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</script>doi: 10.5772/22436
The present study deals with the planning methodology of tests in which the parameters of two exponentially-distributed random variables are compared. The largest application field of such tests is reliability checking of electronics equipment. They are highly cost-intensive, and the requirements as to their resolution capability become stricter all the time. Hence the topicality and importance of an optimal plan permitting decisions at a given risk level on the basis of a minimal sample size. Such comparison tests are required for example in assessing the desirability of replacing a “basic” object whose reliability is unknown, by a “new” one; or when the influence of test conditions on the results has to be eliminated. This is the case when an electronics manufacturing process is transferred to another site and the product undergoes accelerated testing. Recently, equipment and methods were developed for accelerated product testing through continuous observation of a population of copies and replacement of failed objects without interrupting the test. For such a procedure, the sequential approach is a feasible and efficacious solution with substantial shortening – on the average – of the test duration (see e.g. Chandramouli et al. 1998; Chien et al. 2007). In these circumstances there is high uncertainty in the acceleration factor, with the same effect on the estimated reliability parameters of the product. This drawback can be remedied by recourse to comparison testing. The latter serves also for reliability matching in objects of the same design and different origins, or a redesigned product versus its earlier counterpart, or different products with the same function (see e.g. Chien & Yang, 2007; Kececioglu, 2002). The exponential nature of the Time Between Failures (TBF) of repairable objects, or the time to failure of non-repairable ones – is noted in the extensive literature on the reliability of electronic equipment (Kececioglu, 2002; Chandramouli et al, 1998; Drenick, 1960; Sr-332, 2001; MIL-HDBK-781A, 1996). For brevity, the TBF acronym is used in the sequel for both these notations. Mace (1974, Sec. 6.12) proposed, for this purpose, the so-called fixed sample size test with the number of failures of each object fixed in advance – which is highly inconvenient from the practical viewpoint. For example, when the "basic" object has "accumulated" the
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