We consider systems having many independent components connected in a parallel or series configuration with non-identical failure distributions. A time dependent measure is proposed which evaluate the probability that a failure of the system occurred at a specified component under the condition that the system has failed by some time. We proved several properties of this measure for parallel and serial systems. References R. E. Barlow and F. Proschan. Importance of System Components and Fault Tree Events. Stochastic Processes and their Applications, 3:153--173, 1975. F. Beichelt and K. Fischer. General failure model applied to preventive maintenance policies. IEEE Trans. Rel., 29:39--41, 1980. J. H. Cha and J. Mi. Some Probability Functions in Reliability and Their Applications. Naval Research Logistics., 54:128--135, 2007. doi:10.1002/nav.20192 D. R. Cox. Regression models and life-tables (with discussion). J. R. Stat. Soc., B34:187--208, 1972. R. C. Gupta and R. D. Gupta. Proportional reversed hazard rate model and its applications. J. Statist. Plann. Inference, 137:3525--3536, 2007. doi:10.1016/j.jspi.2007.03.029 R. C. Gupta, R. D. Gupta and P. L. Gupta. Modeling failure time data by Lehman alternatives. Comm. Statist. Theory Methods, 27:887--904, 1998. doi:10.1080/03610929808832134 T. Nakagava. Generalized models for determining optimal number of minimal repairs before replacement. J. Operat. Res. Soc. Japan, 24:325--357, 1981. T. J. O'Neill. The inverse Proportional Hazards Model. Stat. and Prob. Letters, 12:125--129, 1991. doi:10.1016/0167-7152(91)90055-V M. Shaked, and J. G. Shanthikumar. Stochastic Orders., Springer, 2007. S. H. Sheu, and W. S. Griffith. Optimal number of minimal repairs before replacement of a system subject to shocks. Naval Res. Logist., 43:319--333, 1996. doi:10.1002/(SICI)1520-6750(199604)43:3<319::AID-NAV1>3.0.CO;2-C
@article{2418,
title = {Properties of some time dependent probability failure functions in reliability theory},
journal = {ANZIAM Journal},
volume = {51},
year = {2010},
doi = {10.21914/anziamj.v51i0.2418},
language = {EN},
url = {http://dml.mathdoc.fr/item/2418}
}
Zardasht, Vali; Asadi, Majid; Zeephongsekul, Panlop. Properties of some time dependent probability failure functions in reliability theory. ANZIAM Journal, Tome 51 (2010) . doi : 10.21914/anziamj.v51i0.2418. http://gdmltest.u-ga.fr/item/2418/