A NEW SHOCK MODEL WITH A CHANGE IN SHOCK SIZE DISTRIBUTION

For a system that is subject to shocks, it is assumed that the distribution of the magnitudes of shocks changes after the first shock of size at least d1, and the system fails upon the occurrence of the first shock above a critical level d2 (> d1). In this paper, the distribution of the lifetime...

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Bibliographic Details
Published inProbability in the engineering and informational sciences Vol. 35; no. 3; pp. 381 - 395
Main Authors Eryilmaz, Serkan, Kan, Cihangir
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.07.2021
Subjects
Control charts
Particle size distribution
Probability distribution functions
Process controls
Random variables
Statistics
matrix-exponential distribution
reliability
shock model
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ISSN0269-9648
1469-8951
DOI10.1017/S0269964819000445

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Summary:For a system that is subject to shocks, it is assumed that the distribution of the magnitudes of shocks changes after the first shock of size at least d1, and the system fails upon the occurrence of the first shock above a critical level d2 (> d1). In this paper, the distribution of the lifetime of such a system is studied when the times between successive shocks follow matrix-exponential distribution. In particular, it is shown that the system's lifetime has matrix-exponential distribution when the intershock times follow Erlang distribution. The model is extended to the case when the system fails upon the occurrence of l consecutive critical shocks.
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ISSN:0269-9648
1469-8951
DOI:10.1017/S0269964819000445