Singh Vijay Pratap, Jain Madhu, Meena Rakesh Kumar, Kumar Pankaj
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee 247667, India.
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.
ISA Trans. 2025 Feb;157:89-106. doi: 10.1016/j.isatra.2024.12.006. Epub 2024 Dec 9.
Redundancy and maintainability-supported fault-tolerant machining systems are used in many industries to achieve pre-specified reliability and system capability. In this investigation, a non-Markov model for the machining system has been developed by involving the concepts of server vacation, server breakdown, and reboot process. The server may fail and undergo primary repair which may be unsuccessful in recovering the server. In case of imperfect server repair, an additional repair is also performed to bring the server back into functional mode. By using the supplementary variable for the residual repair, we obtain the analytic solution of the finite population M/G/1 queueing model for the performance prediction of FTMS. The method of parametric non-linear programming has been implemented to evaluate the performance measures in both crisp and fuzzy environments. The meta-heuristic approaches PSO, GA and classical optimization technique quasi-Newton method are employed to determine the optimal design descriptors by minimizing the total cost. The sensitivity of performance indices with respect to system parameters has been examined for the specific repair time distributions by taking illustrations.
冗余和可维护性支持的容错加工系统在许多行业中被用于实现预先指定的可靠性和系统能力。在本研究中，通过引入服务器休假、服务器故障和重启过程的概念，开发了一种用于加工系统的非马尔可夫模型。服务器可能会发生故障并进行初次修复，但初次修复可能无法成功恢复服务器。在服务器修复不完全的情况下，还会进行额外的修复以使服务器恢复到功能模式。通过使用剩余修复的补充变量，我们获得了用于容错加工系统性能预测的有限总体M/G/1排队模型的解析解。已实施参数非线性规划方法来评估清晰和模糊环境下的性能指标。采用元启发式方法粒子群优化算法（PSO）、遗传算法（GA）和经典优化技术拟牛顿法，通过最小化总成本来确定最优设计描述符。通过举例，针对特定的修复时间分布，研究了性能指标相对于系统参数的敏感性。
