Optimal variable acceptance sampling based on decision tree method: A Bayesian approach under Type-II censoring

Acceptance sampling plans are essential for quality assurance in reliability testing. This study introduces a novel approach to variable acceptance sampling plans under Type-II censoring, assuming an exponential distribution for failure times with an inverse gamma prior. The proposed model applies a decision tree algorithm, simplifying the process compared to traditional methods that rely on complex nonlinear or stochastic optimization. By using Bayesian inference, the model incorporates prior knowledge and updates decisions with new data, minimizing the number of failures required to terminate the test, while ensuring product reliability and reducing testing costs. The decision tree method with backward induction is used to evaluate costs from the leaf nodes to the root, ensuring optimal decision-making with minimum cost. A real-life case study illustrates the practical applications of this method, and a comparative analysis with an existing model demonstrates that it is not only simpler but also has a significantly higher power of test, making it suitable for real-world applications. A sensitivity analysis study is also conducted using simulated data to assess how changes in cost parameters and prior parameters influence the optimal decision cost.