Research Article
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Discrete time shock model with varying success probability

Year 2019, Volume: 12 Issue: 1, 13 - 24, 31.07.2019

Kadir Karakaya Yunus Akdoğan Fatih Şahin İsmail Kınacı Coşkun Kuş

Abstract

    Let us consider a system fails when the time between two consecutive shocks falls below a fixed threshold $\delta \in N$ and the system's  lifetime is measured as the time up to the occurrence of  this event. In this paper, we consider the interarrival times between $(i-1)$ i-th and $i$- th successive shocks follow a geometric distribution with mean 1/pi ,where pi =theta*pi-1, i=1,2,..., ,0<theta<1, 0<p<1. Under the above considerations, the distribution of system lifetime is obtained. Probability generating function and than also moments of system are derived. The proportion estimates of distribution parameters are studied. A numerical example is also presented buy using real data.

Keywords

q-distributions delta-Shock model probabilty generating function

References

  • Sumita, U. and Shanthikumar J.G. (1985). A class of correlated cumulative shock models. Advances in Applied Probability, 17, 347-366.
  • Gut, A. (1990). Cumulative shock models. Advances in Applied Probability, 22, 504-507.
  • Mallor, F. and Omey E. (2001). Shocks, runs and random sums. Journal of Applied Probability, 38, 438-448.
  • Wang, G.J. and Zhang Y.L. (2005). A shock model with two-type failures and optimal replacement policy. International Journal of Systems Science, 36, 209-214.
  • Bai, J-M., Li, Z-H. and Kong, X-B. (2006). Generalized shock models based on a cluster point process. IEEE Transactions on Reliability, 55, 542-550.
  • Li, Z.H. and Kong, X.B. (2007). Life behavior of δ-shock model. Statistics and Probability Letters, 77, 577-587.
  • Li, Z.H. and Zhao, P. (2007). Reliability analysis on the δ-shock model of complex systems. IEEE Transactions on Reliabilit, 56, 340-348.
  • Eryilmaz, S. (2012). Generalized δ-shock model via runs. Statistics and Probability Letters, 82, 326-331.
  • Eryilmaz, S. (2013). On the lifetime behavior of a discrete time shock model. Journal of Computational and Applied Mathematics, 237, 384-388.
  • Charalambides, C.A. (2010). The q-Bernstein basis as a q-binomial distributions. Journal of Statistical Planning and Inference, 140, 2184-2190.
  • Yalcin, F. and Eryilmaz, S. (2014). q-Geometric and q-Binomial distributions of order k. Journal of Computational and Applied Mathematics, 271, 31-38.
  • Khan, M.S.A., Khalique. A. and Abouammoh, A.M. (1989). On estimating parameters in a discrete Weibull distribution. IEEE Transactions on Reliability, 38 (3), 348-350.
  • Phyo, I. (1973). Use of a chain binomial in epidemiology of caries. Journal of Dental Research 52, 750-752.
  • Krishna, H. and Pundir, P.S. (2009). Discrete Burr and discrete Pareto distributions. Statistical Methodology, 6, 177-188.
  • Nakagawa, T. and Osaki, S. (1975). The discrete Weibull distribution. IEEE Transactions on Reliability, 24, 300-301.

