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This paper aims to present two methods for calculating the steady state probability of a repairable fault tree with priority AND gates and repeated basic events when the minimal cut sets are given.

The authors consider a situation that the occurrence of an operational demand and its disappearance occur alternately. We assume that both the occurrence and the restoration of the basic event are statistically independent and exponentially distributed. Here, restoration means the disappearance of the occurring event as a result of a restoration action. First, we obtain the steady state probability of an output event of a single‐priority AND gate by Markov analysis. Then, we propose two methods of obtaining the top event probability based on an Inclusion‐Exclusion method and by considering the sum of disjoint probabilities.

The closed form expression of steady state probability of a priority AND gate is derived. The proposed methods for obtaining the top event probability are compared numerically with conventional Markov analysis and Monte Carlo simulation to verify the effectiveness. The result shows the effectiveness of the authors’ methods.

The methodology presented shows a new solution for calculating the top event probability of repairable dynamic fault trees.

To reduce the flammability exposure assessment time and meet the requirements of airworthiness regulations of transport aircraft, inerting system has become the standard configuration of modern civil aircraft. Therefore, airworthiness regulations put forward definite quantitative index requirements for the safety of inerting system, and to obtain the quantitative data of the safety of inerting system, it is necessary to solve the calculation method. As one of the quantitative/qualitative evaluation techniques for system safety, fault tree analysis is recognized by international airworthiness organizations and national airworthiness certification agencies. When fault tree analysis technology is applied to quantitative analysis of the safety of inerted system, there are still some problems, such as heavy margin of constructing fault tree, great difficulty, high requirement for analysts and poor accuracy of solving when there are too many minimum cut sets. However, based on tens of thousands of flight simulation tests, Monte Carlo random number generation method can solve this problem.

In this paper, the fault tree of airborne inerting system is established, and the top event is airborne inerting system losing air separation function. Monte Carlo method based on random number generation is used to carry out system security analysis. The reliability of this method is verified.

The static fault tree analysis method based on Monte Carlo random number generation can not only solve the problem of quantitative analysis of inerting system, but can also avoid the defects of complicated solution and inaccurate solution caused by the large number of minimum cut sets, and its calculation results have good reliability.

The research results of this paper can be used as supporting evidence for airworthiness compliance of airborne inerting system.

The research results of this paper can provide practical guidance for the current civil airworthiness certification work.

An important characteristic of many engineering systems which cannot be modeled by fault trees to perform system reliability analysis is that they behave dynamically. In this paper, the method of applying Petri Nets (Pns) as a modeling tool to represent the coherent fault trees is discussed. When the repair facility is added into the nets, the dynamic behavior of the repairable system can be studied through the nets by using equivalent Markov chains.

The purpose of this paper is to present a new methodology, named vague lambda‐tau, used for reliability analysis of a combustion system, which could be used for managerial decision making and future system maintenance strategy.

This paper involves the qualitative and quantitative analysis of a combustion system. In qualitative analysis, the Petri net model is obtained from its equivalent fault tree and in quantitative analysis, the reliability parameters are evaluated using vague lambda‐tau methodology. Further, a decision support system based on vague sets is developed to overcome the limitations of traditional risk analysis.

The reliability parameters (such as expected number of failures, mean time between failures, availability, and reliability) of the compressor system are evaluated. The proposed, vague sets‐based reliability analysis and risk analysis not only overcome the limitations associated with traditional approaches but also integrate the confidence level of domain experts and expert's experience, in a more flexible and realistic manner.

Instead of fuzzy sets, this paper used vague sets for reliability analysis with Petri net modelling because in real life problems, there may be hesitation regarding the belongingness of an object to a set or not. In fuzzy set theory, there is no means to incorporate such type of hesitation.

