A supplemental algorithm for the repairable system in the GO methodology

The GO methodology is an effective method of system reliability analysis and it can be used in the repairable system as well. The calculation formulas of the ordinary operators for the repairable components and the quantification algorithm of the steady characteristics of the repairable system have been presented in Ref. [6]. This paper provides a calculation formula of the failure rate for the repairable system with the independent components, and the calculation procedure of the equivalent failure rate and the average operation probability for the repairable system with the shared signals at complex case are presented. This supplemental algorithm is quite universal for the complex repairable system and quite convenient for calculation by computer. An example demonstrates the calculation process and the result shows that the algorithm is correct and available.     

A new quantification algorithm for the GO methodology

This paper provides a new quantification algorithm in the GO methodology, which includes three parts: (1) A signal state cumulative probability is introduced and defined based on the definitions of the signal states in the GO method. (2) The quantitative formulas of signal state cumulative probabilities have been derived, so it is unnecessary to calculate the joint probability of the complex combination of states. (3) The calculation process and the transfer rules about the shared signal have been presented, therefore, the new algorithm permits the direct calculation of all signal state cumulative probability. The new algorithm is very easy for programming. It is an improved algorithm in the GO methodology instead of the joint probability algorithm. The result of an example shows that the algorithm is practical and meaningful for development and application of the GO methodology and useful in practice.     

An exact algorithm dealing with shared signals in the GO methodology

This paper provides an exact quantification algorithm dealing with shared signals in the GO methodology. The exact calculation formulas of the output signal state probability of a logic operator, which includes the input signals with the shared signals, have been derived. All the shared signals should be transferred to the output signal of this logic operator and in the following calculation the formulas are still exact. This exact algorithm permits the direct calculation of all signal state probabilities of the systems. The result of an example shows that the exact algorithm is available and meaningful for more development of the GO methodology, it will be useful for more practical applications.     

Reliability technology using GO methodology: A review

Goal‐oriented (GO) methodology is a graphic inductive method mapping the system structure, its function constitute, characteristics, and working principle visually based on decision tree. Recently, the studies on reliability technologies for GO method of complex systems have been gotten a lot of attention by scholars because of the obvious advantages of modeling and analysis power. Indeed, the GO method has been applied in reliability and safety analysis of various areas, such as transportation and power systems, to prove its value. Thus, this paper provides a brief review of the GO method from aspects of providing its development history and its engineering applications and expounding its development of the theory of the GO method. At last, the future directions of GO method are discussed.     

A new reliability analysis method for repairable systems with multifunction modes based on goal‐oriented methodology

This paper proposes a new systematic reliability analysis method for repairable systems with multifunction modes based on the goal‐oriented (GO) method. First, we create a new function GO operator, a new logical GO operator, and a new auxiliary GO operator, deduce their GO operation formulas, and propose some new rules of the GO operation and an exact algorithm with shared signal of the GO method for such systems. Then, we formulate the analysis process of repairable systems with multifunction modes based on the new GO method. Finally, we apply this new GO methodology to reliability analysis of the control system for a heavy vehicle. To verify the feasibility, advantage, and reasonableness of the new GO methodology, we compare its analysis results with those of fault tree analysis and Monte Carlo simulation. We show that the proposed GO method has clear advantages in system reliability modeling and analysis. All in all, this study not only improves the theory of the GO method and widens its application but also provides a new approach for conducting reliability analysis of complex systems quickly and efficiently.     

Lifetime and reliability estimation of repairable redundant system subject to periodic alternation

Lifetime distribution and reliability are analyzed for redundant systems consisting of units that alternate between operating and standby states periodically to inspect and detect failures of standby units. It is assumed that when a unit fails, a minimal repair with negligible repair time is performed. A cumulative exposure model is used to describe the failure time distribution. The method of maximum likelihood is used to estimate the parameters, and specific formulas for Weibull model are obtained. A simulation model is then developed to assess the system reliability based on the estimated lifetime distribution and the method is applied to a high pressure pump system.     

