Abstract
Reliability is an important index to describe the quality of an individual unit or a complex system. In practice, it is possible that lifetimes of the system units can estimate their probability distributions by previous experience, however, there may be only few or no samples to ascertain their distribution parameters. In order to deal with this case, this paper proposes a discrete time series-parallel system with uncertain parameters, which is studied based on both probability theory and uncertainty theory. Besides, redundant standby methods of improving the system reliability are provided, including cold, warm and hot. The lifetimes of units in redundant systems are assumed to be independent and non-identical discrete distributions, which distribution parameters are uncertain variables. Some formulas are given to calculate the reliability and mean time to failure of these systems. In addition, some numerical examples are given to illustrate different system models.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Amstadter BL (1971) Reliability mathematics. Mcgraw-Hill, New York
Barlow RE, Proschan F (1975) Statistical theory of reliability of life testing. Technometrics 19(2):220–220
Bouhouras AS, Labridis DP, Bakirtzis AG (2010) Cost/worth assessment of reliability improvement in distribution networks by means of artificial intelligence. Int J Electr Power Energy Syst 32(5):530–538
Bracquemond C, Gaudoin O (2003) A survey on discrete lifetime distribution. Int J Reliab Qual Saf Eng 10(01):69–98
Briggs SJ, Bartos MJ, Arno RG (2002) Reliability and availability assessment of electrical and mechanical systems. IEEE Trans Ind Appl 34(6):1387–1396
Gao Y (2009) Analysis of k-out-of-n system with uncertain lifetimes. In: Proceedings of the eighth international conference on information and management sciences, Kunming, pp 794–797
Gao J, Yao K (2015) Some concepts and theorems of uncertain random process. Int J Intell Syst 30(1):52–65
Gao R, Yao K (2016) Importance index of components in uncertain reliability systems. Knowl Based Syst 109(1):208–217
Gao R, Sun Y, Ralescu D (2017) Order statistics of uncertain random variables with application to k-out-of-n system. Fuzzy Optim Decis Mak 16(2):1–23
Gao J, Yao K, Zhou J, Ke H (2018) Reliability analysis of uncertain weighted k-out-of-n systems. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2018.2807378
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2010a) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu B (2010b) Uncertain risk analysis and uncertain reliability analysis. J Uncertain Syst 4(4):163–170
Liu W (2013) Reliability analysis of redundant system with uncertain lifetimes. Inf Jpn 16(2):881–887
Liu Y (2013a) Uncertain random variables: a mixture of uncertainty and randomness. Soft Comput 17(4):625–634
Liu Y (2013b) Uncertain random programming with applications. Fuzzy Optim Decis Mak 12(2):153–169
Liu Y, Ha M (2010) Expected value of function of uncertain variables. J Uncertain Syst 4(4):181–186
Liu Y, Ralescu D (2017) Expected loss of uncertain random system. Soft Comput 1:1–6
Liu Y, Li X, Xiong C (2015) Reliability analysis of unrepairable systems with uncertain lifetimes. Int J Secur Appl 9(12):289–298
Locks MO (1978) System reliability analysis. Microelectr Reliab 18(4):335–345
Papageorgiou E, Kokolakis G (2007) A two-unit general parallel system with (n−2) cold standbys analytic and simulation approach. Eur J Oper Res 176(2):1016–1032
Papageorgiou E, Kokolakis G (2010) Reliability analysis of a two-unit general parallel system with (n−2) warm standbys. Eur J Oper Res 201(3):821–827
Pradlwarter HJ, Pellissetti MF, Schenk CA et al (2005) Realistic and efficient reliability estimation for aerospace structures. Comput Methods Appl Mech Eng 194(12–16):1597–1617
Ruiz-Castro JE, Fernndez-Villodre G (2012) A complex discrete warm standby system with loss of units. Eur J Oper Res 218(2):456–469
Ruiz-Castro JE, Prez-Ocn R, Fernndez-Villodre G (2008) Modelling a reliability system governed by discrete phase-type distributions. Reliab Eng Syst Saf 93(11):1650–1657
Smith D (1975) Statistical theory of reliability and life testing a probability models. Technometrics 19(2):220–220
Vangel M (2009) System reliability theory: models and statistical methods. Technometrics 38(1):79–80
Wang Z (2010) Structural reliability analysis using uncertainty theory. In: Proceedings of the first international conference on uncertainty theory, Urumchi, pp 166–170
Wen M, Kang R (2016) Reliability analysis in uncertain random system. Fuzzy Optim Decis Mak 15:491–506
Yao K, Gao J (2016) Law of large numbers for uncertain random variables. IEEE Trans Fuzzy Syst 24(3):615–621
Acknowledgements
This work is supported in part by the National Natural Science Foundation of China (no.11601469), the Natural Science Foundation of Hebei Province (no. A2018203088) and the Science Research Project of Education Department of Hebei Province (no. ZD2017079), Peoples Republic of China.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Cao, X., Hu, L. & Li, Z. Reliability analysis of discrete time series-parallel systems with uncertain parameters. J Ambient Intell Human Comput 10, 2657–2668 (2019). https://doi.org/10.1007/s12652-018-0952-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-018-0952-7