The objective of this paper is to establish some reliability models for redundant systems based on the assumption that the conversion switches are imperfect and distribution parameters are uncertain variables. Some new concepts of random uncertain distributions associated with random uncertain variables are proposed, which are applied to redundant series-parallel systems, including cold redundant system and warm redundant system. In each type of redundant system, we consider two methods to describe the switch lifetimes: random uncertain 0-1 switch lifetime and random uncertain geometric switch lifetime. The reliability and the mean time to failure of these systems are analyzed. Some numerical examples are presented to demonstrate the proposed reliability models and perform a comparison for the system models with uncertain parameters and constant parameters.
BarlowR.E.and ProschanF., Mathematical Theory of Reliability, Wiley, New York, 1965.
2.
CyrilB. and QlivierG., A Survey on Discrete Lifetime Distribution, International Journal of Reliability Quality and Safety Engineering10(01) (2003), 69–98.
3.
PapageorgiouE. and KokolakisG., A Two-unit General Parallel System with (n-2) Cold Standbys Analytic and Simulation Approach, European Journal of Operational Research176(2) (2007), 1016–1032.
4.
PapageorgiouE. and KokolakisG., Reliability Analysis of a Two-Unit General Parallel System with (n-2) Warm Standbys, European Journal of Operational Research201(3) (2010), 821–827.
5.
GoelL.R. and GuptaR., Analysis of a Two-Unit Standby System with Three Modes and Imperfect Switching Device, Microelectronics Reliability24(3) (1984), 425–429.
6.
ZadehL.A., Fuzzy Sets, Information and Control8(3) (1965)338–353.
7.
OnisawaT., Fuzzy Theory in Reliability Analysis, Fuzzy Sets and Systems30(3) (1989), 361–363.
8.
ParkK.S., Fuzzy Apportionment of System Reliability, IEEE Transactions on ReliabilityR-36(1) (2009)129–132.
9.
CaiK., WenC. and ZhangM., Fuzzy Variables as A Basis for a Theory of Fuzzy Reliability in the Possibility Context, Fuzzy Sets and Systems42(2) (1991), 145–172.
LiuB., Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin, 2010.
12.
LiuB., Some Research Problems in Uncertainty Theory, Journal of Uncertain Systems3(1) (2009), 3–10.
13.
LiuY. and HaM., Expected Value of Function of Uncertain Variables, Journal of Uncertain Systems4(3) (2010), 181–186.
14.
LiuB., Theory and Practice of Uncertain Programming, 2nd edn, Springer-Verlag, Berlin, 2009.
15.
GaoY., GaoR. and YangL., Analysis of Order Statistics of Uncertain Variables, Journal of Uncertainty Analysis and Applications3(1) (2015), 1–7.
16.
YaoK., Uncertain Differential Equation with Jumps, Soft Computing19(7) (2015), 2063–2069.
17.
YangX., NiY. and ZhangY., Stability in Inverse Distribution for Uncertain Differential Equations, Journal of Intelligent and Fuzzy Systems32(3) (2017), 2051–2059.
18.
LiuB., Uncertain Risk Analysis and Uncertain Reliability Analysis, Journal of Uncertain Systems4(3) (2010), 163–170.
19.
ZuT., KangR., WenM. and ZhangQ., Belief Reliability Distribution Based on Maximum Entropy Principle, IEEE Access6 (2018), 1577–1582.
20.
LiuW., Reliability Analysis of Redundant System with Uncertain Lifetimes, Information16(2) (2013), 881–887.
21.
LiuY., LiX. and XiongC., Reliability Analysis of Unrepairable Systems with Uncertain Lifetimes, International Journal of Security and Its Applications9(12) (2015), 289–298.
22.
GaoJ., YaoK., ZhouJ. and KeH., Reliability Analysis of Uncertain Weighted k-out-of-n Systems, IEEE Transactions on Fuzzy Systems26(5) (2018), 2663–2671.
23.
ZengZ., KangR., WenM. and ZioE., Uncertainty Theory as a Basis for Belief Reliability, Information Sciences429 (2018), 26–36.
24.
HuL., HuangW., WangG.F. and TianR., Redundancy Optimization of an Uncertain Parallel-Series System with Warm Standby Elements, Complexity2018 Article ID 3154360, 10 pages, 2018, https://doi.org/10.1155/2018/3154360
25.
LiuY., MaY., QuZ. and LiX., Reliability Mathematical Models of Repairable Systems With Uncertain Lifetimes and Repair Times, IEEE Access6 (2018), 71285–71295.
26.
LiuY., Uncertain Random Variables: A Mixture of Uncertainty and Randomness, Soft Computing17(4) (2013), 625–634.
27.
LiuY., Uncertain Random Programming with Applications, Fuzzy Optimization and Decision Making12(2) (2013), 153–169.
28.
LiuY. and RalescuD.A., Risk Index in Uncertain Random Risk Analysis, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems22(04) (2014), 491–504.
29.
LiuY. and RalescuD.A., Expected Loss of Uncertain Random System, Soft Computing22(17) (2017), 5573–5578.
30.
WenM. and KangR., Reliability Analysis in Uncertain Random System, Fuzzy Optimization and Decision Making15(4) (2016), 491–506.
31.
GaoR. and YaoK., Importance Index of Components in Uncertain Random Systems, Knowledge-Based Systems109 (2016), 208–217.
32.
GaoR., SunY. and RalescuD.A., Order Statistics of Uncertain Random Variables with Application to k-out-of-n System, Fuzzy Optimization and Decision Making16(2) (2017), 159–181.
33.
ZhangQ., R. Kang and M. Wen, Belief Reliability for Uncertain Random Systems, IEEE Transactions on Fuzzy Systems26(6) (2018), 3605–3614.
34.
CaoX., HuL. and LiZ., Reliability Analysis of Discrete Time Series-parallel Systems with Uncertain Parameters, Journal of Ambient Intelligence and Humanized Computing10(7) (2019), 2657–2668.