A non-parametric monotone maximum likelihood estimator of time trend for repairable system data

The trend-renewal process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function λ(·) which is similar to the intensity of a non-homogeneous Poisson process (NHPP). A non-parametric maximum likelihood estimator of the trend function of a TRP is obtained under the often natural condition that λ(·) is monotone. An algorithm for computing the estimate is suggested and examined in detail in the case where the renewal distribution of the TRP is a Weibull distribution. The case where one has data from several systems is also briefly studied.     

An artificial neural network for modeling reliability, availability and maintainability of a repairable system

The paper explores the application of artificial neural networks to model the behaviour of a complex, repairable system. A composite measure of reliability, availability and maintainability parameters has been proposed for measuring the system performance. The artificial neural network has been trained using past data of a helicopter transportation facility. It is used to simulate behaviour of the facility under various constraints. The insights obtained from results of simulation are useful in formulating strategies for optimal operation of the system.     

On the overhaul effect for repairable mechanical units: a Bayes approach

This paper deals with the statistical analysis, from a Bayes viewpoint, of the failure data of repairable mechanical units subjected to minimal repairs and periodic overhauls. A proportional age reduction model is assumed to model the effect of overhauls on the reliability of the unit, whereas the failure process between two successive overhaul epochs is modeled by the power law process. Point and interval estimation of model parameters, as well as of quantities of large interest, are provided on the basis of a number of suitable prior densities, which reflect different degrees of belief on the failure/repair process. Hypothesis tests on the effectiveness of performed overhauls are developed on the basis of Bayes factor, and some guidelines to perform sensitivity analysis versus the prior information are provided. Finally, a numerical application illustrates the proposed inference and testing procedures.     

Determining the optimal maintenance action for a deteriorating repairable system

This paper develops a decision model for risk management of the deterioration of a repairable system. When a failure occurs in a deteriorating system, an optimal maintenance decision that includes the possibility of system replacement, as compared to mere deterioration reduction, should be made. There are many uncertainties associated with deterioration, however, so the decision may require a probabilistic analysis. Here, a well-known nonhomogeneous Poisson process with a power law intensity function is used to model the uncertain behavior of the deteriorating system. A Bayesian statistical approach is adopted to allow for the uncertainty of the parameters of the power law intensity function, which imposes a conjugate prior distribution of the parameters. A power law maintenance cost function and the failure cost are analyzed to determine the magnitude of failure risk reduction by minimizing the expected cost incurred from the maintenance action and future failures. A numerical example is given.     

退化串联可修系统瞬态可靠性分析

可修串联系统是一类经典的可靠性模型,在实际工程中较为常见．为满足工程实际需求,所研究的系统由2个部件和1个维修工组成．假设工作时间、维修时间和部件更换时间均服从指数分布,在维修之后系统不能修复如新．系统采用部件故障N次之后将被更新的维修策略．在这些假设下利用几何过程和马尔科夫过程对系统进行建模,再利用半马尔科夫过程和数值积分方法给出系统瞬态可用度和（0,t］时间内故障次数的计算公式．最后给出算例并应用Monte Carlo方法对所得公式进行验证．为进一步研究复杂机械系统的可靠性提供了理论基础．     

Analysis for a two-dissimilar-component cold standby repairable system with repair priority

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. Assume that working time distributions and repair time distributions of the two components are both exponential, and Component 1 has repair priority when both components are broken down. After repair, Component 1 follows a geometric process repair while Component 2 obeys a perfect repair. Under these assumptions, using the perfect repair model, the geometric process repair model and the supplementary variable technique, we not only study some important reliability indices, but also consider a replacement policy T, under which the system is replaced when the working age of Component 1 reaches T. Our problem is to determine an optimal policy T^? such that the long-run average loss per unit time (i.e. average loss rate) of the system is minimized. The explicit expression for the average loss rate of the system is derived, and the corresponding optimal replacement policy T^? can be found numerically. Finally, a numerical example for replacement policy T is given to illustrate some theoretical results and the model's applicability.     

