Risk analysis of health, safety and environment in chemical industry integrating linguistic FMEA, fuzzy inference system and fuzzy DEA

Abstract

Organizations are continuously endeavoring to provide a healthy work environment without any incident, by Health, Safety, and Environment (HSE) management. As most of the activities and processes in the organizations have risk-taking nature, identification and evaluation of risks can be useful to decrease their negative effects on the system. Although Failure Mode and Effect Analysis (FMEA) technique is used widely for risk assessment, the traditional Risk Priority Number (RPN) score has shortcomings like do not considering different weights and the inherent uncertainty of risk factors as well as do not regarding all viewpoints of the experts in decision making. The aim of this study is presenting 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 some RPN shortcomings and the prioritization of HSE risks. First, after identifying potential risks and assigning values to the RPN determinant factors by linguistic FMEA team members due to the differentiation of these values, FIS is used to reach a consensus opinion about these factors. Then, the outputs of FIS are used by the fuzzy DEA and its supper efficiency model to risk prioritization which can contribute to full prioritization. In addition to considering uncertainty and decreasing dependence on the team’s opinions, in this phase weights of triple factors are calculated based on mathematical programming. To show the ability of the proposed approach in terms of HSE risks prioritization, it has been implemented in an active company in the chemical industry. After identifying risks having high priority based on the proposed score, preventive/corrective actions are presented in accordance with the case study, and for more analysis of results, the self-organizing map has been applied in this study.

Appendices

Appendix 1: Fuzzy SBDEA model

$$ \begin{aligned} & Min(\delta_{k} )_{\alpha }^{U} = q - \frac{1}{m}\sum\limits_{i = 1}^{m} {(S_{i}^{ - } } )^{L} /(x_{ik} )_{\alpha }^{L} \\ & s.t: \\ & \quad q + \frac{1}{s}\sum\limits_{r = 1}^{s} {(S_{r}^{ + } )^{U} } /(y_{rk} )_{\alpha }^{U} = 1 \\ & \quad q(x_{ik} )_{\alpha }^{L} = \sum\limits_{j = 1, \ne k}^{n} {(x_{ij} )_{\alpha }^{U} \lambda_{j}^{/} } + (x_{ik} )_{\alpha }^{L} \lambda_{j}^{/} + (S_{i}^{ - } )^{L} ,\quad i = 1, \ldots ,m \\ & \quad q(y_{rk} )_{\alpha }^{U} = \sum\limits_{j = 1, \ne k}^{n} {(y_{rj} )_{\alpha }^{L} \lambda_{j}^{/} } + (y_{rk} )_{\alpha }^{U} \lambda_{j}^{/} - (S_{r}^{ + } )^{U} ,\quad r = 1, \ldots ,s \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j}^{/} } = q \\ & \quad \lambda_{j}^{/} \ge 0,\quad j = 1, \ldots ,n,\;\;(S_{i}^{ - } )^{L} \ge 0,\quad i = 1, \ldots ,m, \\ & \quad (S_{r}^{ + } )^{U} \ge 0,\quad r = 1, \ldots ,s,\;\;q > 0 \\ \end{aligned} $$

(6)

$$ \begin{aligned} & Min\,(\delta_{k} )_{\alpha }^{L} = q - \frac{1}{m}\sum\limits_{i = 1}^{m} {(S_{i}^{ - } } )^{U} /(x_{ik} )_{\alpha }^{U} \\ & s.t: \\ & \quad q + \frac{1}{s}\sum\limits_{r = 1}^{s} {(S_{r}^{ + } )^{L} } /(y_{rk} )_{\alpha }^{L} = 1 \\ & \quad q(x_{ik} )_{\alpha }^{U} = \sum\limits_{j = 1, \ne k}^{n} {(x_{ij} )_{\alpha }^{L} \lambda_{j}^{/} } + (x_{ik} )_{\alpha }^{U} \lambda_{j}^{/} + (S_{i}^{ - } )^{U} ,\quad i = 1, \ldots ,m \\ & \quad q(y_{rk} )_{\alpha }^{L} = \sum\limits_{j = 1, \ne k}^{n} {(y_{rj} )_{\alpha }^{U} \lambda_{j}^{/} } + (y_{rk} )_{\alpha }^{L} \lambda_{j}^{/} - (S_{r}^{ + } )^{L} ,\quad r = 1, \ldots ,s \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j}^{/} } = q \\ & \quad \lambda_{j}^{/} \ge 0,\quad j = 1, \ldots ,n,\;\;(S_{i}^{ - } )^{U} \ge 0,\quad i = 1, \ldots ,m, \\ & \quad (S_{r}^{ + } \,)^{L} \ge 0,\quad r = 1, \ldots ,s,\;\;q > 0 \\ \end{aligned} $$

