by incorporating the element of reliability along with the decision restriction. This concept enhances the established concepts of type-1 fuzzy numbers and type- 2 fuzzy numbers, where both consider uncertain decision with confidence level (Bakar and Gegov 2014) and inter-intra uncertainty (Bakar et al. 2019; Jana and Ghosh 2018; Wallsten and Budescu 1995; Yaakob et al. 2015 ; John and Coupland 2009), respectively. Based on (Zadeh 2011 ), the definition of Z-number is given as the following Definition $1 .$

Definition 1 (Zadeh 2011) A Z-number is an ordered pair of type-1 fuzzy numbers denoted as $Z=(A, B)$. The first component, $A$, is known as the restriction component where it is a real-valued uncertain on $X$ whereas the second component, $B$, is the measure of reliability for $A$, presented as Fig. 4.1.

With respect to application of Z-numbers in fuzzy risk assessment, risks are represented as an ordered pair of risk restriction and the reliability of the restriction (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018). This can be seen when Z-numbers complement risk assessment problems in the literature such as risk assessment evaluations in failure mode of rotor blades of an aircraft turbine (Jiang et al. 2017), investigation on risk components in manufacturing and medical industries (Wu et al. 2018) and assessment of risk in food security (Abiyev et al. 2018).

## 统计代写|决策与风险作业代写decision and risk代考|Grey Number

The concept of grey numbers is introduced in the literature as to acknowledge the presence of non-homogeneous decision makers’ preferences that are completely known, partially known, completely unknown and partially unknown (Bakar et al. 2020,2019 ; Yang and John 2012; Huang et al. 2008). Definition of grey number and its further extensions are given as follows.

Definition 2 (Yang and John 2012) A grey number, $G_{A}$, is a number with clear upper and lower boundaries but has an unknown position within the boundaries. Mathematically, a grey number for the system is expressed as
$$G_{A} \in\left[g^{-}, g^{+}\right]=\left{g^{-} \leq t \leq g^{+}\right}$$
where $t$ is information about $g^{\pm}$while $g^{-}$and $g^{+}$are the upper and lower limits of information $t$, respectively.

Definition 3 (Bakar et al. 2020; Yang and John 2012) For a set $A \subseteq U$, if its membership function value of each $x$ with respect to $A, g_{A}^{\pm}(x)$, can be expressed with a grey number, $g_{A}^{\pm}(x) \in \bigcup_{i=1}^{n}\left[a_{i}^{-}, a_{i}^{+}\right] \in D[0,1]^{\pm}$, then $A$ is a grey set, where $D[0,1]^{\pm}$is the set of all grey numbers within the interval $[0,1]$.

Definition 4 (White Sets) For a set $A \subseteq U$, if its membership function value of each $x$ with respect to $A, g_{A_{i}}^{\pm}(x), i=1,2, \ldots, n$, can be expressed with a white number, then $A$ is a white set.

Definition 5 (Black Sets) For a set $A \subseteq U$, if its membership function value of each $x$ with respect to $A, g_{A_{i}}^{\pm}(x), i=1,2, \ldots, n$, can be expressed with a black number, then $A$ is a black set.

Definition 6 (Grey Sets) For a set $A \subseteq U$, if its membership function value of each $x$ with respect to $A, g_{A_{i}}^{\pm}(x), i=1,2, \ldots, n$, can be expressed with a grey number, then $A$ is a grey set.

The following Table $4.1$ presents comparison between white number, black number and grey number.

Established fuzzy risk assessment methods based on Z-numbers capable at dealing with the presence of uncertainty (Marhamati et al. 2018; Peng et al. 2019; Hendiani et al. 2020; Azadeh and Kokabi 2016) but the presence of uncertainty the risk faced is not well acknowledged. This is depicted when they consider only the presence of uncertainty when preferences elicited by the risk analysts are partially known (Jiang et al. 2017; Wu et al. 2018; Abiyev et al. 2018). Nonetheless, the presence of uncertainty can also happen when preferences elicited by the risk analysts are completely known, completely unknown and partially unknown (Bakar et al. 2020.

