Non-repairable Systems Research Articles

Failure mechanism dependence and reliability evaluation of non-repairable system

Reliability study of electronic system with the physics-of-failure method has been promoted due to the increase knowledge of electronic failure mechanisms. System failure initiates from independent failure mechanisms, have effect on or affect by other failure mechanisms and finally result in system failure. Failure mechanisms in a non-repairable system have many kinds of correlation. One failure mechanism developing to a certain degree will trigger, accelerate or inhibit another or many other failure mechanisms, some kind of failure mechanisms may have the same effect on the failure site, component or system. The destructive effect will be accumulated and result in early failure. This paper presents a reliability evaluation method considering correlativity among failure mechanisms, which includes trigger, acceleration, inhibition, accumulation, and competition. Based on fundamental rule of physics of failure, decoupling methods of these correlations are discussed. With a case, reliability of electronic system is evaluated considering failure mechanism dependence.

Incorporating Risk in an Optimization Model of Reliability Engineering

A non-repairable system is considered and the problem of finding its optimal preventive replacement time is revisited. In addition to minimizing the expected cost per unit time in a cycle, we also consider its variance as the measure of the risk of the optimal decision. A multi-objective optimization problem is then formulated where the two objective functions are the expectation and the variance. A sufficient condition is given for the existence of finite optimum in the case of the weighting method, where either the weight of the variance or the replacement costs are sufficiently small. In applying the e - constraint method there is always finite optimum if the upper bound for the expectation is close to its minimal value.

Durability Reliability Demonstration Test Methods

A complete product design cycle should include the following three stages: target setting, product design and development, and product validation. In the first target setting stage, it is required to understand the voice of customers (VOC), define the extreme customer usage conditions, acquire the duty cycle or customer usage data for the target, and cascade the top-down VOC targets from vehicle to system and component levels. In the second stage of product design and development, the multi-objective design optimization in the virtual analysis domain needs to be performed, where the analytical tools to design the products for various design criteria should have been developed and in place for analyses. In the final product validation stage, the test methods with a limited sample size are required to demonstrate the reliability of the product population for meeting the specific design functional and performance requirements. Since the test results exhibit significant statistical variations, these test methods (named the reliability demonstration test methods) are the most important mechanism to ensure a successful product launch for durability, reliability and quality. Again, due to the limited sample size for testing, a specific reliability and confidence target should be predetermined to be demonstrated by these test methods.The focus of this paper is to review the theoretical background and discuss the pros and cons of commonly used reliability demonstration test methods. Depending on the failure criterion in product validation testing, these reliability demonstration test methods can be categorized into the methods for non-repairable and repairable systems. For a non-repairable system, the test is considered complete, censored or suspended as the system fails, while a repairable system allows the actions required to restore/renew a failed system to operational status. The methods of interest for non-repairable systems include the test-to-failure method, the test-to-bogey method, the extended life test bogey method, and the step-stress accelerated life test method. Repairable systems are often modeled with the non-homogeneous Poisson process which includes the Duane and the Crow reliability growth models.

Optimal completed work dependent loading of components in cold standby systems

This paper considers the modelling and optimization of 1-out-of-N: G cold standby (CS) systems with non-repairable components functioning at different levels of productivity or load. The productivity heterogeneity leads to difference in component failure behaviour as well as in operational and replacement costs. Thus, the choice of load or productivity of components can greatly affect the system reliability and mission cost. To make the optimal choice of component loading, we first suggest a method for analysing the reliability and expected mission cost of 1-out-of-N: G non-repairable CS systems with heterogeneous components. The optimal dynamic load distribution problem is then formulated and solved, in which the component loading is chosen depending on the amount of work completed prior to the component activation. The optimal loading is aimed at minimizing the expected mission cost, while meeting a certain system reliability constraint. Examples are given to demonstrate the proposed methodology and the improvement in the optimal design solution through introducing the component productivity’s dependence on the completed work.

