Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T00:02:55.994Z Has data issue: false hasContentIssue false
  • English
  • Français

General Conditions for Comparing the Reliability Functions of Systems of Components Sharing a Common Environment

Part of: Design of experiments Multivariate analysis Distribution theory

Published online by Cambridge University Press:  14 July 2016

Steven T. Garren  and
Donald St. P. Richards
Steven T. Garren*
Affiliation:
University of Virginia
Donald St. P. Richards*
Affiliation:
University of Virginia
*
∗Postal address: 104 Halsey Hall, Division of Statistics, University of Virginia, Charlottesville, VA 22903, USA.
∗∗Postal address: 107 Halsey Hall, Division of Statistics, University of Virginia, Charlottesville, VA 22903, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

We present general criteria for analyzing the crossing characteristics of RI, the reliability function of an m-of-n system of components operating within a laboratory (or test-bench) environment, and RO, the reliability function of the same system now operating subject to an external environment. Inside the laboratory the components' lifetimes may be dependently distributed, and the external environment is modeled using the general approach of Lindley and Singpurwalla (1986). Our techniques, which utilize results basic to the theory of order statistics, apply to broad classes of external environment models.

Keywords

Exponential distributiongamma distributionm-of-n systemMarshall-Olkin distributionmultivariate Weibull distributionorder statisticssystem reliability

MSC classification

Primary: 62K10: Block designs 62E10: Characterization and structure theory
Secondary: 62H10: Distribution of statistics 62E15: Exact distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 1 , March 1998 , pp. 124 - 135
Copyright
Copyright © Applied Probability Trust 1998 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M., and Stegun, I.A. (1972). Handbook of Mathematical Functions. Dover, New York.Google Scholar
Bandyopadhyay, D., and Basu, A.P. (1990). On a generalization of a model by Lindley and Singpurwalla. Adv. Appl. Prob. 22, 498–500.CrossRefGoogle Scholar
Barlow, R.E., and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Currit, A., and Singpurwalla, N.D. (1988). On the reliability of a system of components sharing a common environment. J. Appl. Prob. 26, 763–771.Google Scholar
David, H.A. (1970). Order Statistics. Wiley, New York.Google Scholar
Gupta, P.L., and Gupta, R.D. (1990). A bivariate random environmental stress model. Adv. Appl. Prob. 22, 501–503.Google Scholar
Hougaard, P. (1986). A class of multivariate failure time distributions. Biometrika 73, 671–678.Google Scholar
Lindley, D.V., and Singpurwalla, N.D. (1986). Multivariate distributions for the life lengths of components of a system sharing a common environment. J. Appl. Prob. 23, 418–431.CrossRefGoogle Scholar
Marshall, A.W., and Olkin, I. (1967). A multivariate exponential distribution. J. Amer. Statist. Assoc. 62, 30–44.Google Scholar
Peköz, E., and Ross, S.M. (1995). A simple derivation of exact reliability formulas for linear and circular consecutive-k-of-n : F systems. J. Appl. Prob. 32, 554–557.Google Scholar
Singpurwalla, N.D., and Youngren, M.A. (1993). Multivariate distributions induced by dynamic environments. Scand. J. Statist. 20, 251–261.Google Scholar
Woodham, S.-A. and Richards, D.St.P. (1997). Comparison of system reliability functions under laboratory and common operating environments. J. Appl. Prob. 34, 536–545.CrossRefGoogle Scholar
Youngren, M.A. (1991). Dependence in target element detection induced by the environment. Naval Res. Logist. 38, 567–577.Google Scholar