A repetitive group sampling plan based on the lifetime performance index under gamma distribution

Abstract

AbstractAs technology and living standards improve, people are becoming more concerned with the importance of quality. Quality, thus, becomes the key to company competitiveness, and process capability indices (PCIs) are effective means of measuring process performance. Most PCIs have been developed under the assumption that the quality characteristics are normally distributed; however, the lifetime of products generally possesses a non‐normal distribution. A lifetime performance index (LPI) CL has been proposed and used for measuring product lifetime performance. In this high‐quality era, the use of traditional testing methods incurs very high costs, so acceptance sampling plans have been widely used by industry to perform the inspection. This study considers the product lifetime with a gamma distribution and uses the uniformly minimum‐variance unbiased estimator (UMVUE) of the LPI to develop a repetitive group sampling plan (RGSP). For the practical purpose, this study presents a step‐by‐step procedure and tabulates the plan parameters for various combinations of acceptable and rejectable quality levels, producer's and consumer's risks, and shape parameter. Thus, practitioners can easily know the sample size and the corresponding critical values for decision making. This study also uses the results of the proposed plan to compare with the single sampling plan. Lastly, a practical example is used to illustrate how to apply this acceptance sampling plan.