Optimization and estimation in system reliability allocation problem

Highlights: • Two novel approaches for reliability estimation are proposed based on MLEs and UMVUEs. • A simulation algorithm for system reliability estimation is provided. • Reliability functions of some distributions are estimated using the proposed method. • Optimal component allocations are determined at a minimum purchasing cost. • An illustration is provided for the engineering field through a case study. Designing an optimal reliability system with a minimum cost is one of the challenging problems in engineering field over the years. Estimating the subsystem reliability and determining the optimal number of component allocation will give an insight into the adequate performance of the entire system under study. In some scenarios, if a subsystem fails, then the whole system will fail, thus posing a severe threat to the safety of engineers and personnel involved. Hence, the need to optimally determine and allocate the required number of components as well as estimating their reliability so that the system's safety would be guaranteed. In this paper, two procedures for estimating system reliability function are proposed using the maximum likelihood estimators and uniformly minimum variance unbiased estimators. The reliability functions of some selected lifetime distributions are estimated using the proposed procedures via a simulation study. The study presents a hybrid concept of estimation and optimization theory in reliability allocation problem. The work illustrated through a case study, and an optimization technique used to determine the optimal number of components at a minimum cost. The study would be useful for decision-makers in heavy industries/complex systems to help estimate the reliability of system components, optimize the allocation and manufacturer selection problems.