ASN-Minimax double sampling plans by variables for two-sided specification limits when {\sigma} is unknown

TL;DR

This paper introduces ASN-Minimax double sampling plans for normally distributed quality characteristics with unknown standard deviation, utilizing ML and MVU estimators, resulting in plans with smaller average sample sizes than single sampling plans.

Contribution

It proposes a new ASN-Minimax double sampling plan based on ML and MVU estimators for two-sided limits with unknown variance, improving efficiency over single sampling plans.

Findings

Maximum ASN is significantly smaller than single sampling plan size.

Operation characteristic is derived using independent estimators.

Plans are effective for two-sided specification limits with unknown variance.

Abstract

ASN-Minimax double sampling plans by variables for a normally distributed quality characteristic with unknown standard deviation and two-sided specification limits are introduced. These plans base on the essentially Maximum-Likelihood (ML) estimator p* and the Minimum Variance Unbiased (MVU) estimator ^p of the fraction defective p. The operation characteristic (OC) of the ASN-Minimax double sampling plans is determined by using the independent random variables p*_1, p*_2 and ^p_1, ^p_2, which relate to the first and second samples, respectively. The maximum of the average sample number (ASN) of these plans is shown to be considerably smaller than the sample size of the corresponding single sampling plans.