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An application of the MTP2 property on bounds on system reliability

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  • J. Gåsemyr
  • B. Natvig

Abstract

This paper is concerned with the joint prior distribution of the dependent reliabilities of the components of a binary system. When this distribution is MTP2 (Multivariate Totally Positive of Order 2), it is shown in general that this actually makes the machinery of Natvig and Eide [7] available to arrive at the posterior distribution of the system's reliability, based on data both at the component and system level. As an illustration in a common environmental stress case, the joint prior distribution of the reliabilities is shown to have the MTP2 property. We also show, similarly to Gåsemyr and Natvig [3], for the case of independent components given component reliabilities how this joint prior distribution may be based on the combination of expert opinions. A specific system is finally treated numerically. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 741–755, 1997

Suggested Citation

  • J. Gåsemyr & B. Natvig, 1997. "An application of the MTP2 property on bounds on system reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(8), pages 741-755, December.
    • Handle: RePEc:wly:navres:v:44:y:1997:i:8:p:741-755
    DOI: 10.1002/(SICI)1520-6750(199712)44:83.0.CO;2-A
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    References listed on IDEAS

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    1. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    2. Jørund Gåsemyr & Bent Natvig, 1995. "Using Expert Opinions in Bayesian Prediction of Component Lifetimes in a Shock Model," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 227-242, February.
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