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Reliability assessment of a multi-state mixed -shock model based on discrete PH distribution.

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Title: Reliability assessment of a multi-state mixed -shock model based on discrete PH distribution.
Authors: Hu, Zebin1 (AUTHOR) hzbbmhms@163.com, Hu, Linmin1 (AUTHOR) linminhu@ysu.edu.cn
Source: Annals of Operations Research. Oct2025, Vol. 353 Issue 3, p885-916. 32p.
Subjects: Reliability in engineering, Markov processes, Stochastic models, Shock waves, Distribution (Probability theory), Mechanical shock, Statistical reliability, Numerical analysis
Abstract: Both the extreme shock model and the -shock model have been extensively studied and applied in various fields. Nevertheless, the research of these shock models under discrete-time conditions remains limited. Under discrete-time conditions, this paper develops a multi-state mixed -shock model that incorporates both a generalized -shock and an extreme shock. The research has the following two main features: on the one hand, the arrival process of the shocks is generalized by assuming that the shock intervals follow a discrete PH distribution; on the other hand, by constructing a discrete-time Markov chain, the discrete PH distribution representations of the lifetime, operating time in perfect state and operating time in inferior state of the system are given, and the expected values and probability mass functions of the corresponding measures of the system are derived through these discrete PH distributions. Additionally, by means of the numerical experiment, the relationship between various measures and parameters of the system is elucidated. The proposed mixed -shock model can degenerate into the extreme shock model or the -shock model under certain conditions, thereby providing a new perspective and approach for comprehending and utilizing these shock models. [ABSTRACT FROM AUTHOR]
Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Reliability assessment of a multi-state mixed -shock model based on discrete PH distribution.
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  Data: <searchLink fieldCode="AR" term="%22Hu%2C+Zebin%22">Hu, Zebin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hzbbmhms@163.com</i><br /><searchLink fieldCode="AR" term="%22Hu%2C+Linmin%22">Hu, Linmin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> linminhu@ysu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Annals+of+Operations+Research%22">Annals of Operations Research</searchLink>. Oct2025, Vol. 353 Issue 3, p885-916. 32p.
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  Data: <searchLink fieldCode="DE" term="%22Reliability+in+engineering%22">Reliability in engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+processes%22">Markov processes</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+models%22">Stochastic models</searchLink><br /><searchLink fieldCode="DE" term="%22Shock+waves%22">Shock waves</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+shock%22">Mechanical shock</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+reliability%22">Statistical reliability</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink>
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  Label: Abstract
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  Data: Both the extreme shock model and the -shock model have been extensively studied and applied in various fields. Nevertheless, the research of these shock models under discrete-time conditions remains limited. Under discrete-time conditions, this paper develops a multi-state mixed -shock model that incorporates both a generalized -shock and an extreme shock. The research has the following two main features: on the one hand, the arrival process of the shocks is generalized by assuming that the shock intervals follow a discrete PH distribution; on the other hand, by constructing a discrete-time Markov chain, the discrete PH distribution representations of the lifetime, operating time in perfect state and operating time in inferior state of the system are given, and the expected values and probability mass functions of the corresponding measures of the system are derived through these discrete PH distributions. Additionally, by means of the numerical experiment, the relationship between various measures and parameters of the system is elucidated. The proposed mixed -shock model can degenerate into the extreme shock model or the -shock model under certain conditions, thereby providing a new perspective and approach for comprehending and utilizing these shock models. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10479-025-06815-1
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      – Code: eng
        Text: English
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        PageCount: 32
        StartPage: 885
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      – SubjectFull: Reliability in engineering
        Type: general
      – SubjectFull: Markov processes
        Type: general
      – SubjectFull: Stochastic models
        Type: general
      – SubjectFull: Shock waves
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      – SubjectFull: Distribution (Probability theory)
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      – SubjectFull: Mechanical shock
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      – SubjectFull: Statistical reliability
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      – SubjectFull: Numerical analysis
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              Text: Oct2025
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