Optimal test design for reliability demonstration under multi-stage acceptance uncertainties

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A reliability demonstration test (RDT) plays a critical role in safeguarding product reliability and making sure it meets the target requirement. When planning an RDT, the test planning parameters are determined before executing the RDT. There is uncertainty associated with the test result and whether the product will be acceptable and released into the market with additional costs resulting from the warranty service or whether a reliability growth process is needed to further improve the product’s reliability. Potentially, such a process could be repeated multiple times depending on how quickly the reliability growth process can improve product reliability. Existing RDT designs primarily consider the cost of RDT itself or over a single demonstration stage before the next possible RDT, and hence fail to fully address the uncertainty of all possible future RDTs and various pathways a product may go through in a multi-stage demonstration process. By focusing on binomial RDT (BRDT) plans based on failure count data, this paper proposes an optimal Bayesian BRDT design framework by explicitly quantifying the multi-stage acceptance uncertainties resulting from current and subsequent BRDTs. It allows the BRDT planning decision to be determined more holistically by anticipating the costs of warranty service and reliability growth along different pathways over multiple stages. A recursive information propagation algorithm is proposed to incorporate the prior belief of product reliability and allow it to evolve and update over multiple stages of BRDT. A case study is presented to illustrate the proposed multi-stage Bayesian BRDT design framework and demonstrate its cost-efficiency compared to existing strategies. A comprehensive sensitivity analysis is also provided to demonstrate the impact of the relative size of different cost components, reliability growth rate, and prior setting on the performance of the proposed method.