(7)

In Models (6) and (7), $(\delta_{k} )_{\alpha }^{U}$ and $(\delta_{k} )_{\alpha }^{L}$ respectively represent the Upper Bound (UB) and Lower Bound (LB) of the efficiency of the kth DMU under various α levels. Also, $(X_{ik} )_{\alpha }^{U}$ and $(X_{ik} )_{\alpha }^{L}$ respectively represent the UB and LB of ith deterministic input for DMU_j per α level, and UB and LB of rth non-deterministic output for DMU_j per α level.

Appendix 2: Fuzzy super efficiency SBDEA model

$$ \begin{aligned} & (\tau_{k} )_{\alpha }^{U} = Min\frac{1}{m}\sum\limits_{i = 1}^{m} {(\bar{x}_{i}^{\prime } } )^{L} /(X_{ik} )_{\alpha }^{L} \\ & s.t: \\ & \quad \frac{1}{s}\sum\limits_{r = 1}^{s} {(\bar{y}_{r}^{\prime } )^{U} } /(Y_{rk} )_{\alpha }^{U} = 1 \\ & \quad (\bar{x}_{i}^{\prime } )^{L} \ge \sum\limits_{j = 1, \ne k}^{n} {(X_{ik} )_{\alpha }^{L} \lambda_{j}^{/} } ,\quad i = 1, \ldots ,m \\ & \quad (\bar{y}^{\prime}_{r} )^{U} = \sum\limits_{j = 1, \ne k}^{n} {(Y_{rk} )_{\alpha }^{U} \lambda_{j}^{/} ,} \quad r = 1, \ldots ,s \\ & \quad \sum\limits_{j = 1, \ne k}^{n} {\lambda_{j}^{/} } = q \\ & \quad \lambda_{j}^{/} \ge 0,\;j = 1, \ldots ,n, \ne k,\quad (\bar{x}_{i}^{\prime } )^{L} \, \ge q(X_{ik} )_{\alpha }^{L} ,\;i = 1, \ldots ,m, \\ & \quad (\bar{y}^{\prime}_{r} )^{U} \le q(Y_{rk} )_{\alpha }^{U} ,\;(\bar{y}_{r}^{\prime } )^{U} \ge 0,\;r = 1, \ldots ,s,\quad q > 0 \\ \end{aligned} $$

(8)

$$ \begin{aligned} & (\tau_{k} )_{\alpha }^{L} = Min\frac{1}{m}\sum\limits_{i = 1}^{m} {(\bar{x}_{i}^{\prime } } )^{U} /(X_{ik} )_{\alpha }^{U} \\ & s.t: \\ & \quad \frac{1}{s}\sum\limits_{r = 1}^{s} {(\bar{y}^{\prime}_{r} )^{L} } /(Y_{rk} )_{\alpha }^{L} = 1 \\ & \quad (\bar{x}^{\prime}_{i} )^{U} \ge \sum\limits_{j = 1, \ne k}^{n} {(X_{ik} )_{\alpha }^{U} \lambda_{j}^{/} } ,\quad i = 1, \ldots ,m \\ & \quad (\bar{y}^{\prime}_{r} )^{L} = \sum\limits_{j = 1, \ne k}^{n} {(Y_{rk} )_{\alpha }^{L} \lambda_{j}^{/} } ,\quad r = 1, \ldots ,s \\ & \quad \sum\limits_{j = 1, \ne k}^{n} {\lambda_{j}^{/} } = q \\ & \quad \lambda_{j}^{/} \ge 0,\;j = 1, \ldots ,n, \ne k,\quad (\bar{x}_{i}^{\prime } )^{U} \ge q(X_{ik} )_{\alpha }^{U} ,\;i = 1, \ldots ,m, \\ & \quad (\bar{y}^{\prime}_{r} )^{L} \le q(Y_{rk} )_{\alpha }^{L} ,\;(\bar{y}^{\prime}_{r} )^{L} \ge 0,\;r = 1, \ldots ,s,\;q > 0 \\ \end{aligned} $$

(9)

In Models (8) and (9), $(\,\tau_{k} )_{\alpha }^{U}$ and $(\,\tau_{k} )_{\alpha }^{L}$ respectively represent the UB and LB of the super efficiency of the kth DMU under various α levels.