A New Technique for Optimization of Product Acceptance Process in Terms of Misclassification Probability

A New Technique for Optimization of Product Acceptance Process in Terms of Misclassification Probability

Nicholas A. Nechval (University of Latvia, Latvia) and Konstantin N. Nechval (Transport and Telecommunication Institute, Latvia)
DOI: 10.4018/978-1-5225-5045-7.ch001

Abstract

A product acceptance process is an inspecting one in statistical quality control or reliability tests, which are used to make decisions about accepting or rejecting lots of products to be submitted. This process is important for industrial and business purposes of quality management. To determine the optimal parameters of the product acceptance process under parametric uncertainty of underlying lifetime models (in terms of misclassification probability), a new optimization technique is proposed. The most popular lifetime distribution used in the field of product acceptance is a two-parameter Weibull distribution, with the assumption that the shape parameter is known. Such oversimplified assumptions can facilitate the follow-up analyses, but may overlook the fact that the lifetime distribution can significantly affect the estimation of the failure rate of a product. Therefore, the situations are also considered when both Weibull distribution parameters are unknown. An illustrative numerical example is given.
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Introduction

The product acceptance process is used to make decisions of accepting or rejecting a lot of products based on a random sample collected from the lot. Optimization of an acceptance process specifies the minimum sample size required to be used along with the acceptance and non-acceptance criteria for the lot. So the optimized acceptance process specifies the most effective number of units, say n, to be used for testing, and the acceptance criterion for the specified producer and consumer risks. For a given product acceptance process, the consumer’s and producer’s risks are the probabilities that a bad lot is accepted and a good lot is rejected, respectively. Usually, with every product acceptance process, the associated consumer’s and producer’s risks are also provided.

A typical application of product acceptance process 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 this 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 action. While it is customary to think of acceptance sampling as a receiving inspection activity, there are also other uses. For example, frequently a manufacturer samples and inspects its own product at various stages of production. Lots that are accepted are sent forward for further processing, while rejected lots may be reworked or scrapped. For the purpose of reducing the test time and cost, a truncated life test may be conducted to determine the smallest sample size to ensure a certain mean life of products when the life test is terminated at a preassigned time t0 and the number of failures observed does not exceed a given number.

A product acceptance process in the case that the sample observations are lifetimes of products put to test aims at verifying that the actual population mean exceeds a required minimum. The population mean stands for the mean lifetime of the product, say μ. If μ0 is a specified minimum value, then one would like to verify that μμ0, this means that the true unknown population mean lifetime of the product exceeds the specified value. On the basis of a random sample of size n, the lot is accepted, if by means of a suitable decision criterion, the product acceptance model decides in favour of μμ0. Otherwise the lot is rejected.

Extensive work has been done on product acceptance processes since their inception. Several text books and papers are available which provide different acceptance processes of product for different probability distribution functions, see, for example, Epstein (1954), Sobel and Tischendrof (1959), Goode and Kao (1961), Gupta and Groll (1961), Gupta (1962), Fertig and Mann (1980), Kantam and Rosaiah (1998), Kantam et al. (2001), Baklizi (2003), Wu and Tsai (2005), Rosaiah and Kantam (2005), Rosaiah et al. (2006), Tsai and Wu (2006), Balakrishnan et al. (2007), Srinivasa Rao and Kantam (2010), Stephens (2001), Squeglia (2008), and the references cited therein. All these authors considered the design of product acceptance processes based on the population mean or median.

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