System reliability modeling and analysis in the possibility context

This paper presents a general mechanical system reliability modeling and analysis method, which consider the correlations of failure modes. Firstly, the performance functions which mathematically represent the failure modes are linearized based on FORM (First Order Reliability Methods), and the correlation coefficient matrix of those functions is calculated. Then, the PFTA (Probabilistic Fault Tree Analysis) method is adopted to establish the system reliability model which can take the correlations into account. Finally, effective algorithms such as G-FOMN (General First Order Multinormal Method) are used to quantify the system reliability, and the sensitivities of the system reliability index with respect to each failure mode, as well as the mean value and standard deviation of each random variable are also calculated. An engineering example demonstrates the applicability of the proposed method.

The study and analysis of repairable systems is an important topic in reliability. Analytical techniques become very complicated and unrealistic especially for modern complex systems. There have been attempts in the literature to evolve more realistic techniques using simulation approach for reliability analysis of systems. The purpose of this paper is to develop a novel Markov system dynamics (MSD) simulation framework for the reliability modeling and analysis of a repairable system. This paper proposes a hybrid approach called as MSD approach which combines the Markov approach with system dynamics simulation approach for reliability modeling. This approach will have the advantages of both Markov as well as system dynamics methodologies. The proposed framework is illustrated for a repairable two component system. The results of the simulation obtained in this work when compared with that obtained by traditional Markov analysis clearly validate that this novel MSD approach is an alternative approach for reliability modeling and analysis.

Machining center is a complex mechatronical product. Because of numerous influencing factors on its reliability, parts of their inaccurate description and the uncertainty of its failure behaviors, it is very difficult to analyze its reliability by traditional reliability model which is based on probability theory. To solve this problem, grey system theory combined with GO method reliability analysis was presented, and sequentially a practical reliability analysis model considering various operating conditions of the components of machining center was established. The method was used in reliability analysis of hydraulic system of Tray Automatic Exchange Device (TAED) of machining center. Firstly, through a systematical analysis of hydraulic system of tray automatic exchange device of machining center, its basic structure model was summarized, and the model of GO chart for the hydraulic system was established. Then, the gray dynamic analysis for the hydraulic system was derived, and a feasible method of dynamic analysis for the performance reliability of hydraulic system was provided. Finally, the availability and correctness of this method in the analysis and reliability evaluation of machining center was verified by comparing the calculated result of this method with that of the traditional static GO methodology and the FTA. This approach provided a theoretical basis for the prevention of failures of the hydraulic system of tray automatic exchange device, the improvement of the system reliability and security, and the development of security controls.

This paper considers the reliability analysis of a two‐component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensity λ > 0. Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.

In industrial engineering, the reliability analysis, modeling and optimization for complex systems are very important. Although the works about reliability optimization with the traditional method are numerous, researchers still study more efficient and accurate methods to solve these reliability problems. The common cause failures are the multiple failures with a common cause, which is typical and serious in practical systems. Therefore, on the basis of normal optimization methods of system reliability, this paper proposes an optimization method of system with common cause failures based on importance measures. The optimization models of parallel system and the series-parallel system are built and are solved with hybrid genetic algorithm. By analyzing the system reliability and cost increasing, the proposed method gives the more accurate, valid and robust optimization results. Meanwhile, the method provides an idea for the reliability optimization of multistate systems.

Performance and Reliability Analysis of Computer Systems: An Example-Based Approach Using the SHARPE Software Package provides a variety of probabilistic, discrete-state models used to assess the reliability and performance of computer and communication systems. The models included are combinatorial reliability models (reliability block diagrams, fault trees and reliability graphs), directed, acyclic task precedence graphs, Markov and semi-Markov models (including Markov reward models), product-form queueing networks and generalized stochastic Petri nets. A practical approach to system modeling is followed; all of the examples described are solved and analyzed using the SHARPE tool. In structuring the book, the authors have been careful to provide the reader with a methodological approach to analytical modeling techniques. These techniques are not seen as alternatives but rather as an integral part of a single process of assessment which, by hierarchically combining results from different kinds of models, makes it possible to use state-space methods for those parts of a system that require them and non-state-space methods for the more well-behaved parts of the system. The SHARPE (Symbolic Hierarchical Automated Reliability and Performance Evaluator) package is the `toolchest' that allows the authors to specify stochastic models easily and solve them quickly, adopting model hierarchies and very efficient solution techniques. All the models described in the book are specified and solved using the SHARPE language; its syntax is described and the source code of almost all the examples discussed is provided. Audience: Suitable for use in advanced level courses covering reliability and performance of computer and communications systems and by researchers and practicing engineers whose work involves modeling of system performance and reliability.

For different importance of components in equipment system, a cold standby system with two different components is studied when important components enjoy the priority in use and maintenance. Considering the application of exponential distribution, Weibull distribution and other typical distributions in resolving the problems subject to complicated calculation and strict constraints in the past reliability modelling, the highly applicable phase-type (PH) distribution is utilized to describe the life and maintenance time of system components in a unified manner. A system reliability model is built for wider applicability. With the matrix analysis method, expressions are obtained for a number of reliability indicators such as system reliability function, steady-state availability, mean up time and mean down time of system. In the end, examples are presented to verify the correctness and applicability of the model.

