A reliability analysis method for fuzzy multi-state system with common cause failure based on improved the weakest T-norm

Fault Tree Analysis (FTA) is a powerful analytical technique for analyzing system reliability and safety by enumerating any possible safety-critical failure modes, which is very useful for identifying the risks and weaknesses in the system. Therefore, FTA is widely applied to the safety evaluation of large-scale and mission-critical systems. However, the following problems are usually pointed out when building a fault tree for a complex system: 1) System modeling is a hard and time consuming work, and 2) FTA models are difficult to be validated. In this paper, we propose a new method for system reliability analysis based on Multilevel Flow Models (MFM) and Goal Tree-Success Tree (GTST) methods. We use Goal Tree (GT) methodology to model the target system at a higher and system level, and use the Success Tree (ST) together with MFM at a lower and functional level. In this way, modeling effort could be significantly reduced. In this paper, an algorithm is also presented to translate the GTST-MFM model into ST model based on which qualitative reliability analysis can be performed by the Fusell-vesely algorithm. In this paper, a Low Head Safety Injection System (LHSIS) is taken as a case study to exemplify how to apply our proposed GTST-MFM method to model the system and to validate fault trees directly built by deductive method.

This paper addresses the problem of mixed uncertainty in the reliability analysis of multistate systems under common cause failure conditions. Combining the cloud model theory, universal generation function (UGF) method, and common cause failure theory, the universal generation function method is extended based on a probabilistic cloud model, i.e., the cloud universal generation function (CUGF) analysis method. The cloud model represents the random and cognitive uncertainty of the state probability, i.e., mixed uncertainty. Next, through CUGF, according to the calculation rules of cloud operators, we provide steps to obtain the reliability of a multistate system under independent failure and common cause failure conditions and obtain cloud digital features for reliability. The accuracy and feasibility of the method are verified by a numerical example. This paper solves the problem of reliability analysis of multistate systems with mixed uncertainty in unit state probability information under common cause failure conditions. We integrate system multistate, information uncertainty, and common cause failure for reliability analysis to avoid large errors, more in line with a project’s actual situation. We propose new ideas and methods to process randomness and fuzzy information or data in multistate system reliability analysis.

The aim of this paper is introducing a method based on Fuzzy Time-To Failure (FTTF) to improve reliability analysis of complex engineering systems based on fault tree analysis. This method focuses on the quantitative part of fault trees (either static or dynamic) analysis and will compute failure probabilities. FTTF model is developed to estimate the reliability of system and solve aforetime methods problems. The presented FTTF model is able to figure out any construction consist of static and dynamic gates with FTTF distributions integrated on Fuzzy Monte Carlo Simulation (FMCS) techniques to analyzing Possibilistic functions associated with the fuzzy probability distributions for each basic event. Using fuzzy algorithm, gates FTTF are generated, and Top-event TTF evaluated. Some case studies are used to demonstrate the priority of this method in exact evaluation in compared with other solving methods (like: BN, Analytical solution, Markov chain and traditional fuzzy fault tree modeling), but has much less effort while having higher accuracy. Finally, this model is implemented in an Emergency Detection System (EDS) which is a useful system in aerospace and space applications.

PurposeThis paper aims to deal with the problems of failure dependence and common cause failure (CCF) that arise in reliability analysis of complex systems.Design/methodology/approachFirstly, a dynamic fault tree (DFT) is used to capture the dynamic failure behaviours and converted into an equivalent generalized stochastic petri net (GSPN) for quantitative analysis. Secondly, an efficient decomposition and aggregation (EDA) theory is combined with GSPN to deal with the CCF problem, which exists in redundant systems. Finally, Birnbaum importance measure (BIM) is calculated based on the EDA approach and GSPN model, and it is used to take decisions for system improvement and fault diagnosis.FindingsIn this paper, a new reliability evaluation method for dynamic systems subject to CCF is presented based on the DFT analysis and the GSPN model. The GSPN model is easy to capture dynamic failure behaviours of complex systems, and the movement of tokens in the GSPN model represent the changes in the state of the systems. The proposed method takes advantage of the GSPN model and incorporates the EDA method into the GSPN, which simplifies the reliability analysis process. Meanwhile, simulation results under different conditions show that CCF has made a considerable impact on reliability analysis for complex systems, which indicates that the CCF should not be ignored in reliability analysis.Originality/valueThe proposed method combines the EDA theory with the GSPN model to improve the efficiency of the reliability analysis.

In view of the current study on the reliability analysis for complex new equipment systems, the fault tree analysis method is used in reliability engineering (Fault Tree Analysis, FTA). However, qualitative and quantitative analysis for complex equipment systems reliability are difficult problems. In this paper, firstly, fault tree analysis method is introduced, secondly, through an instance of a certain type of equipment, mathematical description and analysis methods for qualitative and quantitative analysis of system reliability are carried out. Finally, the results from fault tree analysis is presented and discussed, which shows that FTA is a method can quickly and accurately analyze equipment systems reliability, and is a designer tool for evaluation and improvement of system reliability.