The purpose of this paper is to analyze the fuzzy reliability of the compressor house unit (CHU) system in a coal fired thermal power plant under vague environment by reducing the accumulating phenomenon of fuzziness and accelerating the computation process. This paper uses different fuzzy membership functions to quantify uncertainty and access the system reliability in terms of different fuzzy reliability indices having symmetric shapes.

This study analyses the fuzzy reliability of the CHU system in a coal fired thermal power plant using T_ω-based generalized fuzzy Lambda-Tau (TBGFLT) technique. This approach applies fault tree, Lambda-Tau method, different fuzzy membership functions and α-cut coupled T_ω-based approximate arithmetic operations to compute various reliability parameters (such as failure rate, repair time, mean time between failures, expected number of failures, availability and reliability) of the system. The effectiveness of TBGFLT technique has been demonstrated by comparing the results with results obtained from four different existing techniques. Moreover, this paper applies the extended Tanaka et al. (1983) approach to rank the critical components of the system when different membership functions are used.

The adopted TBGFLT technique in the present study improves the shortcomings of the existing approaches by reducing the accumulating phenomenon of fuzziness, accelerating the computation process and getting symmetric shapes for computed reliability parameters when different membership functions are used to quantify data uncertainty.

In existing fuzzy reliability techniques which are developed for repairable systems either triangular fuzzy numbers, triangle vague sets or triangle intuitionistic fuzzy sets have been used for quantifying uncertainty. These approaches do not examine the systems for components with different membership functions. The present study is an effort in this direction and evaluates the fuzzy reliability of the CHU system in a coal fired thermal power plant for components with different membership functions. This is the main contribution of the paper.

The main goal of this paper is to develop novel Tω(weakest t-norm)-based fuzzy arithmetic operations to analyze the intuitionistic fuzzy reliability of Printed Circuit Board Assembly (PCBA) using fault tree.

The paper proposes a fuzzy fault tree analysis (FFTA) method for evaluating the intuitionistic fuzzy reliability of any nonrepairable system with uncertain information about failures of system components. This method uses a fault tree for modeling the failure phenomenon of the system, triangular intuitionistic fuzzy numbers (TIFNs) to determine data uncertainty, while novel arithmetic operations are adopted to determine the intuitionistic fuzzy reliability of a system under consideration. The proposed arithmetic operations employ Tω(weakest t-norm) to minimize the accumulating phenomenon of fuzziness, whereas the weighted arithmetic mean is employed to determine the membership as well as nonmembership degrees of the intuitionistic fuzzy failure possibility of the nonrepairable system. The usefulness of the proposed method has been illustrated by inspecting the intuitionistic fuzzy failure possibility of the PCBA and comparing the results with five other existing FFTA methods.

The results show that the proposed FFTA method effectively reduces the accumulating phenomenon of fuzziness and provides optimized degrees of membership and nonmembership for computed intuitionistic fuzzy reliability of a nonrepairable system.

The paper introduces Tω(weakest t-norm) and weighted arithmetic mean based operations for evaluating the intuitionistic fuzzy failure possibility of any nonrepairable system in an uncertain environment using a fault tree.

The purpose of this paper is to analyze the reliability of the washing system in a paper plant in a more promising way under vague environment by reducing the accumulating phenomenon of fuzziness and accelerating the computation process using the T_ω (weakest t-norm) based fuzzy lambda-tau (TBFLT) technique.

This paper presents a unified approach for analyzing the fuzzy reliability of the washing system under vague environment. This approach applies the TBFLT technique which uses triangular fuzzy numbers for incorporating data uncertainty, fault tree and lambda-tau method for finding system failure rate and repair time mathematical expressions while simplified T_ω-based arithmetic operations are applied for computing various reliability parameters of the system. The effectiveness of the TBFLT technique has been demonstrated by analyzing fuzzy reliability of the system using five different techniques including TBFLT. Moreover, this paper applies extended Tanaka’s (1983) approach to rank the critical components of the system.