Mission Cost and Reliability of 1-out-of-$N$ Warm Standby Systems With Imperfect Switching Mechanisms

In this paper, mission cost and reliability of 1-out-of-N: G nonrepairable warm standby systems with imperfect switching are modeled and analyzed using an iterative method. A general switching structure is considered, which consists of an overall fault detection mechanism (FDM) and a set of individual switches (one for each standby element). The failure of the FDM prevents the replacement of the failed online element by any standby element while the failure of an individual switch only makes the corresponding standby element unavailable. The entire mission fails either when the FDM fails before the failure of the online element during the mission, or when all the system elements have failed or become unavailable before the mission completion. Based on the proposed algorithm for the mission cost and reliability analysis, the optimal element sequencing problem is further formulated and solved for 1-out-of-N: G nonrepairable warm standby systems with nonidentical elements and imperfect switching mechanisms. The objective of the problem is to find the optimal initiation sequence of system elements that can minimize the expected mission cost while providing a certain level of system reliability. Examples are given to illustrate the considered problem and the proposed solution methodology.

Reliability evaluation of non-reparable three-state systems using Markov model and its comparison with the UGF and the recursive methods

In multi-state systems (MSS) reliability problems, it is assumed that the components of each subsystem have different performance rates with certain probabilities. This leads into extensive computational efforts involved in using the commonly employed universal generation function (UGF) and the recursive algorithm to obtain reliability of systems consisting of a large number of components. This research deals with evaluating non-repairable three-state systems reliability and proposes a novel method based on a Markov process for which an appropriate state definition is provided. It is shown that solving the derived differential equations significantly reduces the computational time compared to the UGF and the recursive algorithm.

Optimal elements separation in non-repairable phased-mission systems

Enhancement of the survivability of a system can be achieved by separating its elements. Since different elements can play different roles in fulfilling the system mission, the way in which they are separated strongly affects the achieved level of the mission survivability. Thus, the optimal separation problem arises. This paper formulates a new problem of optimal element separation in non-repairable phased-mission systems (PMSs) where the mission consists of multiple, consecutive and non-overlapping phases of operation. An accurate survivability analysis of a PMS must consider the statistical dependence of element states across phases as well as dynamics in system structure function and element failure behaviour. We suggest a method for finding the separation of the system elements that provides a maximal possible level of the PMS survivability while satisfying a certain separation cost constraint. A backward recursion algorithm is applied for determining the survivability of a vulnerable PMS. A genetic algorithm is used as an optimization tool in solving the newly formulated separation problem for PMSs.

Impacts of Life Distributions on Reliability Analysis of Smart Substations

Most of the existing reliability analysis is based on exponential distribution which is convenient to calculation, whereas most intelligent electronic devices exhibit Weibull distribution. What kind of influence will life distribution have on the reliability and availability of a smart substation. This paper compares the reliability and availability of systems with different life distributions based on reliability block diagram and Monte-Carlo simulation, by treating the smart substations as non-repairable and repairable systems respectively. Simulation results proves the feasibility of substituting Weibull distribution with exponential distribution in engineering practice when the smart substations are treated as repairable systems, thus the life data estimation as well as the reliability analysis and calculation will be greatly simplified. DOI : http://dx.doi.org/10.11591/telkomnika.v12i4.4833

Flexible Design and Operation of a Smart Charging Microgrid

Abstract : The reliability theory of repairable systems is vastly different from that of non-repairable systems. The authors have recently proposed a decision-based framework to design and maintain repairable systems for optimal performance and reliability using a set of metrics such as minimum failure free period, number of failures in planning horizon (lifecycle), and cost. The optimal solution includes the initial design, the system maintenance throughout the planning horizon, and the protocol to operate the system. In this work, we extend this idea by incorporating flexibility and demonstrate our approach using a smart charging electric microgrid architecture. The flexibility is realized by allowing the architecture to change with time. Our approach learns the working characteristics of the microgrid. We use actual load and supply data over a short time to quantify the load and supply random processes and also establish the correlation between them. The quantified processes are then used to generate load and supply realizations over the long planning horizon. We show how this can reduce the computational effort when simulating microgrids for the entire planning horizon without impeding on their design under various operating scenarios considering uncertainty.

Optimal component loading in 1-out-of-N cold standby systems

This paper considers the optimal choice of productivity (load) of components in 1-out-of-N non-repairable cold standby systems. It is assumed that each system component can function at different levels of productivity (load) and that the life time acceleration factor as well as operational and replacement costs of each component are affected by its productivity. We present a model for evaluating the standby system reliability and expected mission cost. Furthermore, we formulate and solve the optimal load distribution problems in which the mission cost is minimized subject to system reliability constraint. Both fixed and variable sequences of component initiation are considered. Illustrative examples are provided.

