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On New Multivariate Probability Distributions and Stochastic Processes with System Reliability and Maintenance Applications

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  • Jerzy Filus

    (Oakton Community College)

  • Lidia Filus

    (Northeastern Illinois University)

Abstract

Two distinct methods for construction of some interesting new classes of multivariate probability densities are described and applied. As common results of both procedures three n-variate pdf classes are obtained. These classes are considered as generalizations of the class of univariate Weibullian, gamma, and multivariate normal pdfs. An example of an application of the obtained n-variate pdfs to the problem of modeling the reliability of multicomponent systems with stochastically dependent life-times of their components is given. Obtaining sequences over n = 2, 3, ... of consistent n-variate pdfs, that obey a relatively simple common pattern, for each n, allows us to extend some of the constructions from random vectors to discrete time stochastic processes. Application of one, so obtained, class of highly non-Markovian, but still sufficiently simple, stochastic processes for modeling maintenance of systems with repair, is presented. These models allow us to describe and analyze repaired systems with histories of all past repairs.

Suggested Citation

  • Jerzy Filus & Lidia Filus, 2007. "On New Multivariate Probability Distributions and Stochastic Processes with System Reliability and Maintenance Applications," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 425-446, September.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:3:d:10.1007_s11009-007-9026-6
    DOI: 10.1007/s11009-007-9026-6
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    References listed on IDEAS

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    1. Wang, Hongzhou, 2002. "A survey of maintenance policies of deteriorating systems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 469-489, June.
    2. G. Heinrich & U. Jensen, 1995. "Parameter estimation for a bivariate lifetime distribution in reliability with multivariate extensions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 49-65, December.
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