Tieling Zhang

Availability and reliability of k-out-of-(M+N):G warm standby systems

Redundancy or standby is a technique that has been widely applied to improving system reliability and availability in system design. In most cases, components in standby system are assumed to be statistically identical and independent. However, in many practical applications, not all components in standby can be treated as identical because they have different failure and repair rates. In this paper, one kind of such systems with two categories of components is studied, which is named k-out-of-(M+N):G warm standby system. In the system, one category of the components is of type 1 and the other type 2. There are M type 1 components and N type 2 components. Components of type 1 have a lower failure rate and are preferably repaired if there is one failed. There are r repair facilities available. By using Markov model, the system state transition process can be clearly illustrated, and furthermore, the solutions of system availability and reliability are obtained based on this. An example representing a power-generator and transmission system is given to illustrate the solutions of the system availability and reliability.

Failure Data Analysis with Extended Weibull Distribution

A three-parameter distribution called extended Weibull distribution is investigated in this article. This model is generated by a method of introducing an additional parameter into a family of distributions by Marshall and Olkin (1997). It has two-parameter Weibull distribution as a special case. One of the merits of this distribution is that the hazard-rate can be increasing, decreasing, or initially increasing, then decreasing and eventually increasing. The model characterization based on the Weibull Probability Plot (WPP) is studied in this article. The WPP for actual data set can be concave, convex, or likely S-shaped. A procedure is provided for parameter estimation based on WPP. In addition, the maximum likelihood estimation is also presented. An example is shown to illustrate the procedure and application.

On the upper truncated Weibull distribution and its reliability implications

The characteristics and application of the truncated Weibull distribution are studied in this paper. This distribution is applicable to the situation where the test data are bounded in an interval because of test conditions, cost and other restrictions. An important property of the truncated Weibull distribution is that it can have bathtub-shaped failure rate function. In this paper, the parametric analysis and parameter estimation methods of the distribution are investigated. Both the graphical approach and the maximum likelihood estimation are considered. The applicability of this distribution to modeling lifetime data is illustrated by an example and the results of comparisons to other competitive models in modeling the given data are also presented. Moreover, the possible application of the distribution to modeling component or system failure is discussed.

State probability of a series-parallel repairable system with two-types of failure states

This paper presents a method for the analysis of a series-parallel safety-critical system where the system states can be distinguished into failure-safe and failure-dangerous. The method incorporates the Markov chain and universal generating function technique. In the model considered, both periodic inspection and repair (perfect and imperfect) of system elements are taken into account. The system state distributions and the overall system safety function are derived, based on the developed model. The proposed method is applicable to complex systems for analysing state distributions and it is also useful in decision-making such as determining the optimal proof-test interval or repair resource allocation. An illustrative example is given.

Choosing an optimal model for failure data analysis by graphical approach

Abstract Many models involving combination of multiple Weibull distributions, modification of Weibull distribution or extension of its modified ones, etc. have been developed to model a given set of failure data. The application of these models to modeling a given data set can be based on plotting the data on Weibull probability paper (WPP). Of them, two or more models are appropriate to model one typical shape of the fitting plot, whereas a specific model may be fit for analyzing different shapes of the plots. Hence, a problem arises, that is how to choose an optimal model for a given data set and how to model the data. The motivation of this paper is to address this issue. This paper summarizes the characteristics of Weibull-related models with more than three parameters including sectional models involving two or three Weibull distributions, competing risk model and mixed Weibull model. The models as discussed in this present paper are appropriate to model the data of which the shapes of plots on WPP can be concave, convex, S-shaped or inversely S-shaped. Then, the method for model selection is proposed, which is based on the shapes of the fitting plots. The main procedure for parameter estimation of the models is described accordingly. In addition, the range of data plots on WPP is clearly highlighted from the practical point of view. To note this is important as mathematical analysis of a model with neglecting the applicable range of the model plot will incur discrepancy or big errors in model selection and parameter estimates.

