Optimum inspection policies of reliability analysis for quantal‐response product with Weibull lifetime components

Purpose – The purpose of the paper is to show that modern markets are characterized by rapidly changing environments and numerous external forces. Under these conditions, product lifetimes are rapidly reducing. Therefore, products require optimum inspection policies to maintain high quality and reduce costs in the competitive market. This study aims to establish optimal inspection policies of reliability analysis for quantal‐response product with Weibull lifetime components. Design/methodology/approach – This study considers a product consisting of m different components in series with lifetimes that follow Weibull distributions, and applies a competing failure model to examine the proposed series system for quantal‐response products. The maximum likelihood estimators of parameters of the Weibull distribution are derived based on the quantal‐response data in the proposed series system. The statistical features of the model are illustrated through a numerical example of two‐component series products, and the properties of the maximum likelihood estimators were studied via Monte Carlo simulation under a two‐stage inspected scheme for various sampling sizes and inspection time conditions. Findings – Simulation results demonstrate not only that the optimum inspection condition is the inspection times at T 1 =0.2 and T 2 =0.5 for the two‐stage inspected scheme, but also that the economical sampling size is 150 for both cases. Originality/value – This research results can be applied to the analysis of one‐shot products, e.g. firework, ammunition, airbag, injector, with Weibull components lifetime distribution or the stockpile storage test.