Optimum Multiple Sampling Plan Based on the Process Capability Index $C_{py}$ Under Type-II Hybrid Censoring

2026-07-27

AI Summary

This study addresses the inefficiency of traditional multiple sampling plans, which rely on prior inspection outcomes and often require large sample sizes, making it difficult to balance both producer and consumer risks with economic feasibility. To overcome these limitations, this work proposes a Stage-Independent Multiple Sampling Plan (SIMSP) that, for the first time, integrates the process capability index $C_{py}$ with a Type-II hybrid censoring scheme. A constrained optimization model is formulated to minimize total inspection cost, leveraging the asymptotic distribution of $C_{py}$ to derive the operating characteristic function and employing the exact Fisher information matrix to determine the optimal design. Numerical experiments demonstrate that the proposed SIMSP significantly reduces required sample sizes and total costs while rigorously controlling both manufacturer and consumer risks, offering an efficient and practical approach for warranty acceptance testing of non-repairable products.

Abstract

This paper proposes a stage independent multiple sampling plan (SIMSP) to improve inspection efficiency by reducing the number of samples required at each sampling stage. Unlike conventional multiple sampling plans (MSP), the proposed SIMSP eliminates the dependence of each sampling stage on the outcome of the preceding inspection. The proposed approach is developed for non-repairable products sold under a pro-rata warranty policy based on the generalized process capability index $C_{py}$. The SIMSP is designed under a Type-II hybrid censoring scheme (Type-II HCS), which provides greater flexibility in controlling test time and failure information in life testing experiments. The asymptotic distribution of the process capability index estimate is used to compute the operating characteristic (OC) function, and the exact Fisher information matrix (FIM) is obtained for further statistical analysis. A constraint optimization problem is formulated to determine the optimal design by minimizing the total cost subject to the manufacturer's and consumer's risk. Numerical investigations are conducted to examine the effects of model parameters, warranty policy characteristics, and cost factors on the optimal solution. The results demonstrate that the proposed approach provides an economically efficient and feasible method for lot acceptance while satisfying the tolerable risks requirements.

Problem

• multiple sampling plan
• process capability index
• Type-II hybrid censoring
• pro-rata warranty
• lot acceptance

Innovation

• Stage Independent Multiple Sampling Plan
• Process Capability Index $C_{py}$
• Type-II Hybrid Censoring
• Pro-rata Warranty
• Optimal Inspection Design