Two-Stage Sampling Inspection Plan based on Mean for Lindley Distribution
Keywords:
Acceptance sampling plan, consumer’s risk, non-normal distribution, operating characteristics (OC) curve, producer’s risk, single sampling inspection planAbstract
This study develops Two-Stage Sampling (TSS) inspection plans for lifetime quality characteristics based on the mean, assuming non-normal distributions such as the exponential and the Lindley distribution. The lot mean (µ) is used as the quality measure. Unlike conventional approaches that focus solely on a fixed sample size, the proposed plan emphasizes efficiency by reducing inspection effort through a two-stage decision mechanism, resulting in time and cost savings. The optimal plan parameters are obtained using a non-linear optimization approach under specified acceptable and rejectable quality levels. A comparative analysis of sample size and Average Sample Number (ASN) between the TSS and Single Sampling (SS) plans is presented. An illustrative example is included to demonstrate the applicability of the proposed method. The results indicate that when the underlying data follow the Lindley distribution, the proposed TSS plan provides a more efficient decision-making framework with reduced average inspection requirements. Therefore, the proposed plan is recommended for use in such situations.
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