Optimal Age Replacement in Parallel Systems with Random Components

In this paper, an optimal age replacement policy has been studied for a parallel system with a random number of components. The objective functions have been constructed based on the expected cost rate and the availability functions. It is supposed that the lifetime of the system components has a Weibull distribution. Three famous members of the power series class of distributions, namely geometric, zero-truncated Poisson, and logarithmic distributions have been considered for the number of components. The optimal model and the conditions for finding the optimal solution have been studied in terms of the hazard rate function of the system. Numerical and graphical computations have been given. Finally, a real data set has been used to illustrate the results.