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Determining the sample size for a hybrid life test based on the cost function
Author(s) -
Ebrahimi Nader
Publication year - 1988
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198802)35:1<63::aid-nav3220350106>3.0.co;2-r
Subject(s) - function (biology) , exponential function , mathematics , statistics , fixed cost , sample (material) , scale (ratio) , computer science , mathematical optimization , mathematical analysis , physics , evolutionary biology , biology , business , accounting , quantum mechanics , thermodynamics
The following experiment is considered. n units are tested simultaneously until either the r th failure occurs or a fixed time t o is reached. In the first part of the manuscript, the failure times are assumed to be i.i.d. exponential with an unknown scale parameter 1/λ. The second part deals with the modification where failed units are replaced. In the third part, extensions to nonexponential failure times are outlined. Given r and t o , the goal is to minimize the expected cost as a function of n. Hereby, the cost is defined through three components c 1 , c 2 , and c 3 , respectively, which are associated with (1) the time length of the experiment, (2) the number n of units tested, and (3) some fixed overall cost of the experiment, respectively.