## 统计代写|决策与风险作业代写decision and risk代考|Grey Number

G_{A} \in\left[g^{-}, g^{+}\right]=\left{g^{-} \leq t \leq g^{+}\right}G_{A} \in\left[g^{-}, g^{+}\right]=\left{g^{-} \leq t \leq g^{+}\right}

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|决策与风险作业代写decision and risk代考|Case Study

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|决策与风险作业代写decision and risk代考|Observed Manufacturing Plant

The observed manufacturing plant in which we performed the case study application is located in Germany. It makes plastic production by injection molding. The production includes several processes: Recycled plastic in crushed form is supplied from the supplier in the form of the bale. The bales are divided into pieces for homogenization. Thus, filling material can be added to the mixture. The raw material is brought to the shredder section to reduce the grain size. Raw material with reduced grain size is brought to the grinder. Large particles are removed from the system, and fine particles are brought to the centrifugal washing section. Here, at high temperature, solid plastic particles are melted to become liquid. Liquidized raw material is taken to the silo. Necessary additives are added to the molten raw material in the silo. With the help of the feeder, the raw material is brought to the extrusion section. In this section, the raw material is extracted in strip form. To prevent distortions in the product and achieve homogeneous cooling, the extruded strips are taken into the cooling pool. The extruded raw material is crushed in the grinder and brought to the silo. The final product is produced in the determined mold by sending the raw material with reduced particle size to the injection machine.

## 统计代写|决策与风险作业代写decision and risk代考|Analysis of the Result

The failure prioritization of six failure modes is $F M 5>F M 1>F M 2>F M 4>$ $F M 3>F M 6$. The failure mode of FM5 (Extruder blocking the flow of raw materials) with its highest final RPN score ( $R P N=0.323$ ) should be taken more attention. On the other hand, FM1 is also determined as the second most important failure mode $(R P N=0.320)$. FM3 and FM6 are determined as the least important failure modes.

The main factor in the formation of FM5 is that the raw material taken from recycling is not homogeneous. It is quite challenging to adjust the melt’s optimum temperature due to plastics with different melting temperatures in the supplied bale. In this case, the following measures can be taken. (i) As much as possible, less molten plastic should be sent to the system. This will reduce the production rate but improve flow through the extruder. (ii) It is not possible to provide the production parameters because the raw material used is not homogeneous. Therefore, preliminary tests should be carried out at each supply to determine the optimum melting temperature and pressure amount. Thus, congestion in the extruder is prevented. (iii) Homogeneity should be taken into account in supplier selection. (iv) The grain size in the grinder, feeder speed, silo temperature should be controlled continuously, and necessary precautions should be taken to prevent clogging of the extruder.

The main factor in the occurrence of FMl is the size difference in the raw material supplied. To prevent this failure: (i) A pre-screening process should be carried out on the raw material supplied. Thus, more homogeneous particles will not create clogging in the shredder. (ii) Storing the raw material at appropriate humidity and temperature will increase the shredder performance. (iii) Necessary thread adjustments should be made according to the incoming raw material while setting the shredder. The operators should be given the necessary training in this regard. Since the raw material arrival is irregular, the operator should make the necessary adjustment without delay.

## 统计代写|决策与风险作业代写decision and risk代考|Discussion

A comparative study that considers evaluations of both risk parameters and FMs with respect to three RPN elements via AHP is demonstrated to test the validity of the proposed approach. Figure $3.8$ shows the whole evaluation and obtained weight

values and preference values of six FMs according to these parameters ( $S, O$, and $D)$. All evaluation matrices are found consistent. The CR values of each matrix are also given in Fig. 3.8. By combining preference values of failure modes with respect to each RPN element, the first matrix is gained. Then, final RPN values were obtained by multiplying this matrix and weight matrix. The results are presented in Table 3.4.
As a result of the AHP calculation, FM ranks are as follows: FM5 $>$ FM1 $>$ FM2 $>$ FM4 $>$ FM3 $>$ FM6 When the values of this RPN calculation procedure by AHP and the proposed approach by BWM are compared, it is observed that the ranks are quite similar. Pearson correlation coefficient regarding final RPN values and Spearman rank correlation coefficient regarding rankings in both approaches were determined as $0.98$ and $0.94$, respectively. In this case, it can be said that there is a very strong relationship between these results.

