Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T07:38:48.578Z Has data issue: false hasContentIssue false
  • English
  • Français

Availability measures for coherent systems of separately maintained components

Published online by Cambridge University Press:  14 July 2016

Laurence A. Baxter
Laurence A. Baxter*
Affiliation:
State University of New York at Stony Brook
*
∗ Postal address: Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A coherent system of components, the failure pattern of each of which being assumed to be modelled by an alternating renewal process, is considered. Formulae are derived for the probability that the system is available at a series of points and for the expected numbers of failures and repairs of the system in a fixed interval. It is shown how the model can be generalised to permit each component to exhibit partial availability in the failed state.

Keywords

COHERENT SYSTEMALTERNATING RENEWAL PROCESSAVAILABILITY MEASURERELIABILITY IMPORTANCEPARTIAL AVAILABILITYCUBIC SPLINING ALGORITHM
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 627 - 636
Copyright
Copyright © Applied Probability Trust 1983 

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

Barlow, R. E. and Proschan, F. (1973) Availability theory for multicomponent systems. In Multivariate Analysis III, ed. Krishnaiah, P. R., Academic Press, New York, 319–335.Google Scholar
Barlow, R. E. and Proschan, F. (1975a) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
Barlow, R. E. and Proschan, F. (1975b) Importance of system components and fault tree events. Stoch. Proc. Appl. 3, 153–173.Google Scholar
Barlow, R. E. and Proschan, F. (1976) Theory of maintained systems: distribution of time to first system failure. Math. Operat. Res. 1, 32–42.Google Scholar
Barlow, R. E. and Wu, A. S. (1978) Coherent systems with multi-state components. Math. Operat. Res. 3, 275–281.Google Scholar
Baxter, L. A. (1981a) Availability measures for a two-state system. J. Appl. Prob. 18, 227–235.Google Scholar
Baxter, L. A. (1981b) A two-state system with partial availability in the failed state. Naval Res. Logist. Quart. 28, 231–236.Google Scholar
Baxter, L. A. (1981c) Some remarks on numerical convolution. Commun. Statist. B 10, 281–288.Google Scholar
Birnbaum, Z. W. (1969) On the importance of different components in a multicomponent system. In Multivariate Analysis II, ed. Krishnaiah, P. R., Academic Press, New York, 581–592.Google Scholar
Brown, M. (1975) The first passage time distribution of a parallel exponential system with repair. In Reliability and Fault Tree Analysis, ed. Barlow, R. E., Fussell, J. B. and Singpurwalla, N. D., SIAM, Philadelphia, 365–396.Google Scholar
Cleroux, R. and Mcconalogue, D. J. (1976) A numerical algorithm for recursively-defined convolution integrals involving distribution functions. Management Sci. 22, 1138–1146.Google Scholar
Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Haynes, T. and Davis, E. A. (1970) Waiting-time for a large gap in an alternating renewal process. Technometrics 12, 697–699.Google Scholar
Mcconalogue, D. J. (1978) Convolution integrals involving distribution functions (Algorithm 102). Comput. J. 21, 270–272.Google Scholar
Mcconalogue, D. J. (1981) Numerical treatment of convolution integrals involving distributions with densities having singularities at the origin. Commun. Statist. B 10, 265–280.Google Scholar
Natvig, B. (1979) A suggestion of a new measure of importance of system components. Stoch. Proc. Appl. 9, 319–330.Google Scholar
Ross, S. M. (1975) On the calculation of asymptotic system reliability characteristics. In Reliability and Fault Tree Analysis, ed. Barlow, R. E., Fussell, J. B. and Singpurwalla, N. D., SIAM, Philadelphia, 331–350.Google Scholar
Ross, S. M. (1976) On the time to first failure in multicomponent exponential reliability systems. Stoch. Proc. Appl. 4, 167–173.Google Scholar
Ross, S. M. and Schechtman, J. (1979) On the first time a separately maintained parallel system has been down for a fixed time. Naval Res. Logist. Quart. 26, 285–290.Google Scholar
Ross, S. M., Shahshahani, M. and Weiss, G. (1980) On the number of component failures in systems whose component lives are exchangeable. Math. Operat. Res. 5, 358–365.Google Scholar