Optimal component test plans for a parallel system based on Type-II censoring

Consider a parallel system with nn independent components. Assume that the lifetime of the jjth component follows an exponential distribution with a constant but unknown parameter λjλj, 1≤j≤n1≤j≤n. We test rjrj components of type-jj for failure and compute the total time TjTj of rjrj failures for the jjth component. Based on T=(T1,T2,…,Tn)T=(T1,T2,…,Tn) and r=(r1,r2,…,rn)r=(r1,r2,…,rn), we derive optimal reliability test plans which ensure the usual probability requirements on system reliability. Further, we solve the associated nonlinear integer programming problem by a simple enumeration of integers over the feasible range. An algorithm is developed to obtain integer solutions with minimum cost. Finally, some examples have been discussed for various levels of producer’s and consumer’s risk to illustrate the approach. Our optimal plans lead to considerable savings in costs over the available plans in the literature.