Most methods of reliability analysis of cold standby systems assume that the precise probability distributions of the component times to failure are available. However, this assumption may be unreasonable in a wide scope of cases (software, human‐machine systems). Therefore, the imprecise reliability models of cold standby systems are proposed in the paper. These models suppose that arbitrary probability distributions of the component time to failure are possible and they are restricted only by available information in the form of lower and upper probabilities of some events. It is shown how the reliability assessments may vary with a type of available information. The impact of the independence condition on reliability of systems is studied. Numerical examples illustrate the proposed models.

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.

It is necessary to make the tape winding system have good reliability. Because the power system usually is a pneumatic or hydraulic system, the static reliability analysis lacks the ability to describe the dynamic state transfer, component fault correlation, and propagation effect of the system; it is difficult to accurately reflect the actual behavior of the complex system. Most of the existing research results lack the situation that the importance of bottom events changes with time; only a single number cannot express the impact of bottom events on top events at different times. Therefore, this study uses the dynamic reliability analysis method to quantitatively analyze the reliability of the tape winding power hydraulic system. Firstly, the dynamic reliability model of hydraulic system is established by using the continuous-time T-S dynamic fault tree to solve the fault rate of the system. Secondly, the results are compared with the traditional Markov chain analysis method of dynamic fault tree. The feasibility and advantages of the continuous-time T-S dynamic fault tree analysis method are verified. Finally, the probability importance and key importance of the system unit are calculated, and the law of importance changing with time is expressed. According to the importance of different time, it can help the regular maintenance and fault diagnosis of equipment.

The High voltage static converter systems are deployed at different military and DoD assets in which power electronics is used for the isolated and stabilized AC or DC voltage/frequency conversion process and the Insulated Gate Bipolar Transistor (IGBT) triggering system plays crucial role in such systems. Such type of systems and equipments are being operated by the combat deployed personnel and they rely upon in order to complete their critical missions. Therefore, it is evident that reliability and availability during the mission and maintainability of the system before and after the mission is paramount. The objective of this paper is to present the predicted Reliability, Maintainability, Availability and Failure rate analysis of the IGBT triggering system. The analysis is made in the marine environment by defining specific parameters. The method used to calculate the reliability prediction of the IGBT triggering system is based on the calculation of Mean Time Between Failure (MTBF), which is obtained from the calculation of Failure rate of individual components used in the system. The maintainability analysis is done based on the length of the time required by the repairable components, repair through replaceable components or replacing the whole system. Therefore, this analysis will use the Mean Time To Repair (MTTR). MTBF and MTTR are used as key elements in the availability analysis of the system. Pareto analysis is presented in order to show the individual components failure rate contribution used in the system. The presented analysis shows the relationship between reliability, maintainability and availability of a system and also shows how the reliability and maintainability analysis improves the availability of the designed system. The presented analysis can be viewed with reference to system lifetime calculation as it will help in investment plan of designed system in marine environment.

<p>Cold-standby systems have been widely used for conditions with limited power, which achieve fault tolerance and high-reliability systems. The cold spare (CSP) gate is a common dynamic gate in the dynamic fault tree (DFT). DFT with CSP gates is typically used to model a cold-standby system for reliability analysis. In general, inputs of the CSP gate are considered to be basic events. However, with the requirement of the current system design, the inputs of the CSP gate may be either basic events or top events of subtrees. Hence, the sequence-dependency among basic events in CSP gates becomes much more complex. However, the early conditional binary decision diagram (CBDD) used for the reliability analysis of spare gates does not consider it well. To address this problem, the conditioning event rep is improved to describe the replacement behavior in CSP gates with subtrees inputs, and the related formulae are derived. Further, a combinatorial method based on the CBDD is demonstrated to evaluate the reliability of cold-standby systems modeled by CSP gates with subtrees inputs. The case study is presented to show the advantage of using our method.</p> <p> </p>

Reliability modeling in a predictive maintenance context: A margin-based approach

This paper focuses on system reliability analysis with dependent competing failure process due to soft failure and hard failure. Some new probabilistic methods based on cumulative shock model and nonlinear Wiener process under different shifting thresholds situation are obtained. Considering that nonlinearity exists extensively in practice, the continuous soft failure process is governed by random effected nonlinear Wiener process. Firstly, reliability evaluation models for hard failure and soft failure are obtained under the cumulative shock, respectively. Furthermore, some system reliability models under different shifting thresholds situation are studied, in which failure threshold will decrease after a certain number of shocks. A real numerical example about fatigue crack growth dataset is carried out to demonstrate the proposed procedure. Numerical results indicate that both random shocks and shifting threshold have significant effect on system reliability. Finally, some sensitivity analysis are also been given.

Reliability model of cold standby systems with built-in-test