Control F-policy for Fault Tolerance Machining System with General Retrial Attempts

Abstract

The fault tolerance problem of repairable redundant system with admission restriction is investigated by considering the general distributed retrial policy. Upon failure of a machining unit, if the repairman is occupied, the failed unit is forced to enter into the retrial orbit. From the orbit, the failed units repeat the request for the repair job. When the system reaches its capacity K, the failed units are stopped from entering in the system until the number of failed units is again ceases to the prefixed threshold value F. The life time of operating units and the repair times of failed units follow exponential distributed, whereas retrial time is governed by general distribution. By using the supplementary variable corresponding the remaining retrial time, we establish Chapman–Kolmogorov equations to obtain the steady state queue size distribution of the number of failed units. Various performance measures are obtained explicitly which are further used to facilitate the sensitivity analysis by taking numerical illustration.