Uncertainties and quantification of common cause failure rates and probabilities for system analyses

Simultaneous failures of multiple components due to common causes at random times are modelled by constant multiple-failure rates. A procedure is described for quantification of common cause failure (CCF) basic event probabilities for system models using plant-specific and multiple-plant failure-event data. Methodology is presented for estimating CCF-rates from event data contaminated with assessment uncertainties. Generalised impact vectors determine the moments for the rates of individual systems or plants. These moments determine the effective numbers of events and observation times to be input to a Bayesian formalism to obtain plant-specific posterior CCF-rates. The rates are used to determine plant-specific common cause event probabilities for the basic events of explicit fault tree models depending on test intervals, test schedules and repair policies. Three methods are presented to determine these probabilities such that the correct time-average system unavailability can be obtained with single fault tree quantification. Recommended numerical values are given and examples illustrate different aspects of the methodology.     

Optimizing the performance of a repairable system under a maintenance and repair contract

In this article a number of maintenance models for finite horizons are reviewed. These methods have not been applied as frequently as their infinite horizon counterparts, and yet are very much applicable to systems under maintenance and repair contracts. The emphasis in this paper is on repairable systems under maintenance and repair contracts, where the decision has to be made whether and when to repair or replace the system. Based on a case study, a new finite horizon model will be constructed and new approaches to analyze and improve repair/replacement decisions under a finite horizon introduced. Finally, the meaning of ‘risk’ and ‘criticality’ in the context of maintenance contracts will be discussed and quantified. Copyright © 2007 John Wiley & Sons, Ltd.     

Redundancy analysis for repairable multi-state system by using combined stochastic processes methods and universal generating function technique

This paper discusses a type of redundancy that is typical in a multi-state system. It considers two interconnected multi-state systems where one multi-state system can satisfy its own stochastic demand and also can provide abundant resource (performance) to another system in order to improve the assisted system reliability. Traditional methods are usually not effective enough for reliability analysis for such multi-state systems because of the “dimensional curse” problem. This paper presents a new method for reliability evaluation for the repairable multi-state system considering such kind of redundancy. The proposed method is based on the combination of the universal generating function technique and random processes methods. The numerical example is presented to illustrate the proposed method.     

Availability assessment of a two-unit stand-by pumping system

The paper aims at assessing the availability of a critical pumping system of the Crude Distillation Unit of a refinery with recourse to the Markovian model. Actual field data on failure and the repair times have been collected and analyzed by fitting exponential distribution. Also a simulation model has been developed for assessing the system availability. The availabilities based on both the analytical and the simulation models have been compared. The simulation model has been used for predicting system availability for varying failure and the repair rates. The repair strategies for the increasing failure rate in order to attain the desired availability have also been discussed in the paper.     

A risk-based optimisation methodology for pavement management system of county roads

A pavement management system (PMS) is a strategic and systematic process to maintain and upgrade the road network. When funding is limited, it is very important to identify the best mix of road preservation projects that provides the maximum benefits to society in terms of overall life cycle cost of the road network. The most common factors that play an important role for identifying projects are the following: budget, traffic volume, Present Serviceability Index (PSI) and risk associated with selecting treatment types. This research develops an optimisation methodology for county paved roads that identify the best mix of preservation projects within budget, maximising traffic (passengers and trucks traffic) on treated roads, maximising the weighted average PSI, and minimising the risk. This methodology will facilitate a statewide implementation of PMS for counties in the state of Wyoming.     

A bivariate optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k+1 states, including k failure states and one working state, is studied. It is assumed that the system after repair is not “as good as new” and the deterioration of the system is stochastic. We consider a bivariate replacement policy, denoted by (T,N), in which the system is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy (T,N)^* such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy (T,N)^* is better than the optimal policy N^* for a multistate simple repairable system. We also show that a general monotone process model for a multistate simple repairable system is equivalent to a geometric process model for a two-state simple repairable system in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.     

A condition-based maintenance policy with non-periodic inspections for a two-unit series system

This paper considers a condition-based maintenance policy for a two-unit deteriorating system. Each unit is subject to gradual deterioration and is monitored by sequential non-periodic inspections. It can be maintained by good as new preventive or corrective replacements. Every inspection or replacement entails a set-up cost and a component-specific unit cost but if actions on the two components are combined, the set-up cost is charged only once. A parametric maintenance decision framework is proposed to coordinate inspection/replacement of the two components and minimize the long-run maintenance cost of the system. A stochastic model is developed on the basis of the semi-regenerative properties of the maintained system state and the associated cost model is used to assess and optimize the performance of the maintenance model. Numerical experiments emphasize the interest of a control of the operation groupings.