Reliability modeling and analysis for a novel design of modular converter system of wind turbines

Abstract Converters play a vital role in wind turbines. The concept of modularity is gaining in popularity in converter design for modern wind turbines in order to achieve high reliability as well as cost-effectiveness. In this study, we are concerned with a novel topology of modular converter invented by Hjort, Modular converter system with interchangeable converter modules. World Intellectual Property Organization, Pub. No. WO29027520 A2; 5 March 2009, in this architecture, the converter comprises a number of identical and interchangeable basic modules. Each module can operate in either AC/DC or DC/AC mode, depending on whether it functions on the generator or the grid side. Moreover, each module can be reconfigured from one side to the other, depending on the system’s operational requirements. This is a shining example of full-modular design. This paper aims to model and analyze the reliability of such a modular converter. A Markov modeling approach is applied to the system reliability analysis. In particular, six feasible converter system models based on Hjort’s architecture are investigated. Through numerical analyses and comparison, we provide insights and guidance for converter designers in their decision-making.

Reliability of fault-tolerant systems with parallel task processing

Abstract The paper considers performance and reliability of fault-tolerant software running on a hardware system that consists of multiple processing units. The software consists of functionally equivalent but independently developed versions that start execution simultaneously. The computational complexity and reliability of different versions are different. The system completes the task execution when the outputs of a pre-specified number of versions coincide. The processing units are characterized by different availability and processing speed. It is assumed that they are able to share the computational burden perfectly and that execution of each version can be fully parallelized. The algorithm based on the universal generating function technique is used for determining the distribution of system task execution time. This algorithm allows analysts to evaluate complex hardware–software reliability and performance indices such as expected task execution time and probability that the task is completed within a given time. Illustrative examples are also presented.

Modular converter system reliability & performance analysis in design

Converter system plays an important role in power drive train of a wind turbine. In order to achieve higher reliability, the modular concept is popularly utilized in converter system design in modern wind turbines. A converter module can be a channel composed of AC/DC/AC or a module composed of AC/DC or DC/AC. AC/DC module can be used on either generator side or grid side which depends on system operation. This is the full-modular concept in converter system design. This paper is focused on modular converter system reliability and performance analysis in design. Markov model is applied to system reliability modeling. Six system modules are studied, in which a converter module is an AC/DC or DC/AC module. The system reliability and performance indices serve as guideline in system module selection in design.

Calibrating Markov Chain-Based Deterioration Models for Predicting Future Conditions of Railway Bridge Elements

Existing nonlinear optimization-based algorithms for estimating Markov transition probability matrix (TPM) in bridge deterioration modeling sometimes fail to find optimum TPM values, and hence lead to invalid future condition prediction. In this study, a Metropolis-Hasting algorithm (MHA)-based Markov chain Monte Carlo (MCMC) simulation technique is proposed to overcome this limitation and calibrate the state-based Markov deterioration models (SBMDM) of railway bridge components. Factors contributing to rail bridge deterioration were identified; inspection data for 1,000 Australian railway bridges over 15 years were reviewed and filtered. The TPMs corresponding to a typical bridge element were estimated using the proposed MCMC simulation method and two other existing methods, namely, regression-based nonlinear optimization (RNO) and Bayesian maximum likelihood (BML). Network-level condition state prediction results obtained from these three approaches were validated using statistical hypothesis tests with a test data set, and performance was compared. Results show that the MCMC-based deterioration model performs better than the other two methods in terms of network-level condition prediction accuracy and capture of model uncertainties.

Analyzing Highly Censored Reliability Data without Exact Failure Times: An Efficient Tool for Practitioners

ABSTRACT There are many real-life situations where exact failure times are not available or not easily available for reliability analysis. Motivated by this problem, this work is concerned with the analysis of reliability data without exact failure times. The unavailability of exact failure times has compelled us to develop a simplified version of the maximum likelihood (ML) estimation for reliability parameters and measures. The approach is applicable to single-parameter reliability models including the exponential reliability model and the Weibull reliability model with an assumed or known shape parameter value. In the latter case, it takes advantage of the fact that in many practical situations a reasonable estimate of the Weibull shape parameter is attainable by certain means. This is particularly valuable for reliability assessment of highly censored Weibull data with only a few failures, because in such situations it is highly desirable or necessary to exploit prior knowledge of the Weibull shape parameter to compensate for the limited information contained in the data in the hope of making a sound assessment. This is an application in a sense of the ideas and principles of the emerging paradigm of statistical engineering. The methods are developed by practitioners and for practitioners. We show that they offer practitioners a handy and efficient tool for reliability analysis, using hard disk drive product testing as examples.