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Further results of replacement problem of a parallel system in random environment

Published online by Cambridge University Press:  14 July 2016

Toshio Nakagawa
Toshio Nakagawa*
Affiliation:
Meijō University
*
∗Postal address: Department of Mathematics, Meijō University, Tenpaku-Cho, Tenpaku-Ku, Nagoya 468, Japan.
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Abstract

We have recently discussed the replacement problem of a parallel system in a random environment. This paper extends the same replacement problem for the following two cases which are more plausible: (i) The probability that an operating component fails by the j th shock depends on the number j. (ii) The replacement cost is a linear function of failed components. The expected cost of the above model is obtained. A numerical example is finally presented when the probability of failure time of a component is a negative binomial distribution.

Keywords

PARALLEL SYSTEMRANDOM ENVIRONMENTREPLACEMENT PROBLEMDEPENDENT SHOCK NUMBERLINEAR COST
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 923 - 926
Copyright
Copyright © Applied Probability Trust 1979 

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References

[1] Nakagawa, T. (1979) Replacement problem of a parallel system in random environment. J. Appl. Prob. 16, 203–205.Google Scholar
[2] Nakagawa, T. and Osaki, S. (1975) The discrete Weibull distribution. IEEE Trans. Reliability R–24, 300–301.Google Scholar
[3] Råde, T. (1976) Reliability systems in random environment. J. Appl. Prob. 13, 407–410.Google Scholar