UNIFORM STOCIIASTIC ORDERING ON A SYSTEM OF COMPONENTS WITH DEPENDENT LIFETIMES INDUCED BY A COMMON ENVIRONMENT

SUMMARY. A system of n non-renewable components sharing a common random environment is considered. In terms of the uniform stochastic orderings, it is shown how the random environment can aect the number of components functioning and the lifetime of a k-out-of-n system.

[1]  J. Keilson,et al.  Uniform stochastic ordering and related inequalities , 1982 .

[2]  Mark A. Youngren,et al.  Dependence in target element detections induced by the environment , 1991 .

[3]  T. Nayak Multivariate Lomax distribution: properties and usefulness in reliability theory , 1987, Journal of Applied Probability.

[4]  Steven T. Garren,et al.  General conditions for comparing the reliability functions of systems of components sharing a common environment , 1998 .

[5]  Moshe Shaked,et al.  5 Stochastic ordering of order statistics , 1998, Order statistics.

[6]  Moshe Shaked,et al.  A Concept of Positive Dependence for Exchangeable Random Variables , 1977 .

[7]  T. Egeland Mixing dependence and system reliability , 1992 .

[8]  Nozer D. Singpurwalla,et al.  On the reliability function of a system of components sharing a common environment , 1988 .

[9]  Chunsheng Ma,et al.  Likelihood ratio ordering of order statistics , 1998 .

[10]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[11]  S. M. Samuels On the Number of Successes in Independent Trials , 1965 .

[12]  D. Lindley,et al.  Multivariate distributions for the life lengths of components of a system sharing a common environment , 1986, Journal of Applied Probability.

[13]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[14]  Tail Ordering and Asymptotic Efficiency of Rank Tests , 1988 .

[15]  Donald St. P. Richards,et al.  Multivariate Liouville distributions, III , 1987 .

[16]  P. Hougaard A class of multivanate failure time distributions , 1986 .

[17]  Martin Crowder,et al.  A Multivariate Distribution with Weibull Connections , 1989 .

[18]  D. Yao,et al.  Bivariate characterization of some stochastic order relations , 1991, Advances in Applied Probability.

[19]  Philip Hougaard,et al.  Modelling multivariate survival , 1987 .

[20]  G. A. Whitmore,et al.  A multivariate survival distribution generated by an inverse Gaussian mixture of exponentials , 1991 .

[21]  F. Proschan,et al.  Applications of the hazard rate ordering in reliability and order statistics , 1994 .

[22]  Frank Proschan,et al.  A general composition theorem and its applications to certain partial orderings of distributions , 1995 .

[23]  A. D. Barbour,et al.  Stochastic ordering of order statistics , 1991 .

[24]  J. D. Esary,et al.  Relationship Between System Failure Rate and Component Failure Rates , 1963 .

[25]  D. Al-Mutairi Multivariate failure models generated by random environments : A unified approach , 1996 .

[26]  Claude Lefèvre,et al.  On a system of components with joint lifetimes distributed as a mixture of independent exponential laws , 1989 .

[27]  J. Pfanzagl On the Topological Structure of Some Ordered Families of Distributions , 1964 .

[28]  D. Richards,et al.  Comparison of system reliability functions under laboratory and common operating environments , 1997, Journal of Applied Probability.

[29]  J. Lynch,et al.  Uniform stochastic orderings and total positivity , 1987 .

[30]  Dilip Roy,et al.  Generalised mixtures of exponential distributions , 1988 .