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

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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|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

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## MATLAB代写

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