The TBFLT technique has the advantage of low computation complexity in comparison to other techniques and effectively reduces the accumulating phenomenon of fuzziness. This main finding verifies the conclusion made by Chen (1994).

The author has suggested a simple and more applicable technique for analyzing the fuzzy reliability of any complex process industrial system under vague environment. The effectiveness of the technique has been demonstrated by computing various reliability parameters of the washing system of a paper plant.

The puprose of this paper is to analyse the stochastic behavior of an industrial system using a novel hybridized technique NGABLT. The forming unit of a paper mill situated in north India producing approximately 200 tons of paper per day has been considered for analysis. The authors have made efforts to incorporate vague, ambiguous, imprecise and conflicting information quantified by fuzzy numbers.

Field data for repairable industrial systems are in the form of failures and repair rates are vague, ambiguous, qualitative and imprecise in nature. Using the data, system stochastic behavior in terms of six well‐known reliability indices is analysed considering some desired degree of accuracy. A practical case of forming unit in a paper mill is considered to compute the reliability indices by using NGABLT technique. Sensitive of system behavior is analysed through surface plots by taking different combinations of reliability indices. The findings have been supplied to the nearby industry for future course of action in maintenance.

The behavior analysis results computed by NGABLT technique have reduced region of prediction in comparison of existing Lambda‐Tau technique region i.e. uncertainties involved in the analysis are reduced. It may be a more useful tool to assess the current system condition and to improve the system performance.

The authors have suggested a hybridized technique for analyzing the stochastic behavior of the repairable industrial system by computing its reliability indices.

The purpose of this paper is to demonstrate the potential of simulation approach for performance evaluation in a complex environment with a case of application from Indian Nuclear Power Plant.

In this work, stochastic simulation approach is applied to availability evaluation of AC Power supply system of Indian Nuclear Power Plant (INPP). In the presently followed test, maintenance policies on diesel generators and circuit breakers are considered to exactly model the practical scenario. System success logic incorporates the functional dependencies and dynamics in the sequence of operations and maintenance policies. In each iteration (random experiment), from simulated random behaviour of the system, uptime and down time are calculated based on system success logic. After sufficient number of iterations, unavailability and other required reliability measures are estimated from the results.

The subsystems of AC Power Supply System of NPP are having multi‐states due to surveillance tests and scheduled maintenance activities. In addition, the operation of DG involves starting and running (till its mission time) which is a sequential (or conditional) event. Furthermore, the redundancies and dependencies are adding to the complexity.

This paper emphasizes the importance of realistic reliability modelling in complex operational scenario with Monte‐Carlo simulation approach. Simulation procedure for evaluating the availability/reliability of repairable complex engineering systems having stand‐by tested components is presented. The same simulation model finds application in importance measures calculation, technical specification optimization and uncertainty quantification.

The purpose of this paper is to present a hybridized technique for analyzing the behavior of an industrial system stochastically utilizing vague, imprecise, and uncertain data. The press unit of a paper mill situated in a northern part of India, producing 200 tons of paper per day, has been considered to demonstrate the proposed approach. Sensitivity analysis of system's behavior has also been done.

In the proposed approach, two important tools namely traditional Lambda‐Tau technique and genetic algorithm have been hybridized to build genetic algorithms‐based Lambda‐Tau (GABLT) technique to analyze the behavior of complex repairable industrial systems stochastically up to a desired degree of accuracy. This technique has been demonstrated by computing six well‐known reliability indices used for behavior analysis of the considered system in more promising way.

The behavior analysis results computed by GABLT technique have reduced region of prediction in comparison of existing Lambda‐Tau technique region, i.e. uncertainties involved in the analysis are reduced. Thus, it may be a more useful analysis tool to assess the current system conditions and involved uncertainties. The paper suggested an approach to improve the system's performance.

The paper suggests a hybridized technique for analyzing the stochastic behavior of an industrial subsystem by computing six well‐known reliability indices in the form of fuzzy membership function.