Optimal variable acceptance sampling plan for exponential distribution using Bayesian estimate under Type I hybrid censoring

Acceptance sampling plans with censoring schemes are crucial for improving quality control by efficiently managing incomplete information. This approach improves cost and time effectiveness compared to traditional methods, providing a more accurate assessment of product quality. In this study, a variable acceptance sampling plan under Type-I hybrid censoring is designed for a lot of independent and identical units with exponential lifetimes using Bayesian estimation of the mean life. This novel approach diverges from conventional methods in acceptance sampling plans, which rely on maximum likelihood estimation and the minimization of Bayes risk. Bayesian estimation is obtained using both squared error loss and Linex loss functions. Under each method, a nonlinear optimization problem is solved to minimize the testing cost, and the optimal values of the plan parameters are determined. The proposed plans are illustrated using various numerical examples, with each plan presented in tables. The acceptance sampling plan using the squared error loss function proves to be more cost-effective than the plan using the Linex loss function. A comparative analysis of the proposed plans with existing work in the literature demonstrates that our cost is much lower than the cost of existing plans using maximum likelihood estimation. Additionally, a real-life case study is conducted to validate the approach.