On the generalized N-critical shock model

Dheeraj Goyal; Min Xie

doi:10.1080/16843703.2024.2448643

On the generalized N-critical shock model

Dheeraj Goyal^*
, Min Xie

^*Corresponding author for this work

Department of Systems Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

Abstract

According to the N-critical shock model, a system fails if the total number of critical shocks reaches N. The central assumption in this model is that after the arrival of a critical shock, the next shock will be critical with the same probability. This is a restrictive and unrealistic assumption in many natural situations. This paper defines a generalized N-critical shock model that overcomes this limitation. We study the model for two well-known shock arrival processes and derive reliability indices such as reliability function and mean remaining lifetime. © 2025 International Chinese Association of Quantitative Management.

Original language	English
Pages (from-to)	1112-1131
Number of pages	20
Journal	Quality Technology & Quantitative Management
Volume	22
Issue number	6
Online published	20 Jan 2025
DOIs	https://doi.org/10.1080/16843703.2024.2448643
Publication status	Published - Nov 2025

Funding

This work is supported by National Natural Science Foundation of China (72371215), Research Grant Council of Hong Kong (11200621, 11201023). and by Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA). It is also supported by Indian Institute of Technology Kanpur, India, through its institute post-doc fellowship grant (PDF423).

Research Keywords

homogeneous Poisson generalized gamma process
N-critical shock model
phase-type distribution
Reliability

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10.1080/16843703.2024.2448643

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title = "On the generalized N-critical shock model",

abstract = "According to the N-critical shock model, a system fails if the total number of critical shocks reaches N. The central assumption in this model is that after the arrival of a critical shock, the next shock will be critical with the same probability. This is a restrictive and unrealistic assumption in many natural situations. This paper defines a generalized N-critical shock model that overcomes this limitation. We study the model for two well-known shock arrival processes and derive reliability indices such as reliability function and mean remaining lifetime. {\textcopyright} 2025 International Chinese Association of Quantitative Management.",

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author = "Dheeraj Goyal and Min Xie",

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T1 - On the generalized N-critical shock model

AU - Goyal, Dheeraj

AU - Xie, Min

PY - 2025/11

Y1 - 2025/11

N2 - According to the N-critical shock model, a system fails if the total number of critical shocks reaches N. The central assumption in this model is that after the arrival of a critical shock, the next shock will be critical with the same probability. This is a restrictive and unrealistic assumption in many natural situations. This paper defines a generalized N-critical shock model that overcomes this limitation. We study the model for two well-known shock arrival processes and derive reliability indices such as reliability function and mean remaining lifetime. © 2025 International Chinese Association of Quantitative Management.

AB - According to the N-critical shock model, a system fails if the total number of critical shocks reaches N. The central assumption in this model is that after the arrival of a critical shock, the next shock will be critical with the same probability. This is a restrictive and unrealistic assumption in many natural situations. This paper defines a generalized N-critical shock model that overcomes this limitation. We study the model for two well-known shock arrival processes and derive reliability indices such as reliability function and mean remaining lifetime. © 2025 International Chinese Association of Quantitative Management.

KW - homogeneous Poisson generalized gamma process

KW - N-critical shock model

KW - phase-type distribution

KW - Reliability

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U2 - 10.1080/16843703.2024.2448643

DO - 10.1080/16843703.2024.2448643

M3 - RGC 21 - Publication in refereed journal

SN - 1684-3703

VL - 22

SP - 1112

EP - 1131

JO - Quality Technology & Quantitative Management

JF - Quality Technology & Quantitative Management

IS - 6

ER -

On the generalized N-critical shock model

Abstract

Funding

Research Keywords

RGC Funding Information

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GRF: Intelligent Prognostics and Health Management of Modular Systems

GRF: New Approaches for Reliability Analysis of Industrial Systems Subject to Multivariate Degradation

Cite this

On the generalized N-critical shock model

Abstract

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

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Projects

GRF: Intelligent Prognostics and Health Management of Modular Systems

GRF: New Approaches for Reliability Analysis of Industrial Systems Subject to Multivariate Degradation

Cite this