Bi-objective optimization problem of a parallel system with random number of units

This paper considers a parallel system that has a random number of units. The number of units follows a power series distribution which includes several distributions such as geometric, logarithmic and zero-truncated Poisson distributions. Pareto distribution is considered for the lifetime distribution of units. The optimal parameter is obtained for the distribution of sample size so that the expected cost is minimized and the whole reliability of the system is maximized. The weighted sum method has been utilized to convert this bi-objective model into a one-objective model. Numerical calculations have been performed to evaluate the obtained results.