Acceptance Sampling Plans from Life Tests Based on Percentiles of Half Normal Distribution

The design of acceptance sampling plans is developed under truncated life testing based on the percentiles of half normal distribution. The minimum sample size necessary to ensure the specified life percentile is obtained under a given consumer’s risk. The operating characteristic values of the sampling plans as well as the producer’s risk are presented. The results are illustrated by examples. 1. Introduction Acceptance sampling is concerned with inspection and decision making regarding lots of products and constitutes one of the oldest techniques in quality control. If the lifetime of the product represents the quality characteristics of interest, the acceptance sampling is as follows: a company receives a shipment of product from a vendor. This product is often a component or raw material used in the company’s manufacturing process. A sample is taken from the lot and the relevant quality characteristic of the units in the sample is inspected. On the basis of the information in the sample, a decision is made regarding lot disposition. Traditionally, when the life test indicates that the mean life of products exceeds the specified one, the lot of products is accepted, otherwise it is rejected. Accepted lots are put into production, while rejected lots may be returned to the vendor or may be subjected to some other lot disposition actions. For the purpose of reducing the test time and cost, a truncated life test may be conducted to determine the sample size to ensure a certain mean life of products when the life test is terminated at a time , and the number of failures does not exceed a given acceptance number . A common practice in life testing is to terminate the life test by a predetermined time and note the number of failures. One of the objectives of these experiments is to set a lower confidence limit on the mean life. It is then to establish a specified mean life with a given probability of at least which provides protection to consumers. The test may be terminated before the time is reached or when the number of failures exceeds the acceptance number in which case the decision is to reject the lot. Studies regarding truncated life tests can be found in Epstein [1], Sobel and Tischendrof [2], Goode and Kao [3], Gupta and Groll [4], Gupta [5], Fertig and Mann [6], Kantam and Rosaiah [7], Baklizi [8], Wu and Tsai [9], Rosaiah and Kantam [10], Rosaiah et al. [11], Tsai and Wu [12], Balakrishnan et al. [13], Srinivasa Rao et al. [14], Srinivasa Rao et al. [15], Aslam et al. [16], and Srinivasa Rao et al. [17]. All these authors designed acceptance