Imprecise reliability of cold standby systems

Components within a system may be related to one another in two primary ways: in either a serial or a parallel configuration. The other way associated system components is developed on the basis of series and parallel systems. Although some complex systems cannot generate from series and parallel system, the result of this paper is helpful to study more complex gradual system reliability problems. In this paper, a hypothesis is formed that the reliability of the components of the system is variable with time. Then, the reliability of the system is gradual, on condition that the components are combined by some related way. If the system reliability analysis is based on the static analysis, it may be different from the actual value of the reliability because the components of the system would afford stochastic load or generate degradation of performance. The method considering the random resistant degradation may make the result of reliability accurate. In this paper, gamma process is used to simulate the use of the components of the system, as deterioration is generally uncertain and non-decreasing, it can best be regarded as a gamma process. Combining the Edgeworth series method and forth moment technique, the method that calculate the reliability of series and parallel system is deduced. Then, the reliability of different systems and the failure rate of the systems are illustrated with time. The results show that the reliability of the systems will decline in different ways with time.

In consideration of some drawbacks of stochastic reliability method in theoretical and practical aspects, as well as the existence of insufficient and vague data in actual equipments design, the possbilistic reliability models of typically general systems are constructed in this paper. Characterizing the systems(components) failure behavior by possibility measures in place of probability measures, treating the systems (components) lifetime as fuzzy variables in the possibility space, and introducing possibilistic approaches into system reliability modeling and analysis, the possibilistic reliability theories are advanced based on possibilistic measurements. By expanding the universe of discourse, the derivation of system reliability models is simplified without loss of the nature of the problems to be solved, and proofs and calculations of possibilistic reliability of typical systems including series, parallel, series-parallel, parallel-series, and cold standby systems are much more straightforward than the traditional ones. The detailed application examples in system reliability analysis verify a possibilistic design framework on the general reliability models background, which provide some technical supports and guarantees for possibilistic reliability design and possibilistic reliability management in the case of limited statistical data.

Conventional reliability analysis of load-sharing parallel systems is mainly based on failure rate of components, in which failure dependence of components and load redistribution are also characterized by specified failure rates. However, the failure rate of mechanical components always varies with time, which is difficult to measure. Therefore, in this paper, quantitative dynamic reliability models of mechanical load-sharing parallel systems are developed in terms of stress parameters and strength parameters rather than failure rate of components, which consider the degradation mechanism of mechanical components. The proposed models take into account the strength degradation path dependence (SDPD) of a component, the strength degradation process dependence between different components in a system, and the random load redistribution. In addition, Monte Carlo simulation is carried out to verify the proposed models. The results show that SDPD and the load-sharing effect have considerable influences on dynamic reliability of mechanical load-sharing parallel systems.

Chapter 4 - Review on mechanical system reliability models

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.

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.

<div class="section abstract"><div class="htmlview paragraph">A study of the cockpit information system architecture of current single-engine single-pilot aircraft was performed to establish a baseline for the evaluation of the reliability of new cockpit systems being developed through the Advanced General Aviation Transport Experiments (AGATE) program. That study defines a “typical” General Aviation (GA) cockpit information system architecture consisting of 38 components making up 32 subsystems. It also developed a reliability (fault tree) model for the system and utilized a proprietary analysis tool to compute system reliability.</div><div class="htmlview paragraph">Fault tree reliability models have gained wide acceptance since their introduction in the 1960’s to analyze the probability of success of military defense systems. Fault trees use logic gates to express the relationships between failures of the components and resulting failures of subsystems and of the system.</div><div class="htmlview paragraph">In a subsequent study an analytical model corresponding to the specific cockpit system reliability model was developed and implemented in a spreadsheet format. In addition to the system reliability equation, all of the subsystem reliability equations were also derived. From the analytic reliability model, the sensitivities of all of the subsystem and system reliabilities to changes in the component reliabilities were derived. These equations were also implemented in the spreadsheet tool. The resulting tool allows a user to modify the component reliability parameters and compute and display the system and subsystem reliabilities and the sensitivities of these reliabilities to changes in the component reliabilities.</div><div class="htmlview paragraph">This paper describes the single-engine single-pilot aircraft cockpit information system reliability model, explains the derivation of the analytical model for reliability and sensitivity computation, discusses the insight obtained from the analytical model, and presents the application of the spreadsheet tool.</div></div>

In most mechanical and structural systems, a certain amount of uncertainty exists in both strength and load values. The uncertainty of these values must be taken into consideration when quantifying the safety and reliability of a system. Fuzzy set theory has been used for the description and analysis of such systems. A means for comparing fuzzy strength and load values is needed to determine the safety and reliability of fuzzy mechanical and structural systems. The concepts of fuzzy bounds and subsethood are used here to define a safety index for mechanical or structural systems based on fuzzy load and strength values. Similarly, a criticality index for fracture damage assessment is defined based on fuzzy stress intensity factors. The concept of a fuzzy factor of safety is also introduced. The proposed safety and criticality indices and the fuzzy factor of safety could provide useful measures for rating designs in terms of strength-based reliability and damage tolerance. The application of the proposed measures in the assessment of damage as reported by online structural damage detection systems is also suggested.

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.

