Availability Analysis and Cost Optimization of M/G/1 Fault-Tolerant Machining System with Imperfect Fault Coverage

The prediction of availability and maintainability is a key concern for the system designers to examine the effect of unexpected failures/faults on the system functioning. The main objective of this study is to present the availability analysis and cost optimization for the fault-tolerant machining system with recovery along with replacement facility. A recursive algorithm is suggested for the M / G /1 model of machining system to evaluate the steady-state probabilities and various queueing indices by treating remaining repair time of failed machines as supplementary variable. The system availability for K - out - of - N: Gd configuration is derived analytically for specific repair time distributions such as exponential, three-stage Erlang and deterministic. The numerical results are provided to examine the trends of the analytical metrics and to facilitate the comparative study of different architectures from the system availability viewpoint. Furthermore, the total cost is determined to obtain the optimal repair rate by using quasi-Newton method (QNM).