Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy Lz-transform.

Abstract

Article citation info:on a continuous scale. In such situations, the lifetimes and repair times can be expressed in terms of the number of working and repairing periods (cycles), respectively. Thus, it is essential to construct discrete time reliability models for repairable multi-state systems.The discrete time reliability has drawn continuous attention in both model analysis and problem solution. Bracquemond and Gaudoin [5] presented a good overview of discrete probability distributions used in reliability for modeling discrete lifetimes of non-repairable systems. The discrete time reliability modeling for general binary systems can be found in [4,22,34]. Eryilmaz [14], Guerry [16] and Sadek and Limnios [35], presented the discrete time reliability models for Markov multi-state systems. The discrete time reliability models for semi-Markov multi-state systems were investigated in [1,4,10]. However, most of the reported works mainly focus on the issues of IntroductionThe availability, as a performance measure, is one of the most important indicators for characterizing a repairable system and its components. For repairable multi-state systems with various performance levels, the availability is more meaningful than reliability to measure the effectiveness of the system to satisfy consumer demand.In the past few years, a variety of methods are available in the literature for analyzing the availability of repairable multi-state systems. Some of them are Monte Carlo simulation [41,42], stochastic Petri nets [19,21], universal generating function [24,32], Markov models [6,37] and the combinations of the above methods [9]. However, conventional availability analysis methods for repairable multi-state systems are based on the continuous time models. In some engineering circumstances, it is sometimes impossible or inconvenient to measure the lifetimes and repair times length of some systems (components) HU L, SU P, PENG R, ZHANG Z. Fuzzy Availability Assessment for Discrete Time Multi-State System under Minor Failures and Repairs by Using Fuzzy L z -transform. Eksploatacja i Niezawodnosc - Maintenance and Reliability 2017; 19 (2): 179-190 discrete time systems with the exact reliability data. As stated in Garg [15], the complicated system has the massive fuzzy uncertainty due to which it is difficult to get the exact probability of the events. Thus, it is of large practical value to investigate the availability assessment for discrete time repairable system with fuzzy uncertainty. fuzzy discrete time Markov model with fuzzy transition probability matrix is proposed to analyze the fuzzy state probability of each component at any discrete time. The fuzzy L z -transform of the discrete-state discrete-time fuzzy Markov chain is developed to extend the L z -transform of the discrete-state continuous-time Markov model with crisp sets. Based on the α-cut approach and the fuzzy L z -transform, the dynamic fuzzy availability of the system is computed by using parametric programming technique. To illustrate the proposed method,...

Reliability Assessment of Random Uncertain Multi-State Systems

“…Eqs. (18) and ( 12) are the same. Thus, the uncertainty distribution function and the inverse uncertainty distribution of g s,k (γ ) = g 1,k 1 (γ )+g 2,k 2 (γ ) can be determined in the same manners as Eqs.…”

“…Recently, Bamrungsetthapong and Pongpullponsak [17] studied parameter interval estimation of system reliability for a repairable multi-state series-parallel system with fuzzy data. Hu et al [18] provided an assessment approach for dynamic fuzzy availability of a discrete time multi-state system under minor failures and repairs.…”

Improved Availability Index for Repairable Fuzzy Multi-State Systems

“…Subsequently, Hu et al [12] applied the approach proposed by Liu et al [11] to a reparable FMSS. Further, Hu et al [13] calculated the FMSS reliability of a discrete time-repairable MSS using trapezoidal fuzzy numbers based on the approach presented in [11]. Javid et al [14] focused on the special structure of ready-to-use systems to propose a reliability model based on the Markov models and fuzzy theory.…”

“…In summary, the FMSS reliability models reported in [13,15,16,[18][19][20] are based on the approach proposed by Ding et al [10], whereas those presented in [12] and [13] are an application of the approach presented in [11] involving the use of an FMSS reliability index to compensate for the drawbacks of the method presented in [10] that utilizes linear TFN to quantify circumstances with non-probabilistic uncertainties. The approach proposed in [11] considers the αcut value in determining the extent to which the stateperformance membership function meets the mission demand.…”

Reliability modeling for a discrete time multi-state system with random and dependent transition probabilities

“…Thus, the fuzzy MSS reliability models [27][28][29][30][31] have been studied by many scholars. More recently, Hu and colleagues 32,33 investigated the fuzzy reliability for discrete time repairable MSS with uncertainties and provided the analytical procedure to calculate the a-cut of the dynamic fuzzy reliability of the system.…”