Decision making based on single and double acceptance sampling plans for assessing quality of lots

Ksenija Dumičić,Berislav Žmuk

doi:10.2478/v10305-012-0010-4

Abstract

Decision making based on single and double acceptance sampling plans for assessing quality of lots Background: Acceptance sampling is a statistical tool of quality control. Sampling plans and operating characteristic (OC) curves are very useful for conducting acceptance sampling and provide the quality manager with tools to evaluate the quality of a production run or shipment. There are developed different sampling plans, but common used in practise are single and double acceptance sampling plans. Objectives: The goal of the paper is to test if applying of single and double sampling plan can lead to statistically significant different conclusion about quality level of observed lot. Methods/Approach: Statistical tests of difference in proportions are used to test if there is some statistically significant difference in probabilities of lot fraction defectives between a single and a double sampling plan at the same levels of probability of acceptance. Results: The results of the analysis show that in some cases there is statistically significant difference. Namely, the quality manager should be careful when he chooses to use, instead of the first, the second sampling plan with different parameters because on that way he could make statistically significant different conclusion about quality level of observed lot. Conclusions: The paper shows that some intentional manipulations by using different sampling plans are possible.

Highlights

An acceptance sampling is one of three major statistical areas which are used for quality control and improvement
Acceptance sampling plans for attributes are more common in practice and in this paper focus is on this type of acceptance sampling plans
Using different sample sizes and maximum allowed numbers of defective units in a lot and a test for the difference in proportions, this paper indirectly analyses the probability of acceptance of lots when using a single or a double acceptance sampling plan

Summary

Introduction

An acceptance sampling is one of three major statistical areas which are used for quality control and improvement. The aim of this paper is to investigate how usage of different acceptance sampling plans could lead to different conclusions and decisions about accepting or rejecting a lot Both single and double sampling plans in different cases are considered and compared. The OC curve shows the probability that a lot, submitted with a certain fraction defective, will be either accepted, or rejected (Montgomery et al, 2011). If the lot size N is large enough to be declared as infinite, the distribution of the number of defectives x in a random sample of n units will be binomial with parameters n and p In this case, the probability of observing exactly x defectives is: P{x defectives}=. These points are the acceptable quality level (AQL), the lot tolerance percent defective (LTPD) and the neutral quality level (Pn).

X1 C2 From the lot is taking another sample of n2 units

Discussion and Conclusion