In the realm of dynamic reliability analysis, this research paper presents a novel mathematical model for the weighted k-out-of-n system with two heterogeneous components also said to be weighted (k1, k2)-out-of-n repairable system. This innovative framework comprises two distinct component types, whose simultaneous functioning yields system operation if and only if the cumulative weight of the operational type 1 component is at least k1, and that of the type 2 component is at least, k2. Each component type has a number of distinct individual components with variable states that change over time, making the state probabilities of those components time-dependent. By employing an algorithm grounded in Lz-transform, dynamic reliability measures comprising reliability, availability, mean expected performance, and expected profit are derived for the system taken into consideration. This study also introduces a pioneering connection between the Lz-transform and queueing theory and extends its implications to various intricate engineering systems meeting the established criteria.
EryilmazS.(k1, k2,…, km)-out-of-n system and its reliability. J Comput Appl Math2019; 346: 591–598.
2.
KuoWZuoMJ. Optimal reliability modeling: principles and applications. Hoboken, NJ: John Wiley & Sons, 2003.
3.
LiWZuoMJ.Reliability evaluation of multi-state weighted k-out-of-n systems. Reliab Eng Syst Saf2008; 93(1): 160–167.
4.
WangXNingRZhaoX, et al. Reliability evaluations for a multi-state k-out-of-n: F system with m subsystems supported by multiple protective devices. Comput Ind Eng2022; 171: 108409.
5.
ZuoMJTianZ.Performance evaluation of generalized multi-state k-out-of-n systems. IEEE Trans Reliab2006; 55(2): 319–327.
6.
AsadiMBayramogluI.The mean residual life function of a k-out-of-n structure at the system level. IEEE Trans Reliab2006; 55(2): 314–318.
7.
BishtVSinghSB.Lz-transform approach to evaluate reliability indices of multi-state repairable weighted K-out-of-n systems. Qual Reliab Eng2023; 39(3): 1043–1057.
8.
KhorshidiHAGunawanIIbrahimMY.A value-driven approach for optimizing reliability-redundancy allocation problem in multi-state weighted k-out-of-n system. J Manuf Syst2016; 40: 54–62.
9.
ZhangXLuZChengK, et al. A novel reliability sensitivity analysis method based on directional sampling and Monte Carlo simulation. Proc IMechE, Part O: J Risk and Reliability2020; 234(4): 622–635.
10.
YuHYangJZhaoY.Reliability of nonrepairable phased-mission systems with common bus performance sharing. Proc IMechE, Part O: J Risk and Reliability2018; 232(6): 647–660.
LiWZuoMJ.Optimal design of multi-state weighted k-out-of-n systems based on component design. Reliab Eng Syst Saf2008; 93(11): 1673–1681.
13.
NegiSSinghSB.Reliability analysis of non-repairable complex system with weighted subsystems connected in series. Appl Math Comput2015; 262: 79–89.
14.
QinJLiZ.Reliability and sensitivity analysis method for a multistate system with common cause failure. Complexity2019; 2019: 6535726.
15.
ZhaoXWuCWangS, et al. Reliability analysis of multi-state k-out-of-n: G system with common bus performance sharing. Comput Ind Eng2018; 124: 359–369.
16.
BishtVSinghSB.Reliability Analysis of 8 × 8 SEN- Using UGF Method. In: RamMPhamH (eds) Reliability and maintainability assessment of industrial systems. Springer series in reliability engineering. Cham: Springer, 2022, pp.329–342.
17.
BishtVSinghSB.Reliability estimation of 4× 4 SENs using UGF Method. J Reliab Stat Stud2021; 14(1): 173–198.
18.
KhatiASinghSB.Reliability assessment of replaceable shuffle-exchange network by using interval-valued universal generating function. In: KumarARamM (eds) The handbook of reliability, maintenance, and system safety through mathematical modeling. Cham, Switzerland: Academic Press, 2021, pp.419–455.
19.
YehWC.A simple universal generating function method for estimating the reliability of general multi-state node networks. IIE Trans2008; 41(1): 3–11.
20.
LisnianskiA.Lz-Transform for a discrete-state continuous-time Markov process and its applications to multi-state system reliability. In: LisnianskiAFrenkalI (eds) Recent advances in system reliability. Springer series in reliability engineering. London: Springer, 2012, pp.79–95.
21.
FrenkelIKhvatskinLDaichmanS, et al. Assessing water cooling system performance: Lz-transform method. In: 2013 International conference on availability, reliability and security, Regensburg, Germany, 2–6 September 2013, pp. 737–742. New York: IEEE.
22.
LisnianskiABen HaimH.Short-term reliability evaluation for power stations by using Lz-transform. J Mod Power Syst Clean Energy2013; 1(2): 110–117.
23.
FrenkelIBolvashenkovIKhvatskinL, et al. The Lz-transform method for the reliability and fault tolerance assessment of Norilsk-type ship’s diesel-geared traction drives. Transp Telecommun2018; 19(4): 284–293.
24.
LiTJZhangYMSuY, et al. Dynamic reliability of thermally deduced positioning precision of ball screw systems based on random moving difference method. J Manuf Syst2021; 61: 171–182.
25.
LisnianskiAFrenkelIKhvatskinL. Modern dynamic reliability analysis for multi-state systems. Springer series in reliability engineering. Cham, Switzerland: Springer, 2021.
26.
FaghihRSXieMNgKM, et al. Dynamic availability assessment and optimal component design of multi-state weighted k-out-of-n systems. Reliab Eng Syst Saf2014; 123: 57–62.
27.
ZhangTXieMHorigomeM.Availability and reliability of k-out-of-(M+ N): G warm standby systems. Reliab Eng Syst Saf2006; 91(4): 381–387.