This paper proposes a new goal-oriented (GO) method for reliability analysis of repairable systems with multiple-input and multi-function component (MIMFC). First, a new GO operator combination, which is composed of a new function GO operator and a new auxiliary GO operator, is created to represent MIMFC. The new function GO operator named as Type 22 operator is created to represent MIMFC itself, and the auxiliary GO operator named as Type 15B operator is created to represent multi-condition control signals of MIMFC. Then, GO operation formulas of the new GO operator combination are deduced based on logical relationships among inputs, outputs, and the component itself. The reliability analysis process of the new GO method is formulated. Furthermore, this new GO method is applied for the first time in steady availability analysis and qualitative analysis of the fan drive system of a power-shift steering transmission. Finally, the results obtained by the new GO method are compared with the results of fault tree analysis (FTA) and Monte Carlo simulation (MCS), and the comparison results show that this new GO method is reasonable and advantageous in reliability analysis of repairable systems with MIMFC. Moreover, the analysis process shows that it is more advantageous in the aspect of building system models and conducting reliability analysis. Overall, this paper not only improves the basic theory of the GO method and expands the application of the GO method, but it also provides a new approach for reliability analysis of repairable systems with MIMFC.

Fault tree analysis (FTA) is one of the most prominent techniques used in risk analysis, this method aimed to identify how component failures lead to system failure using logical gates (i.e. AND, OR gates). However, some limitations appear on FTA due to its static structure. Bayesian networks (BNs) have become a popular technique used in reliability analysis; it represents a set of random variables and their conditional dependencies. This paper discusses the advantages of Bayesian networks over fault tree in reliability and safety analysis. Also, it shows the ability of BN to update probabilities, to represent multi-state variables, dependent failures, and common cause failure. An example taken from the literature is used to illustrate the application and compare the results of both fault tree and bayesian networks techniques.

“Fault Tree Analysis” uses the logical model and mapping methods to analyse, calculate or estimate the probability of phylogenetic. Thus, the reliability of the system, safety and risk could be assessed. They have been widely used in system's reliability study and to quantify the correlation of potential risk of the system. In the existing of reliability analysis, the time factor generally doesn't need to be taken into account. However, composition properties of the materials decrease would lead to the reduction of the level of structural reliability. Therefore, structure's reliability is actually an amount of time-varying. Comprehensive consideration of the above factors, the analysis of a variety of factors will impact on the service life of pre-stressed concrete girder bridge, to build bridge structure analysis model. From the calculation of time-varying structure system's reliability, the service life of bridge could be evaluated to find safety and reliability of structure.

PurposeDegraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.Design/methodology/approachThe research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.FindingsThe proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.Research limitations/implicationsThe models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.Practical implicationsThese models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.Originality/valueA unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.

Fault tree analysis (FTA) has been widely utilized as a reliability evaluation technique for complex systems, such as nuclear power plants and aerospace systems. However, it is hard to obtain the crisp failure probabilities of basic events, owning to the insufficient information about some complex engineering systems. Hence, fuzzy set theory and fuzzy arithmetic operation (FAO) have been used as effective methods to analyze system reliability. However, it is cumbersome to evaluate complex systems based on FAO. To improve the evaluation efficiency, stochastic computational models are proposed in this paper to perform reliability analysis of a fuzzy system. Due to the features of Gaussian distribution in stochastic computation, a basic event’s failure possibility given by a fuzzy number is transformed into the expected value of it. The standard deviation of stochastic computational results gives the spread of the fuzzy number. A fuzzy system is then converted into a deterministic system. The analysis of an illustrating example shows that the proposed stochastic approach can efficiently evaluate the failure probability of a system.

This paper proposes a quantitative reliability analysis method for power systems with multi-level standby structure based on GO method. First, the GO model used to describe the multi-level standby structure is proposed. Then, the reliability analysis process for such systems based on GO method is formulated. Finally, the proposed GO method is applied in reliability analysis of AC power system for single unit with 100% capacity divisions in nuclear power plant. In order to verify the feasibility, advantage and reasonable of the proposed GO method, its analysis result compared with the analysis result of GO method without considering standby correlations among the multi-level standby structure. All in all, this study provides guidance of reliability analysis for power systems with multi-level standby structure.

Even though Fault Tree Analysis (FTA) is used in the majority of risk assessments, there is a persistent gap between creating a plausible‐looking fault tree diagram and producing a valid, quantifiable risk assessment from it. Stoelinga, Ruijters and Krčál's The Concise Guide to Fault Tree Analysis: Models, Methods and Algorithms (Springer/Birkhäuser, 2026) bridges this gap by treating Fault Tree Analysis (FTA) as a combination of a logical discipline of engineering and a set of computational methods for generating results from FTA models. The book provides a clear connection between the process disciplines involved in developing FTA models and the algorithms that are actually used to generate cut sets, top event probabilities and importance values, while emphasizing the need to be cautious when interpreting these values as objective facts. As such, the Concise Guide to Fault Tree Analysis will provide a useful resource to anyone who builds, reviews, or interprets fault trees, regardless of domain, by improving the accuracy and transparency of FTA and the overall quality of FTA reports.

Development of a computer code AFTC for fault tree construction using decision table method and super component concept

Multi-state components, common cause failures (CCFs) and data uncertainty are the general problems for reliability analysis of complex engineering systems. In this paper, a method incorporating fuzzy probability and Bayesian network (BN) into multi-state systems (MSSs) with CCFs is proposed. In particular, basic theories of multi-state BN and fuzzy probability are developed. Moreover, a model integrating CCFs with BN has also been illustrated. In order to incorporate fuzzy probability into MSSs reliability evaluation considering common parent node generated by CCFs, fuzzy probability has to be translated into accurate probability through defuzzification and normalization methods which are both elaborated. In addition, quantitative analysis based on BN is carried out. In this paper, feed system of boring spindle in computer numerical control machine is analyzed as an example to validate the feasibility of the proposed method. It can improve the ability of BN on reliability evaluation of complex system with uncertainty issues.

Reliability analysis and initial requirements for FC systems and stacks