统计代写|决策与风险作业代写decision and risk代考|The Proposed Risk Assessment Model

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• 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|Bayesian BWM

In order to more objective integrate the opinions of multiple risk analysts, Mohammadi and Rezaei $(2020)$ developed a probabilistic model of BWM, called Bayesian BWM. Because the judgments provided by each decision-maker in BWM are different, the two vectors information would be different (risk analysts may choose

different best/worst evaluated item). Therefore, it is not possible to aggregate the opinions of multiple risk analysts by using arithmetic averages. The weight vector of the MCDM is $w_{j}=\left(w_{1}, w_{2}, \ldots, w_{j}, \ldots, w_{n}\right)$, with $\sum_{j=1}^{n} w_{j}=1$ and $w_{j} \geq 0$ required. Each $w_{j}$ is represented as the weight of the corresponding evaluated item $C_{j}$. The evaluated item $C_{j}$ can be regarded as a random event, and the weight $w_{j}$ is their occurrence probability. According to probability theory, the same is true for $\sum_{j=1}^{n} w_{j}=1$ and $w_{j} \geq 0$. Therefore, it is feasible to construct a probability model from the perspective of decision-making. The execution steps are as follows (Mohammadi and Rezaei 2020):
Steps 1-4. The same as Steps $1-4$ of conventional BWM.
Step 5. Calculate the best weight value of the group of evaluated items.
The input data $A_{B}$ and $A_{W}$ of the BWM can be builded as a probability model of polynomial distribution. The contents of the two vectors are both positive integers, the probability mass function of the polynomial distribution of a given $A_{W}$ is
$$P\left(A_{W} \mid w\right)=\frac{\left(\sum_{j=1}^{n} a_{j w}\right) !}{\prod_{j=1}^{n} a_{j w} !} \prod_{j=1}^{n} w_{j}^{a_{j w}}$$
where $w$ is the polynomial distribution, the probability of event $j$ is proportional to the number of occurrences and the total number of experiments.
$$w_{j} \propto \frac{a_{j w}}{\sum_{j=1}^{n} a_{j w}}, \forall j=1,2, \ldots, n .$$
Similarly, the worst evaluated item $C_{W}$ can be written as follows:
$$w_{W} \propto \frac{a_{W W}}{\sum_{j=1}^{n} a_{j W}}=\frac{1}{\sum_{j=1}^{n} a_{j W}} .$$
Equations (2.6) and (2.7) can be integrated to obtain the following:
$$\frac{w_{j}}{w_{W}} \propto a_{j w}, \forall j=1,2, \ldots, n$$
Besides, $A_{B}$ is modeled using polynomial distribution. However, the concepts of the generation of $A_{B}$ and $A_{W}$ are different. The former is the optimal evaluated item $B$ compared to the other evaluated items $j$. The larger the evaluation value, the smaller the weight of the compared evaluated item $j$; the latter refers to other evaluated items. The evaluation item $j$ is compared with the worst evaluated item $W$. The larger the evaluation value, the greater the weight of the evaluated item $j$. Therefore, the conversion of the assessment content of $A_{B}$ into the weight should be reciprocal.

统计代写|决策与风险作业代写decision and risk代考|Classifiable TOPSIS Technique

TOPSIS technique is one of the most popular sorting methods for ranking the evaluated items. This method is to determine the relative position of each evaluated item by determining the degree of separation between each evaluated item and the positive and negative ideal solutions (PIS and NIS). The optimal evaluated item is the one closest to the PIS and the farthest away from the NIS. In risk management, the

closer to the positive ideal solution, the greater the degree of risk. TOPSIS will not affect the time and quality of the solution due to the number of evaluated items. In addition, this paper applies classifiable TOPSIS technique (Liaw et al. 2020), which can not only obtain a more reliable ranking, but also divide all the evaluated items into four risk levels. When a new evaluated item is added, the method can be used to immediately assign a level to it. The detailed classifiable TOPSIS technique steps are described as follows (Liaw et al. 2020):
Step 1. Build the initial evaluation matrix $\boldsymbol{X}$
Assume that there are $i$ evaluated items in the risk assessment framework, $i=1$, $2, \ldots, m ; j$ represents 4 risk factors, $\mathrm{S}, \mathrm{O}, \mathrm{D}$, and $\mathrm{E}$. Under each risk factor, the risk values of the evaluated items are evaluated to obtain the initial evaluation matrix. In the paper, Bayesian BWM is used to obtain the content of the matrix.
$$\mathcal{X}=\left[\begin{array}{cccc} d_{1 S} & d_{1 O} & d_{1 D} & d_{1 E} \ d_{2 S} & d_{2 O} & d_{2 D} & d_{2 E} \ \vdots & \vdots & \vdots & \vdots \ d_{i S} & d_{i O} & d_{i D} & d_{i E} \ \vdots & \vdots & \vdots & \vdots \ d_{m S} & d_{m O} & d_{m D} & d_{m E} \end{array}\right], i=1,2,$$
Step 2. Calculate the normalized evaluation matrix $X^{*}$
Because the data range obtained through Bayesian BWM is already between 0 and 1. Therefore, this step does not need to be executed.