With the proliferation of client-server systems there is a need for new approaches to determine their reliability in the uncertain environment of the internet. The proposed methods analyze client-server reliability by accounting for uncertainties in the operational environment of the internet. The uncertainties are addressed with a fuzzy paradigm applied in a tractable, verifiable reliability model of client-server systems. For computer hardware, fuzzy sets were used to address vague reliability data using bi-state fuzzy probabilistic theories. For software and operating systems, fuzzy sets account for the uncertainties in bi-state failure data using fuzzy possibility theories. Client-server architectures, such as hypercubes, and multistage interconnection networks are examined via logical and numerical approaches. Addressing uncertainties in the communication performance and expectations of client-server transactions requires a possibility-based fuzzy state model. Resulting from these approaches are fuzzy models that can handle uncertainty in failure data and the uncertain state of communication performance of the internet. The effect of fuzzy system reliability on the reliability of fault-tolerant networks was evaluated by fuzzy entropy and shown to be system-dependent. The possibility-based fuzzy Internet state was shown to have a large impact on the reliability of the system, depending upon the performance expectations. In conclusion, major sources of uncertainty in client-server systems are incorporated into a validated model for determining the reliability of client-saver systems placed on the internet.

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.

Increasing the complexity of power transmission networks has led power systems to be more vulnerable to cascading failures. Thus, hardening and reliability assessment of such complex networks have become a must. In addition, the commonly used N - 1 security criterion does not guarantee the reliability of the system against possible cascading failures. In this paper, given a hardening plan, we develop two models to evaluate the reliability of the power transmission system under N - k security criterion. In the first model, we quantify the probability of no load-shedding in the system to assess the possibility of load curtailment. Then, to have a better insight of the amount of load-shed in the second model, we use the conditional value-at-risk as a risk measure to evaluate the reliability of the system. To perform reliability assessment, the information of contingency probabilities is required. However, such probability information is usually unknown and cannot be estimated precisely. Therefore, in this paper, we assume the probability of contingencies as unknown and ambiguous. Then, we construct an ambiguity set for the unknown probability distribution of contingencies. Our approaches are robust because they analyze the reliability of the transmission system with respect to the worst-case distribution in the ambiguity set. We formulate both models as bilevel programs and solve them using the Bender's decomposition technique. Finally, we conduct numerical experiments on 6-bus and IEEE 118-bus test systems to show the effectiveness of the proposed approaches.

The relationship between the reliability probabilities of the component and the system is hard to get. If this relationship can be obtained easily, the reliability of the system can be calculated by using the reliability structures of the components. The common method to express this relationship is using the linear correlation index, which only shows the linear correlation between the components failure rather than the relationship between high nonlinear functions. In order to describe this relationship accurately and calculate the system reliability using the component reliability structures, a Uniform Design (UD)-Saddlepoint Approximation (SA)-based system reliability analysis method is proposed. The system reliability analysis method is decomposed to three simple steps: (1) calculating the weight coefficient which represents the contribution rate of each component to system reliability, (2) approximating Cumulant Generation Function (CGF) of each component, (3) calculating CGF of the system and approximating the system reliability with SA method. The weight coefficient of each component is derived from UD method, and a variable interval selection method is developed to decrease the required number of samples and increase the accuracy of the weight coefficients. First-Order Saddlepoint Approximation (FOSA) method or Mean-Value First-Order Saddlepoint Approximation (MVFOSA) method is used to analyze the CGF of a component performance function. Then the CGF of the system can be obtained by the weighted addition law by combining the CGFs of components performance functions with the weight coefficients. Finally, the system reliability can be approximated by SA method. Four examples are employed to demonstrate that the new method outperforms other methods for system reliability analysis in terms of efficiency and accuracy.

In this paper, structural systems reliability analysis was used to estimate the system reliability of a typical semi-submersible based on the characteristic structure failure mechanisms under extreme wave loads. First, a three-dimensional simulation model was created for the chosen semi-submersible platform using an elastic-perfectly plastic material model, neglecting the effect of the strain hardening assumption. Then, under design wave conditions, and characteristic structural failure mechanisms of a semi-submersible platform were examined, and a system reliability model was developed based on the failure mechanism of the chosen platform. Finally, system reliability methods were used to determine the platform’s system reliability. It was discovered that the main node’s system reliability makes a significant contribution to the overall structure reliability, so it is strongly advised that the reliability of the main nodes be taken into account when determining the overall structure’s reliability. This research aims to apply reliability theory in offshore engineering and, ideally, to encourage the reliability-based design of semi-submersible platforms and other similar structures.

This paper presents a Generalized Complementary Intersection Method (GCIM) that can predict system reliability for series, parallel, and mixed systems. The GCIM is an extension of the original study, referred to as the Complementary Intersection Method (CIM). The CIM was developed to assess system reliability for series systems. The contribution of this paper is to generalize the original CIM so that it can be used for system reliability analysis regardless of system structures (series, parallel, and mixed system). First, we derive a closed-form system reliability formula for a parallel system through its transformation into a series system using De Morgan’s law. Second, a unified system reliability analysis framework is proposed for mixed systems by defining a new System Structure matrix (SS-matrix) and employing the Binary Decision Diagram (BDD) technique. The SS-matrix is used to present any system structure in a comprehensive matrix form. Then the BDD technique together with the SS-matrix automates the process to identify system’s mutually exclusive path sets, of which each path set is a series system. As a result, system reliability with any system structure can be decomposed into the probabilities of the mutually exclusive path sets. Five engineering examples are used to demonstrate that the proposed GCIM can assess system reliability regardless of the system structures.