Year 2019, Volume: 12 Issue: 1, 13 - 24, 31.07.2019

Kadir Karakaya Yunus Akdoğan Fatih Şahin İsmail Kınacı Coşkun Kuş

Abstract

References

  • Sumita, U. and Shanthikumar J.G. (1985). A class of correlated cumulative shock models. Advances in Applied Probability, 17, 347-366.
  • Gut, A. (1990). Cumulative shock models. Advances in Applied Probability, 22, 504-507.
  • Mallor, F. and Omey E. (2001). Shocks, runs and random sums. Journal of Applied Probability, 38, 438-448.
  • Wang, G.J. and Zhang Y.L. (2005). A shock model with two-type failures and optimal replacement policy. International Journal of Systems Science, 36, 209-214.
  • Bai, J-M., Li, Z-H. and Kong, X-B. (2006). Generalized shock models based on a cluster point process. IEEE Transactions on Reliability, 55, 542-550.
  • Li, Z.H. and Kong, X.B. (2007). Life behavior of δ-shock model. Statistics and Probability Letters, 77, 577-587.
  • Li, Z.H. and Zhao, P. (2007). Reliability analysis on the δ-shock model of complex systems. IEEE Transactions on Reliabilit, 56, 340-348.
  • Eryilmaz, S. (2012). Generalized δ-shock model via runs. Statistics and Probability Letters, 82, 326-331.
  • Eryilmaz, S. (2013). On the lifetime behavior of a discrete time shock model. Journal of Computational and Applied Mathematics, 237, 384-388.
  • Charalambides, C.A. (2010). The q-Bernstein basis as a q-binomial distributions. Journal of Statistical Planning and Inference, 140, 2184-2190.
  • Yalcin, F. and Eryilmaz, S. (2014). q-Geometric and q-Binomial distributions of order k. Journal of Computational and Applied Mathematics, 271, 31-38.
  • Khan, M.S.A., Khalique. A. and Abouammoh, A.M. (1989). On estimating parameters in a discrete Weibull distribution. IEEE Transactions on Reliability, 38 (3), 348-350.
  • Phyo, I. (1973). Use of a chain binomial in epidemiology of caries. Journal of Dental Research 52, 750-752.
  • Krishna, H. and Pundir, P.S. (2009). Discrete Burr and discrete Pareto distributions. Statistical Methodology, 6, 177-188.
  • Nakagawa, T. and Osaki, S. (1975). The discrete Weibull distribution. IEEE Transactions on Reliability, 24, 300-301.
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Kadir Karakaya 0000-0002-0781-3587

Yunus Akdoğan 0000-0003-3520-7493

Fatih Şahin This is me

İsmail Kınacı 0000-0002-0992-4133

Coşkun Kuş 0000-0002-7176-0176

Publication Date July 31, 2019
Acceptance Date November 7, 2019
Published in Issue Year 2019 Volume: 12 Issue: 1

Cite

APA Karakaya, K., Akdoğan, Y., Şahin, F., Kınacı, İ., et al. (2019). Discrete time shock model with varying success probability. Istatistik Journal of The Turkish Statistical Association, 12(1), 13-24.
AMA Karakaya K, Akdoğan Y, Şahin F, Kınacı İ, Kuş C. Discrete time shock model with varying success probability. IJTSA. July 2019;12(1):13-24.
Chicago Karakaya, Kadir, Yunus Akdoğan, Fatih Şahin, İsmail Kınacı, and Coşkun Kuş. “Discrete Time Shock Model With Varying Success Probability”. Istatistik Journal of The Turkish Statistical Association 12, no. 1 (July 2019): 13-24.
EndNote Karakaya K, Akdoğan Y, Şahin F, Kınacı İ, Kuş C (July 1, 2019) Discrete time shock model with varying success probability. Istatistik Journal of The Turkish Statistical Association 12 1 13–24.
IEEE K. Karakaya, Y. Akdoğan, F. Şahin, İ. Kınacı, and C. Kuş, “Discrete time shock model with varying success probability”, IJTSA, vol. 12, no. 1, pp. 13–24, 2019.
ISNAD Karakaya, Kadir et al. “Discrete Time Shock Model With Varying Success Probability”. Istatistik Journal of The Turkish Statistical Association 12/1 (July 2019), 13-24.
JAMA Karakaya K, Akdoğan Y, Şahin F, Kınacı İ, Kuş C. Discrete time shock model with varying success probability. IJTSA. 2019;12:13–24.
MLA Karakaya, Kadir et al. “Discrete Time Shock Model With Varying Success Probability”. Istatistik Journal of The Turkish Statistical Association, vol. 12, no. 1, 2019, pp. 13-24.
Vancouver Karakaya K, Akdoğan Y, Şahin F, Kınacı İ, Kuş C. Discrete time shock model with varying success probability. IJTSA. 2019;12(1):13-24.
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