In this paper, a novel reliability model for bolt joint systems is proposed, which incorporates multiple dependent competing failure processes (DCFP). The multiple DCFP model is constructed by the DCFP of individual bolts and the bolt joint system. The DCFP model of a component is developed by hard failure due to fatal shocks and soft failure resulting from degradation. The component failure process is stochastic dependent, as the stochastic shock process affects both the hard and the soft failure processes. Additionally, a system failure model is established by arranging N components in a circle, which is location-dependent. The failed components lead to either a K/N failure model or a k/r/N failure model for the bolt joint system. In the K/N (F) system model, failure occurs when the number of failed components (NOFC) reaches K. For the k/r/N system model, failure occurs when the NOFC reaches k within any consecutive r set out of N. A closed-form formula is derived from the system reliability model, which is applicable when there are fewer than two separate k/r/N patterns. The practicality of the proposed model is demonstrated through a case study involving a bolt joint system.
PiSLiuYChenH, et al. Probability of loss of assured safety in systems with weak and strong links subject to dependent failures and random shocks. Reliab Eng Syst Saf2021; 209: 107483.
2.
LyuHZhangXYangZ, et al. Reliability analysis for the dependent competing failure with wear model and its application to the turbine and worm system. IEEE Access2021; 9: 50265–50280.
3.
ZhangYZhaoYLuY, et al. Bayesian identification of bolted-joint parameters using measured power spectral density. Proc IMechE, Part O: J Risk Reliability2019; 234: 260–274.
4.
XieLZhouJHaoC.System-level load–strength interference based reliability modeling of k-out-of-n system. Reliab Eng Syst Saf2004; 84: 311–317.
5.
ShaoJLambersonLR.Modeling a Shared-Load k-out-of-n:G System. IEEE Trans Reliab1991; 40: 205–209.
6.
EryilmazS.Review of recent advances in reliability of consecutive k-out-of-n and related systems. Proc IMechE, Part O: J Risk Reliability2010; 224: 225–237.
7.
GongMLiuHPengR.Redundancy allocation of mixed warm and cold standby components in repairable K-out-of-N systems. Proc IMechE, Part O: J Risk Reliability2020; 234: 696–707.
8.
CuiLDongQ. Consecutive k and related models–a survey. Stochastic Models in Reliability, Network Security and System Safety: Essays Dedicated to Professor Jinhua Cao on the Occasion of His 80th Birthday1. Singapore: Springer, 2019, pp. 3–18.
9.
ShenJCuiLDuS.Birnbaum importance for linear consecutive-k-out-of-n systems with sparse d. IEEE Trans Relia2015; 64: 359–375.
10.
ZhaoXCuiLKuoW.Reliability for sparsely connected consecutive-k systems. IEEE Trans Reliab2007; 56: 516-524. DOI: 10.1109/tr.2007.903202.
11.
ÖzbeyF.Reliability evaluation of m-consecutive- k, l-out-of-n: F system subjected to shocks. Proc IMechE, Part O: J Risk Reliability2022; 236(6): 1135–1146.
12.
NakamuraTYamamotoHAkibaT.Reliability of a toroidal connected-(r,s)-out-of-(m,n):F lattice system. Proc IMechE, Part O: J Risk Reliability2020; 236: 329–338.
13.
HabibAAl-SeedyRORadwanT.Reliability evaluation of multi-state consecutive k-out-of-r-from-n: G system. Appl Math Model2007; 31: 2412–2423.
14.
AntonopoulouIPapastavridisS.Fast recursive algorithm to evaluate the reliability of a circular consecutive-k-out-of-n:F System. IEEE Trans Reliab2009; 36: 83–84.
15.
AtalaySDMertAGultekinOEJ, et al. On the profust reliabilities of consecutive k-out-of-n systems. Proc IMechE, Part O: J Risk Reliability2014; 228: 62–71.
16.
YiHCuiLGaoH.Reliabilities of some multistate consecutive κ systems. IEEE Trans Reliab2020; 69: 414–429.
17.
AmirianYKhodadadiA.Exact reliability for a multi-state consecutive linear (Circular) k-out-of-r-from-n:F system. Qual Saf Eng2021; 28(2): 2150014.
18.
RadwanT.New bounds for all types of multi-state consecutive k-out-of-r-from-n: F system reliability. IEEE Access2019; 7: 172562–172570.
19.
CaoSWangX.Mission abort strategy for generalized k-out-of-n: F systems considering competing failure criteria. Proc IMechE, Part O: J Risk Reliability2024; 238(4): 839–852.
20.
ZhangJZhaoYMaX.A new reliability analysis method for load-sharing k-out-of-n: F system based on load-strength model. Reliab Eng Syst Saf2019; 182: 152–165.
21.
LevitinGAmariSV.Approximation algorithm for evaluating time-to-failure distribution of k-out-of-n system with shared standby elements. Reliab Eng Syst Saf2010; 95: 396–401.
22.
ZhangTZhangYDuX.Reliability analysis for k-out-of-n systems with shared load and dependent components. Struct Multidisc Optim2018; 57: 913–923.
23.
BianLWangGDuanF.Reliability analysis for systems subject to mutually dependent degradation and shock processes. Proc IMechE, Part O: J Risk Reliability2021; 235: 1009–1025.
24.
QiuQLiuBLinC, et al. Availability analysis and maintenance optimization for multiple failure mode systems considering imperfect repair. Proc IMechE, Part O: J Risk Reliability2021; 235: 982–997.
25.
WilliamsJGAnleyRENashDH, et al. Analysis of externally loaded bolted joints: Analytical, computational and experimental study. Int J Pres Ves Pip2009; 86: 420–427.
26.
YangLYangBYangG, et al. Analysis of competitive failure life of bolt loosening and fatigue. Eng Fail Anal2021; 129: 105697.
27.
JiangXZhuYHongJ, et al. Investigation into the loosening mechanism of bolt in curvic coupling subjected to transverse loading. Eng Fail Analy2013; 32: 360–373.
28.
QinZHanQChuF.Bolt loosening at rotating joint interface and its influence on rotor dynamics. Eng Fail Analy2016; 59: 456–466.
29.
CaoYLiuSFangZ, et al. Modeling ageing effects for multi-state systems with multiple components subject to competing and dependent failure processes. Reliab Eng Syst Saf2020; 199: 106890.
30.
LyuHYangZWangS, et al. Reliability modeling for multistage systems subject to competing failure processes. Qual Reliab Eng Int2021; 37: 2936–2949.