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 统计代写|决策与风险作业代写decision and risk代考|Methods

statistics-lab™ 为您的留学生涯保驾护航 在代写决策与风险decision and risk方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策与风险decision and risk方面经验极为丰富，各种代写决策与风险decision and risk相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|决策与风险作业代写decision and risk代考|FMEA

The FMEA is commonly implemented in the risk assessment process as a powerful method for risk assessment and reliability analysis that is developed for the aerospace industry in the 1960 s at Grumman Aircraft Corporation (Bowles and Peláez 1995; Stamatis 2003). The preidentified failure modes’ risk priority orders are determined by the RPN approach (Liu et al. 2019; Chin et al. 2009). A ten point-scale is used for each parameter in FMEA. Limitations to the conventional FMEA method lead to the emergence of some new FMEA-based approaches. While in some studies, MCDM is merged with FMEA, artificial intelligence, inference systems, soft computing, and some miscellaneous tools are also integrated with FMEA (Chai et al. 2016).

## 统计代写|决策与风险作业代写decision and risk代考|BWM

BWM was proposed by Rezaei (2015) to solve MCDM problems. BWM is a pairwise comparison-based weighting method. The proposed method is beneficial in a way. ( $i$ ) Decision-makers determine the best and worst criteria among all criteria, pairwise comparison of best criterion with other criteria and worst criterion with others. There is no need for a pairwise comparison for all criteria. (ii) Some of the pairwise comparison-based MCDM methods use single vectors. (e.g., Swing and SMART family) Although these methods are data and time-efficient, they do not allow consistency checks. Some pairwise comparison-based methods (e.g., AHP) require a full pairwise comparison matrix. These methods allow consistency check, but they are not data and time-efficient. BWM requires less pairwise comparison compared to methods. It also allows for consistency check by having best to others and other to worst vectors. BWM is superior to other MCDMs in these aspects (Rezaei et al. 2016; Rezaei 2020).

Step 1. The criteria to be evaluated are determined. The criteria to be used in decision making are shown with $\left(c_{1}, c_{2} \ldots, c_{n}\right)$.

Step 2. Best (most significant, most desired) and worst (least significant, least desired) criteria are determined among the determined criteria. Pairwise comparison is not performed at this stage.

Step 3. Using the numbers 1-9, it is determined how the best criterion differs from other criteria. The Best to other vector is created as:
$$A_{B}=\left(a_{B 1}, a_{B 2}, \ldots, a_{B n}\right)$$
where $a_{B j}$ shows the predilection of the best criterion $B$ over criterion $j$ Comparison of the criteria with themselves $\left(a_{B B}=1\right)$

Step 4. Using the numbers 1-9, it is determined how the worst criterion differs from other criteria. Others-to-Worst vector is created as:
$$A_{B}=\left(a_{1 W}, a_{2 W}, \ldots, a_{n W}\right)$$
where $a_{j w}$ shows the predilection of the criterion $j$ over the worst criterion $W$.
Step 5. Determination of weight (( $\left.W_{1}^{}, W_{2}^{}, \ldots W_{n}^{*}\right)$.
The optimum weight for the criteria is the one where for each pair of $w_{B} / w_{j}$ and $w_{j} / w_{w}$ we have $w_{B} / w_{j}=a_{j w}$. To satisfy these for all $j$, we should find a solution where the maximum absolute differences $\left|\frac{w_{p}}{w_{j}}-a_{B j}\right|$ and $\left|\frac{w_{j}}{w_{w}}-a_{j w}\right|$ for all $j$ is minimized. Given that the variables cannot be negative, and the sum of the variables is equal to one, the problem to be solved is:

