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On generalized start-up demonstration tests

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  • Xian Zhao

Abstract

Start-up demonstration tests and various extensions have been discussed, in which a unit under the test is accepted or rejected according to some criteria. CSTF, CSCF, TSCF and TSTF are most well known start-up demonstration tests. In this paper, two kinds of more general start-up demonstration tests are introduced. CSTF, TSTF, TSCF and CSCF are all special situations of the new tests. For the new generalized start-up demonstration tests, under the assumption of independent and identically distributed trials for each test, the analytic expressions for the expectation, the probability mass function and the distribution of the test length, as well as the probability of acceptance or rejection of the unit are given. All the analyses are based on the finite Markov chain imbedding approach which avoids the complexities of the probability generating function approach and makes the results readily understood and easily extended to the non-i.i.d. cases. Furthermore, an optimal model for generalized start-up demonstration tests is proposed. Finally, a numerical example is presented to make our results more transparent, and it can demonstrate the advantages of the new tests. Copyright Springer Science+Business Media New York 2014

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  • Xian Zhao, 2014. "On generalized start-up demonstration tests," Annals of Operations Research, Springer, vol. 212(1), pages 225-239, January.
    • Handle: RePEc:spr:annopr:v:212:y:2014:i:1:p:225-239:10.1007/s10479-012-1279-y
    DOI: 10.1007/s10479-012-1279-y
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    References listed on IDEAS

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    1. N. Balakrishnan & S. Mohanty & S. Aki, 1997. "Start-Up Demonstration Tests Under Markov Dependence Model with Corrective Actions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 155-169, March.
    2. N. Balakrishnan & P. Chan, 2000. "Start-Up Demonstration Tests with Rejection of Units upon Observing d Failures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(1), pages 184-196, March.
    3. Martin, Donald E. K., 2004. "Markovian start-up demonstration tests with rejection of units upon observing d failures," European Journal of Operational Research, Elsevier, vol. 155(2), pages 474-486, June.
    4. DePoy Smith, Michelle L. & Griffith, William S., 2008. "The analysis and comparison of start-up demonstration tests," European Journal of Operational Research, Elsevier, vol. 186(3), pages 1029-1045, May.
    5. Martin, Donald E.K., 2008. "Application of auxiliary Markov chains to start-up demonstration tests," European Journal of Operational Research, Elsevier, vol. 184(2), pages 574-583, January.
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    Cited by:

    1. Yin, Juan & Cui, Lirong & Balakrishnan, Narayanaswamy, 2022. "Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. N. Balakrishnan & M. V. Koutras & F. S. Milienos, 2017. "On the identifiability of start-up demonstration mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 717-735, August.

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