A Multiple-Valued Decision-Diagram-Based Approach to Solve Dynamic Fault Trees

Dynamic fault trees (DFTs) have been used for many years because they can easily provide a concise representation of the dynamic failure behaviors of general non-repairable fault tolerant systems. However, when repeated failure events appear in real-life DFT models, the traditional modularization-based DFT analysis process can still generate large dynamic subtrees, the modeling of which can lead to a state explosion problem. Examples of these kinds of large dynamic subtrees abound in models of real-world dynamic software and embedded computing systems integrating with various multi-function components. This paper proposes an efficient, multiple-valued decision-diagram (MDD)-based DFT analysis approach for computing the reliability of large dynamic subtrees. Unlike the traditional modularization methods where the whole dynamic subtree must be solved using state-space methods, the proposed approach restricts the state-space method only to components associated with dynamic failure behaviors within the dynamic subtree. By using multiple-valued variables to encode the dynamic gates, a single compact MDD can be generated to model the failure behavior of the overall system. The combination of MDD and state-space methods applied at the component or gate level helps relieve the state explosion problem of the traditional modularization method, for the problems we explore. Applications and advantages of the proposed approach are illustrated through detailed analyses of an example DFT, and through two case studies.

Minimum Mission Cost Cold-Standby Sequencing in Non-Repairable Multi-Phase Systems

This paper considers the optimal cold standby element sequencing problem (SESP) for 1-out-of- n: G heterogeneous non-repairable cold-standby systems that accomplish multi-phase missions. Given a fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected mission cost while providing a desired level of system reliability. It is assumed that during different mission phases the elements are exposed to different stresses, which affects their time-to-failure distributions. The startup and exploitation costs of system elements are also phase dependent. We suggest an algorithm for evaluating the mission reliability and expected mission cost based on a discrete approximation of time-to-failure distributions of the system elements. A genetic algorithm is used as an optimization tool for solving the formulated SESP for multi-phase cold-standby systems. Examples are given to illustrate the considered problem and the proposed solution methodology.

A Multiple-Valued Decision Diagram Based Method for Efficient Reliability Analysis of Non-Repairable Phased-Mission Systems

Many practical systems are phased-mission systems (PMSs), where the mission consists of multiple, consecutive, and non-overlapping phases of operation. An accurate reliability analysis of a PMS must consider statistical dependence of component states across phases, as well as dynamics in system configurations, success criteria, and component behavior. This paper proposes a new method based on multiple-valued decision diagrams (MDDs) for the reliability analysis of a non-repairable binary-state PMS. Due to its multi-valued logic nature, the MDD model has recently been applied to the reliability analysis of multistate systems. In this work, we present a novel way to adapt MDDs for the reliability analysis of systems with multiple phases. Examples show how the MDD models are generated and evaluated to obtain the mission reliability measures. Performance of the MDD-based method is compared with an existing binary decision diagram (BDD)-based method for PMS analysis. Empirical results show that the MDD-based method can offer lower computational complexity as well as a simpler model construction and improved evaluation algorithms over those used in the BDD-based method.

On the Deterioration of Nonrepairable Multistate Strongly Coherent Systems

In the present paper, results given in Natvig (1990) are generalized to a multistate, strongly coherent, nonrepairable system of independent components by considering the reduction in remaining system time above a certain state due to a jump downwards of a component. This reduction also equals the increase in remaining system time above a certain state due to a minimal repair of the component at its time of jump downwards. The expected value of the sum of such reductions/increases for the different possible jumps downwards of the component is the building block of the Natvig measure of the importance of the component in the multistate case. Hence, the whole distributions of these reductions/increases are arrived at, not only the expectations, throwing more light on the consequences for the system of the deterioration of the components.

On the Deterioration of Nonrepairable Multistate Strongly Coherent Systems

In the present paper, results given in Natvig (1990) are generalized to a multistate, strongly coherent, nonrepairable system of independent components by considering the reduction in remaining system time above a certain state due to a jump downwards of a component. This reduction also equals the increase in remaining system time above a certain state due to a minimal repair of the component at its time of jump downwards. The expected value of the sum of such reductions/increases for the different possible jumps downwards of the component is the building block of the Natvig measure of the importance of the component in the multistate case. Hence, the whole distributions of these reductions/increases are arrived at, not only the expectations, throwing more light on the consequences for the system of the deterioration of the components.

