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ON THE RESIDUAL AND PAST LIFETIMES OF COHERENT SYSTEMS UNDER RANDOM MONITORING

Published online by Cambridge University Press:  02 March 2020

Ebrahim Amini-Seresht ,
Maryam Kelkinnama  and
Yiying Zhang Open the ORCID record for Yiying Zhang [Opens in a new window]
Ebrahim Amini-Seresht
Affiliation:
Department of Statistics, Bu-Ali Sina University, Hamedan, Iran E-mail: e.amini64@yahoo.com
Maryam Kelkinnama
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran E-mail: m.kelkinnama@iut.ac.ir
Yiying Zhang
Affiliation:
School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin 300071, P. R. China E-mail: yyzhang@nankai.edu.cn
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Abstract

This paper discusses stochastic comparisons for the residual and past lifetimes of coherent systems with dependent and identically distributed (d.i.d.) components under random monitoring in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orders. Some stochastic comparisons results are also established on the residual lifetimes of coherent systems under random observation times when all of the components are alive at that time. Sufficient conditions are established in terms of the aging properties of the components and the distortion functions induced from the system structure and dependence among components lifetimes. Numerical examples are provided to illustrate the theoretical results as well.

Keywords

agingcoherent systempast lifetimeresidual lifetimestochastic orders
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 465 - 480
Copyright
© Cambridge University Press 2020

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References

1.Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Silver Spring, MD: To Begin With.Google Scholar
2.Bartoszewicz, J. & Skolimowska, M. (2006). Preservation of classes of life distributions and stochastic orders under weighting. Statistics & Probability Letters 76: 587–596.CrossRefGoogle Scholar
3.Cai, N. & Zheng, Y. (2012). Preservation of generalized ageing class on the residual life at random time. Journal of Statistical Planning and Inference 142: 148–154.CrossRefGoogle Scholar
4.Cao, J. & Wang, Y. (1991). The NBUC and NWUC classes of life distributions. Journal of Applied Probability 28: 473–479.CrossRefGoogle Scholar
5.Deshpande, J.V., Kochar, S.C., & Singh, H. (1986). Aspects of positive ageing. Journal of Applied Probability 23: 748–758.Google Scholar
6.Dewan, I. & Khaledi, B.-E. (2014). On stochastic comparisons of residual life time at random time. Statistics & Probability Letters 88: 73–79.CrossRefGoogle Scholar
7.Goli, S. (2019). On the conditional residual lifetime of coherent systems under double regularly checking. Naval Research Logistics 66(4): 352–363.Google Scholar
8.Gupta, N., Misra, N., & Kumar, S. (2015). Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components. European Journal of Operational Research 240: 425–430.CrossRefGoogle Scholar
9.Hürlimann, W. (2004). Distortion risk measures and economic capital. North American Actuarial Journal 8: 86–95.CrossRefGoogle Scholar
10.Karlin, S. (1968). Total positivity, vol. I. California: Stanford University Press.Google Scholar
11.Kayid, M. & Izadkhah, S. (2015). Characterizations of the exponential distribution by the concept of residual life at random time. Statistics & Probability Letters 107: 164–169.Google Scholar
12.Kelkinnama, M. & Asadi, M. (2019). Stochastic and ageing properties of coherent systems with dependent identically distributed components. Statistical Papers 60(3): 455–471.CrossRefGoogle Scholar
13.Kundu, C. & Patra, A. (2017). Some results on residual life and inactivity time at random time. Communications in Statistics - Theory and Methods 47: 372–384.CrossRefGoogle Scholar
14.Li, X. & Fang, R. (2018). Stochastic properties of two general versions of the residual lifetime at random times. Applied Stochastic Models in Business and Industry 34(4): 528–543.CrossRefGoogle Scholar
15.Li, X. & Zuo, M.J. (2004). Stochastic comparison of residual life and inactivity time at a random time. Stochastic Models 20(2): 229–235.CrossRefGoogle Scholar
16.Misra, N. & Naqvi, S. (2017). Stochastic properties of inactivity lifetimes at random times: Some unified results. American Journal of Mathematical and Management Sciences 36(2): 85–97.CrossRefGoogle Scholar
17.Misra, N. & Naqvi, S. (2018). Some unified results on stochastic properties of residual lifetimes at random times. Brazilian Journal of Probability and Statistics 32(2): 422–436.CrossRefGoogle Scholar
18.Misra, N., Gupta, N., & Dhariyal, I.D. (2008). Preservation of some aging properties and stochastic orders by weighted distributions. Communications in Statistics - Theory and Methods 37: 627–644.CrossRefGoogle Scholar
19.Misra, N., Gupta, N., & Dutt Dhariyal, I. (2008). Stochastic properties of residual life and inactivity time at a random time. Stochastic Models 24: 89–102.CrossRefGoogle Scholar
20.Müller, A. & Stoyan, D. (2002). Comparison methods for stochastic models and risks. New York: John Wiley.Google Scholar
21.Nanda, A.K., Singh, H., Misra, N., & Paul, P. (2003). Reliability properties of reversed residual lifetime. Communications in Statistics - Theory and Methods 32: 2031–2042.CrossRefGoogle Scholar
22.Navarro, J. (2018). Distribution-free comparisons of residual lifetimes of coherent systems based on copula properties. Statistical Papers 59: 781–800.CrossRefGoogle Scholar
23.Navarro, J. & Calì, C. (2019). Inactivity times of coherent systems with dependent components under periodical inspections. Applied Stochastic Models in Business and Industry 35(3): 871–892.CrossRefGoogle Scholar
24.Navarro, J. & Durante, F. (2017). Copula-based representations for the reliability of the residual lifetimes of coherent systems with dependent components. Journal of Multivariate Analysis 158: 87–102.CrossRefGoogle Scholar
25.Navarro, J., del Aguila, Y., Sordo, M.A., & Suarez-Llorens, A. (2014). Preservation of reliability classes under the formation of coherent systems. Applied Stochastic Models in Business and Industry 30: 444–454.CrossRefGoogle Scholar
26.Parvardeh, A., Balakrishnan, N., & Arshadipour, A. (2017). Conditional residual lifetimes of coherent systems under double monitoring. Communications in Statistics - Theory and Methods 46(7): 3401–3410.CrossRefGoogle Scholar
27.Shaked, M. & Shanthikumar, J.G. (2007). Stochastic orders. New York: Springer.CrossRefGoogle Scholar
28.Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: John Wiley.Google Scholar
29.Yue, D. & Cao, J. (2000). Some results on the residual life at random time. Acta Mathematicae Applicatae Sinica 16: 436–443.Google Scholar
30.Zhang, Z. & Meeker, W.Q. (2013). Mixture representations of reliability in coherent systems and preservation results under double monitoring. Communication in Statistics - Theory and Methods 42: 385–397.CrossRefGoogle Scholar