Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-27T00:36:48.869Z Has data issue: false hasContentIssue false
  • English
  • Français

A NEW SHOCK MODEL WITH A CHANGE IN SHOCK SIZE DISTRIBUTION

Published online by Cambridge University Press:  26 December 2019

Serkan Eryilmaz Open the ORCID record for Serkan Eryilmaz [Opens in a new window]  and
Cihangir Kan
Serkan Eryilmaz
Affiliation:
Department of Industrial Engineering, Atilim University, 06836, Incek, Ankara, Turkey E-mail: serkan.eryilmaz@atilim.edu.tr
Cihangir Kan
Affiliation:
Xi'an Jiaotong-Liverpool University, Suzhou, China
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

matrix-exponential distributionreliabilityshock model
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 381 - 395
Copyright
© Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Asmussen, S. & Bladt, M. (1997). Renewal theory and queueing algorithms for matrix-exponential distributions. In A. Alfa and S.R. Chakravarthy, editors, Matrix-analytic methods in stochastic models. Boca Raton: Taylor and Francis, pp. 313–341.Google Scholar
2.Balakrishnan, N. & Koutras, M.V. (2002). Runs and scans with applications. New York: Wiley.Google Scholar
3.Bladt, M. & Nielsen, B.F (2010). Multivariate matrix-exponential distributions. Stochastic Models 26: 1–26.CrossRefGoogle Scholar
4.Bladt, M. & Nielsen, B.F. (2017). Matrix-exponential distributions in applied probability. New York: Springer.Google Scholar
5.Eryilmaz, S. & Kan, C (2019). Reliability and optimal replacement policy for an extreme shock model with a change point. Reliability Engineering & System Safety 190: 106513.CrossRefGoogle Scholar
6.Eryilmaz, S. & Tekin, M (2019). Reliability evaluation of a system under a mixed shock model. Journal of Computational and Applied Mathematics 352: 255–261.CrossRefGoogle Scholar
7.Gao, H., Cui, L., & Qiu, Q (2019). Reliability modeling for degradation-shock dependence systems with multiple species of shocks. Reliability Engineering and System Safety 185: 133–143.CrossRefGoogle Scholar
8.Gong, M., Xie, M., & Yang, Y (2018). Reliability assessment of system under a generalized run shock model. Journal of Applied Probability 55: 1249–1260.CrossRefGoogle Scholar
9.Gut, A. & Hüsler, J (1999). Extreme shock models. Extremes 2: 295–307.CrossRefGoogle Scholar
10.Gut, A (2001). Mixed shock models. Bernoulli 7: 541–555.CrossRefGoogle Scholar
11.Sloughter, J.M., Louie, H (2014). Probabilistic modeling and statistical characteristics of aggregate wind power. Large Scale Renewable Power Generation, Green Energy and Technology, Singapore: Springer Science+Business Media, pp. 19–51.Google Scholar
12.Mallor, F. & Omey, E (2001). Shocks, runs and random sums. Journal of Applied Probability 38: 438–448.CrossRefGoogle Scholar
13.Parvardeh, A. & Balakrishnan, N (2015). On mixed δ-shock models. Statistics & Probability Letters 102: 51–60.CrossRefGoogle Scholar
14.Qiu, Q. & Cui, L (2019). Optimal mission abort policy for systems subject to random shocks based on virtual age process. Reliability Engineering and System Safety 189: 11–20.CrossRefGoogle Scholar
15.Rafiee, K., Feng, Q., & Coit, D.W. (2014). Reliability modeling for dependent competing failure processes with changing degradation rate. IIE Transactions 46: 483–496.CrossRefGoogle Scholar
16.Rafiee, K., Feng, Q., & Coit, D.W (2017). Reliability assessment of competing risks with generalized mixed shock models. Reliability Engineering & System Safety 159: 1–11.CrossRefGoogle Scholar
17.Wang, X.Y., Zhao, X., & Sun, J.L. (2019). A compound negative binomial distribution with mutative termination conditions based on a change point. Journal of Computational and Applied Mathematics 351: 237–249.CrossRefGoogle Scholar
18.Zhao, X., Guo, X., & Wang, X (2018). Reliability and maintenance policies for a two-stage shock model with self-healing mechanism. Reliability Engineering and System Safety 172: 185–194.CrossRefGoogle Scholar
19.Zhao, X., Wang, S.Q., Wang, X.Y., & Fan, Y (2020). Multi-state balanced systems in a shock environment. Reliability Engineering and System Safety 193: 106592.CrossRefGoogle Scholar