Selection of Non-Repairable Series Systems’ Components with Weibull-Life and Lognormal-Repair Distributions through Minimizing Expected Total Cost of Ownership Approach

In this paper a model for selecting Weibull-life and Lognormal-repair components for a series system using Total Cost of Ownership (TCO) approach is proposed. The model has been used for selecting the suppliers of the different components constituting the system. The TCO of the system is calculated for each possible combination of components available in the market and then the combination that gives the minimum TCO is considered for purchasing. The results have showed that the model is able to compromise between the different cost categories such that the optimal cost elements values are between the minimum and maximum values of the cost categories.

Structure Optimization of Nonrepairable Phased Mission Systems

System structure optimization is a well-studied problem in the field of reliability engineering, which aims to achieve the best possible reliability versus cost solutions for the system design. This problem is usually solved for systems that do not change their task and configuration during the mission. However, many practical systems are phased-mission systems (PMS), where the mission involves multiple, consecutive, and nonoverlapping phases of operation. An accurate analysis of PMS must consider the dynamics in system configuration, success criteria, and element behavior as well as statistical dependence of element states across phases. In this paper, we propose a method for solving the structure optimization problem of multistate PMS consisting of nonidentical nonrepairable binary elements. The system configuration and demand as well as the failure distributions of system elements can change from phase to phase. The proposed approach is based on a recursive algorithm for the reliability evaluation of PMS and a genetic algorithm for the structure optimization of PMS. The method is illustrated using an example of a six-phased mission running on an airborne distributed computing system.

Reliability optimization of binary state non-repairable systems: A state of the art survey

Article history: Received September 22 2013 Received in Revised Format April 6 2014 Accepted May 18 2014 Available online May 25 2014 The purpose of this paper is to discuss the state of the art on models and methods for reliability optimization problems (ROPs) including reliability allocation, redundancy allocation and reliability-redundancy allocation. There are literally few surveys for reviewing the literature of the ROPs. Tillman et al. (1980) classified the related papers by system structure, problem type, and solution methods, separately. In another work, Tzafestas (1980) reviewed system reliability optimization models and the optimization techniques. Yearout (1986) reviewed the literature related to standby redundancy. Kuo (2000) studied the system reliability optimization based on system structure and solution methods. Kuo and Prasad (2004) overviewed system reliability optimization methods. Later, Kuo (2007) reviewed recent advances in optimal reliability allocation problems. The present study adds to the previous literature surveys and focuses mainly on papers after year 2000 but with a quick review on the previous works so that the readers become familiar with the existing approaches. This research investigates the literature from system structure, system performance, uncertainty state and solution approach standpoints, simultaneously.

Cold vs. hot standby mission operation cost minimization for 1-out-of-N systems

It is well recognized that using the hot standby redundancy provides fast restoration in the case of failures. However the redundant elements are exposed to working stresses before they are used, which reduces the overall system reliability. Moreover, the cost of maintaining the hot redundant elements in the operational state is usually much greater than the cost of keeping them in the cold standby mode. Therefore, there exists a tradeoff between the cost of losses associated with the restoration delays and the operation cost of standby elements. Such a trade-off can be obtained by designing both hot and cold redundancy types into the same system. Thus a new optimization problem arises for the standby system design. The problem, referred to in this work as optimal standby element distributing and sequencing problem (SE-DSP) is to distribute a fixed set of elements between cold and hot standby groups and select the element initiation sequence so as to minimize the expected mission operation cost of the system while providing a desired level of system reliability. This paper first formulates and solves the SE-DSP problem for 1-out-of-N: G heterogeneous non-repairable standby systems. A numerical method is proposed for evaluating the system reliability and expected mission cost simultaneously. This method is based on discrete approximation of time-to-failure distributions of the system elements. A genetic algorithm is used as an optimization tool for solving the formulated optimization problem. Examples are given to illustrate the considered problem and the proposed solution methodology.

Reliability of Series-Parallel Systems With Random Failure Propagation Time

This paper presents an algorithm for evaluating the reliability and performance distribution of complex non-repairable series-parallel multi-state systems with common cause failures caused by propagation of failures in system elements. The failure propagation can have a selective effect, which means that the failures originating from different elements can cause failures of different subsets of system elements. The failure propagation time is assumed to be a random value with a given distribution. The suggested algorithm is based on the universal generating function approach, and a generalized reliability block diagram method (recursive aggregation of pairs of elements and their replacement by an equivalent one). The evaluation procedure is repeated for each combination of elements affected by the common cause failures. Illustrative examples are provided.