Economic Optimization of Group Chain Sampling Plans for Lifetime Distributions

Acceptance sampling techniques play a pivotal role in industries by determining whether to accept or reject lots through the inspection of samples. To mitigate the risk of defective outgoing products and minimize production costs, acceptance sampling doesn't guarantee defect-free items. Instead, it involves scrutinizing a sample from a batch to make decisions regarding the overall lot quality. Most acceptance sampling plans are traditionally designed without an economic basis to meet both producer and consumer quality and risk requirements. This study focuses on constructing an economic model of the group chain sampling plan (GChSP) for minimizing the producer's total cost, encompassing inspection and failure costs. The study explores various lifetime distributions such as inverse Rayleigh, Log-logistic, and Generalized Pareto distributions. The research unfolds in four stages: first, identifying design parameters; second, developing procedures to minimize total costs; third, obtaining the operating characteristic (OC) function using life- time distributions; and lastly, measuring performance using numerical data. The minimized total cost is calculated for different distributions and design parameters, including the minimum number of groups and the acceptance number. Results indicate that the minimized total cost tends to increase with decreasing consumer risk and increasing termination time and pre-specified testing time.