Two-Sided Group Chain Sampling Plans Based on Truncated Life Test for Generalized Exponential Distribution

Nazrina Aziz,Zahirah Hasim,Zakiyah Zain

doi:10.13189/ms.2021.090404

Abstract

Acceptance sampling is an important technique in quality assurance; its main goal is to achieve the most accurate decision in accepting lot using minimum resources. In practice, this often translates into minimizing the required sample sizes for the inspection, while satisfying the maximum allowable risks by consumer and producer. Numerous sampling plans have been developed over the past decades, the most recent being the incorporation of grouping to enable simultaneous inspection in the two-sided chain sampling which considers information from preceding and succeeding samples. This combination offers improved decision accuracy with reduced inspection resources. To-date, two-sided group chain sampling plan (TSGCh) for characteristic based on truncated lifetime has only been explored for Pareto distribution of the 2<sup>nd</sup> kind. This article introduces TSGCh sampling plan for products with lifetime that follows generalized exponential distribution. It focuses on minimizing consumer's risk and operates with three acceptance criteria. The equations that derived from the set conditions involving generalized exponential and binomial distributions are mathematically solved to develop this sampling plan. Its performance is measured on the probability of lot acceptance and number of minimum groups. A comparison with the established new two-sided group chain (NTSGCh) indicates that the proposed TSGCh sampling plan performs better in terms of sample size requirement and consumers' protection. Thus, this new acceptance sampling plan can reduce the inspection time, resources, and costs via smaller sample size (number of groups), while providing the desired consumers' protection.

Highlights

Acceptance sampling is a statistical technique used in a process of making decision or judgement to either reject or accept a lot based on information acquired from its sample
In order to cater for wider potential applications, this study proposes a two-sided group chain sampling (TSGChSP) with three acceptance criteria and is based on generalized exponential distribution
A smaller number of minimum groups can be achieved if more information is gathered from more preceding samples, or more products are considered in each group, or consumer is willing to compromise the risk of accepting bad lots

Summary

Introduction

Acceptance sampling is a statistical technique used in a process of making decision or judgement to either reject or accept a lot based on information acquired from its sample. Such inference using a sample of a certain proportion from the population instead of inspecting the entire lot is preferable due to its saving of time, resources, and costs. The detailed procedure of the inspection which aims to minimize these inevitable risks is known as acceptance sampling plan. Sampling plans are often categorized into two types which are attribute and variable. Attribute sampling plan considers “go, no-go” or “pass or fail” as a basis of measurement, while variable involves the quantitative measurement of a continuous variable. Numerous attribute sampling plans have been established, for instance, chain sampling plan (ChSP-1), single sampling plan (SSP), new two-sided complete group chain (NTSCGChSP), new two-sided group chain sampling plan (NTSGChSP), and group chain sampling plan (GChSP), which are described

Methods

Results

Conclusion