$$\min {j}\left{\left|\frac{w{B}}{w_{j}}-a_{B j}\right|,\left|\frac{w_{j}}{w_{W}}-a_{j w}\right|\right}$$
S.t
$$\sum w_{j}=1$$
$w_{j} \geq 0$ for all $j$.
With the necessary conversion done, the problem is:
$\min \xi$
\mid \begin{aligned}&\frac{w_{\beta}}{w_{j}}-a_{B j} \mid \leq \xi \text { for all } j . \&\frac{w_{j}}{w w}-a_{j w} \mid \leq \xi \text { for all } j\end{aligned}
$$\sum w_{j}=1$$
$w_{j} \geq 0$, for all $j$.
Solving problem, the optimum weights $\left(\left(W_{1}^{}, W_{2}^{}, \ldots W_{n}^{}\right)\right.$ and $\xi^{}$ are calculated. Following the procedure in Rezaei (2015), the Consistency Ratio (CR) is calculated. The higher the $\xi^{*}$, higher CR and less reliable results will be obtained.

As a result of the solution of the problem, the variable weights $\left(\left(W_{1}^{}, W_{2}^{}, \ldots W_{n}^{}\right)\right.$ ind $\xi^{}$ are calculated. Then the consistency ratio is calculated. When the number of rariables exceeds three, CR can never be equal to zero. It can be said that the lower he CR, the more consistent the evaluation is made.

## 统计代写|决策与风险作业代写decision and risk代考|Proposed Framework

The proposed FMEA framework is based on BWM method. The initial steps are about preparation for FMEA (determine failure modes and define RPN elements). The failure modes are identified that cause faulty products in the observed manufacturing plant. Then, the importance weights of the RPN elements and ranking of failure modes are calculated using BWM procedure. Preference values of each failure mode are computed with respect to $S, O$, and D. The flowchart of this proposed framework is provided in Fig. 3.2.

## 统计代写|决策与风险作业代写decision and risk代考|FMEA

FMEA 通常在风险评估过程中实施，作为一种强大的风险评估和可靠性分析方法，该方法是 1960 年代格鲁曼飞机公司为航空航天工业开发的（Bowles 和 Peláez 1995；Stamatis 2003）。预先确定的故障模式的风险优先顺序由 RPN 方法确定（Liu 等人 2019；Chin 等人 2009）。FMEA 中的每个参数使用十点量表。传统 FMEA 方法的局限性导致出现了一些基于 FMEA 的新方法。而在一些研究中，MCDM 与 FMEA 合并，人工智能、推理系统、软计算和一些杂项工具也与 FMEA 集成（Chai et al. 2016）。

## 统计代写|决策与风险作业代写decision and risk代考|BWM

BWM 由 Rezaei (2015) 提出来解决 MCDM 问题。BWM 是一种基于成对比较的加权方法。所提出的方法在某种程度上是有益的。(一世) 决策者确定所有标准中的最佳和最差标准，将最佳标准与其他标准以及最差标准与其他标准进行成对比较。不需要对所有标准进行成对比较。(ii) 一些基于成对比较的 MCDM 方法使用单个向量。（例如，Swing 和 SMART 系列）尽管这些方法具有数据效率和时间效率，但它们不允许进行一致性检查。一些基于成对比较的方法（例如，层次分析法）需要一个完整的成对比较矩阵。这些方法允许进行一致性检查，但它们不是数据和时间效率的。与方法相比，BWM 需要较少的成对比较。它还允许通过对他人最好和对最差向量进行一致性检查。BWM 在这些方面优于其他 MCDM（Rezaei 等人 2016；Rezaei 2020）。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。