A Markov System Dynamics Approach for Repairable Systems Reliability Modeling

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.

A novel approach for software reliability analysis of digital instrumentation and control systems in nuclear power plants

This paper presents an approach for reliability analysis of repairable systems with two-unit parallel structure considering Common Cause Failure (CCF) and maintenance correlation based on GO methodology. First, the GO algorithm for dealing with CCF is introduced. Then, the common cause failure probability formulas of two-unit parallel structure considering maintenance correlation are deduced based on Markov theory. Furthermore, the analysis process of the new GO method is formulated. Finally, the dynamic availability analysis of HTOSS is conducted by the GO method. And the result is compared with the result of system considering CCF, and the result of system without considering CCF and maintenance correlation. The results show that the CCF and maintenance correlation are not ignored for reliability analysis of such system. All in all, this study not only widens the application of GO method. But it also provides guidance and an approach for reliability analysis of repairable systems with two-unit parallel structure considering CCF and maintenance correlation.

Reliability analysis of repairable systems has been widely conducted based on collected information such as the systems’ failure counting processes. In many real-life situations, the failure counting processes may not be completely observed when some failure times are not recorded or missing due to various practical reasons. In the literature, only a limited number of reliability studies focus on missing failure time data for repairable systems with an assumption that the system repair is either perfect or minimal. When the repair effect is general as in many real-world situations, challenges arise for reliability analysis in that the observed and unobserved failure times are statistically dependent in a complex manner, and the time censoring problem becomes unconventional. In this paper, to overcome these challenges, we propose a reliability model for repairable systems with incomplete failure time data under general repair. The proposed model is suitable for modeling both a single system and multiple systems subject to failure heterogeneity. A maximum likelihood estimation method is developed to estimate the model parameters. Based on the proposed model, statistical inference of the missing times is developed. Simulation and real-life case studies are conducted to verify the developed methods.

System reliability is considered as an important performance index. Performance of engineering systems can be assessed by various techniques. The traditional analytical approach consists of developing a mathematical model that represents the system and to evaluate its reliability indices. There have been attempts in the literature to derive more realistic approaches for the reliability analysis of systems, for example, based on simulations. This paper proposes a hybrid approach called Markov System Dynamics (MSD) approach which combines the Markov approach with system dynamics simulation approach for performing a reliability analysis and for studying the dynamic behavior of systems. This approach will have the advantages of both the methodologies that of Markov processes as well as system dynamics. The proposed framework is illustrated by a numerical example for a single component system with increasing failure rates. The results of the simulation when compared with those obtained by the traditional Markov analysis clearly validate the Markov System Dynamics (MSD) approach as an alternative for reliability analysis.

This paper combines time varying failure rates and Markov chain analysis to obtain a hybrid reliability and availability analysis. However, combining these techniques can, depending on the size of the system, result in solutions of the Markov chain differential matrix equations that are intractable. This paper identifies solutions that are tractable, These form the analytical baseline for the reliability and availability analysis of systems with time varying failure rates. Tractable solutions were found for the 1-component 2-state and the 2-component 4-state configurations. Time varying failure rates were characterized by a general polynomial expression. Constant, linear, and Weibull failure rate functions are special cases of this polynomial. The general polynomial failure rate provides flexibility in modeling the time varying failure rates that occur in practice.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

Purpose: The main purpose of this research is to highlights the problems in the various fields of Business Management, where SD can be applied effectively. Design/Methodology/Approach: This paper is designed to give a brief overview of the System dynamics (SD) methodology in terms of its foundations, foundations, philosophy and conceptual framework and it also tries to demonstrate the areas where the system dynamics methodology can be applied effectively to solve the different managerial problems in the various fields and levels of Business Management. Findings: The conclusion of the Research is that the Researcher has analysed a large number of studies and have been reported on SD applications at the corporate level, and in different functional areas. Research Limitations: The main limitation for this study is that it is based on limited secondary data. Replicating the research approach with more comprehensive data would result in deriving better conclusion. Managerial Implications: The implications of the management is that system dynamics has been applied in many fields, among them medicine, law, urban studies, global studies, environmental studies, information science, literature, history, economics, finance, chemistry, physics, etc. Originality/Value: This study showcased the original work of the authors in the field of System Dynamics (SD), a methodology that judiciously combines the traditional management with cybernetics and computer simulation so as to carry out sound policy analysis.

ABSTRACTA framework for reliability and maintenance analysis of job shop manufacturing systems is proposed in this paper. An efficient preventive maintenance (PM) policy in terms of failure effects analysis (FEA) is proposed. Subsequently, reliability evaluation and component importance measure based on FEA are performed under the PM policy. A job shop manufacturing system is applied to validate the reliability evaluation and dynamic maintenance policy. Obtained results are compared with existed methods and the effectiveness is validated. Some vague understandings for issues such as network modelling, vulnerabilities identification, the evaluation criteria of repairable systems, as well as PM policy during manufacturing system reliability analysis are elaborated. This framework can help for reliability optimisation and rational maintenance resources allocation of job shop manufacturing systems.

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 engineering practice, structural system with dynamic output performance has gained more and more attention. Reliability analysis of these dynamic systems based on the real performance function is normally time-consuming, which is hard to accept in engineering. An SVR-NARX (Support vector machine regression-Nonlinear autoregressive with exogenous input) model is, therefore, established in this paper to replace the real performance function for reliability analysis. To further improve the efficiency for dynamic systems with small failure probability, importance sampling is combined with SVR-NARX model. Two nonlinear examples in this paper show that the established SVR-NARX model can accurately describe the dynamic behavior of the systems, and the proposed method is efficient and accurate for the reliability analysis of dynamic systems.

This paper presents a novel and simple approach to reliability analysis of phased-mission systems. The technique presented in this paper transforms a phased-mission system into several non-phased-mission systems, and thus allows each phase to be modeled separately. The mission succeeds as long as every phase successively executes its requirements, and failed component(s) of any phase is(are) repaired so that the system is in a successful state before as well as after it begins the next phase. Alternative mission success scenarios are also readily definable within this context. The benefit of this simplified approach is that it provides a practical implementation for the reliability analysis of phased-mission systems. The different phases of the system are computed independently, and the duration and the structure of the phases are left to the designer or manager. If the requirements of the mission change during execution of the mission (duration of a phase or the sequence of phases), the impact of the change in mission objectives is easily found without recomputing the applicable or operative Markov model. This is due to the fact that all of the reliability analysis data are presented over the entire mission duration consisting for all phases, and the initial and final probabilities can easily be found by examining the output reliability data instead of recomputing the model

Reliability and safety analysis for systems of fusion device

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.

Reliability analysis of repairable systems using Petri nets and vague Lambda-Tau methodology