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Planning of Truncated Sequential Binomial Test via Relative Efficiency
Author(s) -
Michlin Yefim Haim,
Shaham Ofer
Publication year - 2013
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1387
Subject(s) - sequential probability ratio test , truncation (statistics) , binomial distribution , reliability (semiconductor) , mathematics , test plan , quality (philosophy) , sample (material) , mathematical optimization , statistics , computer science , power (physics) , physics , philosophy , chemistry , epistemology , chromatography , quantum mechanics , weibull distribution
A planning methodology is proposed for the sequential probability ratio test (SPRT) for the purpose of practical application. The SPRT is the most common acceptance test in the field of reliability and quality control. In it, the hypothesis is checked that the percentage of defective items does not exceed a specified value. Truncation is resorted to compensate for the absence of a limit on the test duration, but it complicates the planning process. Moreover, the discreteness and multidimensionality of the characteristics of such tests prevent their direct comparison and optimization. To remedy these drawbacks, quality features of the test are proposed, one of which—the relative efficiency—represents the ratio of the test's weighted average sample number till its stopping and its counterpart for the nontruncated SPRT. It facilitates solution of the problems in automatic planning of the test. Another important advantage of this relative efficiency is that it yields accurate and simple formulas for the stopping boundary. Besides, these formulas permit sound choice of the truncation level already at early stages of the planning process. A planner's algorithm and an industrial example are also included. The proposed methodology can also be applied to exponential SPRT. The advantages of tests based on the proposed methodology over those in IEC‐61123 (the binomial case) and IEC‐61124 (the exponential case) are demonstrated, and revision of the standards is recommended. Copyright © 2012 John Wiley & Sons, Ltd.