统计代写|决策与风险作业代写decision and risk代考|Problem Description

The practicality and effectiveness of the developed risk assessment model can be illustrated through a practical case. The reliability and robustness of machine tools are very important to the manufacturing industry, because it is the main production equipment in the manufacturing industry. Quality control engineers or risk analysts must implement risk assessment and improvement plans for new products to reduce the occurrence of product failures. The company in this case is a multinational manufacturer of machine tool parts in Taiwan. The company’s machine tool components include computer numerical control (CNC) rotary tables, indexing tables, hydraulic indexing tables, auto-pallet changer with worktable, etc. In the face of a competitive global market, the company must develop products that are more stable, more precise, faster, and more functional. Therefore, the company implements FMEA activities before the launch of various new products.

The FMEA team was composed of senior department heads of the company. There were seven risk analysts from six different departments, including business department, design department, manufacturing department, quality control department, management department, and sales service department. The seven risk analysts had more than 15 years of experience in the machine tool manufacturing industry and have participated in machine tool related international exhibitions for many times. In addition to their professional technical knowledge, they also understood the development trend of machine tools. In the study, the case company used a newly developed computer numerical control (CNC) rotary table as the product of FMEA analysis, which is CNC rotary tilting Table 250 (TRT-250). As an NC controlled 2 axis table, TRT-250 is suitable for larger workloads in 5 axis machining. A one-piece housing structure with a powerful hydraulic clamping system offers a greater clamping torque and high loading capacities. It is also designed for easy installation and alignment. The FMEA team listed all the failure modes and evaluated the key failure modes, as shown in Table 2.7.

It can be seen from Table $2.7$ that there are nine critical failure modes. They are the rotating shaft segmentation accuracy exceeding the standard (FM1), the rotating shaft reproducibility exceeding the standard (FM2), the positive/negative clearance of the rotating shaft exceeding the standard (FM3), the inclined shaft reproducibility exceeding the standard (FM4), the positive/negative clearance of the inclined shaft exceeding the standard (FM5), the machine making noise when the inclined shaft rotates (FM6), abnormal proximity switch (FM7), oil leakage from the disk surface (FM8), and improper waterproof measures (FM9). FMEA was performed to further analyze them.

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

Step 5. 计算评估项目组的最佳权重值。

统计代写|决策与风险作业代写decision and risk代考|Classifiable TOPSIS Technique

TOPSIS技术是最流行的排序方法之一，用于对评估项目进行排名。该方法是通过确定每个被评估项目与正负理想解（PIS和NIS）之间的分离程度来确定每个被评估项目的相对位置。最优评价项目是最接近 PIS 和最远离 NIS 的项目。在风险管理中，

X=[d1小号d1这d1Dd1和 d2小号d2这d2Dd2和 ⋮⋮⋮⋮ d一世小号d一世这d一世Dd一世和 ⋮⋮⋮⋮ d米小号d米这d米Dd米和],一世=1,2,

统计代写|决策与风险作业代写decision and risk代考|Problem Description

FMEA团队由公司高级部门负责人组成。风险分析师7人，分别来自业务部、设计部、制造部、品管部、管理部、销售服务部六个部门。七位风险分析师在机床制造行业拥有超过15年的经验，并多次参加机床相关的国际展会。除了专业的技术知识外，他们还了解机床的发展趋势。在研究中，案例公司使用了新开发的计算机数控（CNC）转台作为FMEA分析的产品，即CNC转台250（TRT-250）。作为 NC 控制的 2 轴工作台，TRT-250 适用于 5 轴加工中较大的工作量。具有强大液压夹紧系统的一体式外壳结构提供更大的夹紧扭矩和高负载能力。它还设计为易于安装和对齐。FMEA 团队列出了所有失效模式并评估了关键失效模式，如表 2.7 所示。

广义线性模型代考

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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。