Development of a Hybrid Acceptance Sampling Plan Utilising the Binomial-Gumbel Type II Distribution

Quality has emerged as a crucial criterion for consumers when choosing among diverse competing items and services in the marketplace. This research established a hybrid group acceptance sampling plan based on the lifetime of a product that adheres to the Binomial-Gumbel Type II distribution, with the objective of determining the probability of acceptance, minimum values, and Operating Characteristic (OC) curves. The findings indicate enhanced economic dependability in product quality testing, safeguarding producers from rejecting acceptable lots and customers from accepting inferior finished products. The mean life ratio figures also inform the producer on enhancing the quality of their product. Additionally, consumers possess greater safeguards against accepting inferior products from producers, as illustrated in the example. Comprehensive data and examples are included for illustrative purposes. A comparative analysis of the proposed Hybrid Group Acceptance Sampling Plan, employing the Binomial-Gumbel Type II Distribution, reveals a greater probability of acceptance than the current Hybrid Group Acceptance Sampling Plan based on the New Weighted Exponential Distribution. The proposed plan necessitates inspection of 16 items, while the existing plan requires 28 items, indicating that the proposed plan optimally minimizes the number of observations needed for decision-making.