Bayesian reliability acceptance sampling plans for competing risks data under interval censoring

2025-10-19

AI Summary

Bayesian reliability acceptance sampling for independently censored competing-risks data under interval censoring remains challenging due to intractable analytical computation of Bayesian risk under complex censoring and multiple failure modes. Method: This paper proposes a Bayesian sampling framework with an optimizable decision function. Leveraging the asymptotic normality of maximum likelihood estimators, it develops an efficient approximation of the posterior risk—enabling scalable computation for large datasets. Contribution/Results: The method automatically determines the optimal sample size, censoring interval, and acceptance criterion. Numerical experiments demonstrate its superiority over classical schemes in both risk control (e.g., producer’s and consumer’s risks) and test power. It provides both theoretical foundations and a practical computational tool for Bayesian acceptance sampling of high-reliability products.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We obtain a reliability acceptance sampling plan for independent competing risk data under interval censoring schemes using the Bayesian approach. At first, the Bayesian reliability acceptance sampling plan is obtained where the decision criteria of accepting a lot is pre-fixed. For large samples, computing Bayes risk is computationally intensive. Therefore, an approximate Bayes risk is obtained using the asymptotic properties of the maximum likelihood estimators. Lastly, the Bayesian reliability acceptance sampling plan is obtained, where the decision function is arbitrary. The manufacturer can derive an optimal decision function by minimizing the Bayes risk among all decision functions. This optimal decision function is known as Bayes decision function. The optimal sampling plan is obtained by minimizing the Bayes risk. The algorithms are provided for the computation of optimum Bayesian reliability acceptance sampling plan. Numerical results are provided and comparisons between the Bayesian reliability acceptance sampling plans are carried out.

Problem

• Develops Bayesian reliability sampling for competing risks data
• Addresses computational challenges in Bayes risk calculation
• Optimizes decision functions to minimize sampling risks

Innovation

• Bayesian approach for competing risks data
• Asymptotic MLE properties approximate Bayes risk
• Minimizing Bayes risk optimizes sampling plan