Integrating order statistics in reliability acceptance sampling plans for a compound distribution: a case study

Quality denotes the extent of distinction or supremacy exhibited by a product, service, or process. Employing state of the art technologies and data analytics within manufacturing is termed as "smart manufacturing," that aims to refine production costs and enhance overall production efficiency. Order statistics delve into the scrutiny and organization of data points, whether in descending or ascending sequences with the intent of furnishing distribution patterns. This article presents the pioneering evolution of a novel methodology that constitutes a substantial advancement in the realms of reliability acceptance sampling and reliability engineering. The objective of this research is to utilize principles of order statistics within the realm of reliability acceptance sampling with the intention of reducing both the time and expense associated with inspection procedures. This entails leveraging the Exponential—Poisson distribution to determine percentiles in scenarios where product life testing is terminated at a predetermined interval. The required minimum sample size is essential to ascertain the attainment of the designated percentile lifetime under a predetermined level of consumer risk. The operating characteristics including both values and curves of the sampling plans are established along with the elucidation of the producer's risk. Furthermore, a comprehensive case study was undertaken, accompanied by numerical elucidations to enhance understanding of the proposed methodology.