Application of auxiliary Markov chains to start-up demonstration tests
Application of auxiliary Markov chains to start-up demonstration tests
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DOI：
10.1016/j.ejor.2006.12.009
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发表时间：
2008-01
期刊：
影响因子：
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通讯作者：
D. Martin
中科院分区：
文献类型：
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作者：
D. Martin
我们使用辅助马尔可夫链来获得概率结果的五种类型的启动演示测试，与启动的马尔可夫的一般顺序。其中四个测试是基于连续（或总）成功启动和连续（或总）失败;第五个有两个拒绝标准。对于每种测试类型，我们获得测试结束时单元验收的概率、测试中启动次数的概率分布和矩、指定试验次数中设备验收（或拒绝）的概率以及给定单元验收或拒绝的测试中启动次数的条件分布。给出了数值算例。尽管结果适用于这些特定类型的启动演示测试，但推导方法也可用于具有其他停止标准的测试以及其他情况。
We use auxiliary Markov chains to derive probabilistic results for five types of start-up demonstration tests, with start-ups that are Markovian of a general order. Four of the tests are based on consecutive (or total) successful start-ups and consecutive (or total) failures; the fifth has two rejection criteria. For each test type, we obtain the probability of the test ending with acceptance of the unit, the probability distribution and moments of the number of start-ups in the test, the probability of acceptance (or rejection) of the equipment in a specified number of trials, and the conditional distribution of the number of start-ups in the test given that the unit is accepted or rejected. Numerical examples are given. Though the results are for these specific types of start-up demonstration tests, the method of derivation may be used for tests with other stopping criteria, and in other situations as well.