Reliability demonstration test plan for degraded products subject to Gamma process with unit heterogeneity

The reliability demonstration test (RDT) is widely used to verify the product reliability requirements. Generally, the sampling plan of RDT can be divided into the qualification sampling plan (QSP) in the product design phase and the acceptance sampling plan (ASP) in the batch production phase. Previous works designed RDTs under given sampling plans, they often ignored the unit heterogeneity of products in the degradation modeling and did not distinguish QSP from ASP, which are not enough in practice. Therefore, taking the Gamma process degradation test as an example, an optimal RDT design method considering unit heterogeneity is proposed to solve these problems. Firstly, a multi-objective optimization problem is presented to determine the sampling plan by optimizing the model parameters estimation accuracy. For QSP, with the likelihood ratio order and the monotonicity of average failure time on the common factor of model parameters, the qualification test problem is simplified, and the decision-making criterion considering the existence of QSP is obtained from the risk constraint equations. Similarly, the decision-making criterion considering the existence of ASP is obtained from the QSP data. Finally, numerical examples and a real case study are presented to demonstrate the effectiveness and implementation of the proposed method.