Markovian start-up demonstration tests with rejection of units upon observing d failures

By conditioning on the time of the first failure, several results are derived for demonstration tests of the start-up reliability of equipment. The start-ups are assumed to follow a Markov chain. The equipment is accepted if k consecutive successful start-ups occur before d failures. We compute the...

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Bibliographic Details
Published inEuropean journal of operational research Vol. 155; no. 2; pp. 474 - 486
Main Author Martin, Donald E.K.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.06.2004
Elsevier
Elsevier Sequoia S.A
SeriesEuropean Journal of Operational Research
Subjects
Applied probability
Markov analysis
Markov chain
Operations research
Probability
Reliability
Run probability
Start-up reliability
Studies
Waiting-time distribution
Markov chain
Run probability
Waiting-time distribution
Applied probability
Start-up reliability
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Summary:By conditioning on the time of the first failure, several results are derived for demonstration tests of the start-up reliability of equipment. The start-ups are assumed to follow a Markov chain. The equipment is accepted if k consecutive successful start-ups occur before d failures. We compute the probability of the demonstration test ending with acceptance of the unit and the expectation and variance of the number of start-ups until termination of the test. We also give recursive formulas for computing the probability distribution of the number of start-ups and the probability of acceptance or rejection of the equipment in a specified number of trials. The conditional distribution of the number of start-ups in the test given that the unit is accepted or rejected is obtained as a by-product. Examples are given to illustrate the usefulness of these results.
ISSN:0377-2217
1872-6860
DOI:10.1016/S0377-2217(02)00872-X