Hong-Zhong Huang

Bayesian reliability analysis for fuzzy lifetime data

Lifetime data are important in reliability analysis. Classical reliability estimation is based on precise lifetime data. It is usually assumed that observed lifetime data are precise real numbers. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. Bayesian methods have proved to be very useful when the sample size is small. There is little study on Bayesian reliability estimation based on fuzzy lifetime data. Most of the reported works in this area is limited to single parameter lifetime distributions. In this paper, we propose a new method to determine the membership function of the estimates of the parameters and the reliability function of multi-parameter lifetime distributions. An artificial neural network is used to approximate the calculation process of parameter estimation and reliability prediction. The genetic algorithm is used to find the boundary values of the membership function of the estimate of interest at any cut level. This method can be used to determine the membership functions of the Bayesian estimates of multi-parameter distributions. The effectiveness of the proposed method is illustrated with normal and Weibull distributions.

An efficient method for reliability evaluation of multistate networks given all minimal path vectors

The multistate networks under consideration consist of a source node, a sink node, and some independent failure-prone components in between the nodes. The components can work at different levels of capacity. For such a network, we are interested in evaluating the probability that the flow from the source node to the sink node is equal to or greater than a demanded flow of d units. A general method for reliability evaluation of such multistate networks is using minimal path (cut) vectors. A minimal path vector to system state d is called a d-MP. Approaches for generating all d-MPs have been reported. Given that all d-MPs have been found, the issue becomes how to evaluate the probability of the union of the events that the component state vector is greater than or equal to at least one of the d-MPs. There is a need for a more efficient method of determining the probability of this union of events. In this paper, we report an efficient recursive algorithm for this union probability evaluation based on the Sum of Disjoint Products (SDP) principle, and name it the Recursive Sum of Disjoint Products (RSDP) algorithm. The basic idea is that, based on the SDP principle and a specially defined “maximum” operator, “⊕”, the probability of a union with L vectors can be calculated via calculating the probabilities of several unions with L−1 vectors or less. The correctness of RSDP is illustrated. The efficiency of this algorithm is investigated by comparing it with an existing algorithm that is generally accepted to be efficient. It is found that RSDP is more efficient than the existing algorithm when the number of components of a system is not too small. RSDP provides us with an efficient, systematic and simple approach for evaluating multistate network reliability given all d-MPs.

Optimal reliability, warranty and price for new products

The success of a new product depends on both engineering decisions (product reliability) and marketing decisions (price, warranty). A higher reliability results in a higher manufacturing cost and higher sale price. Consumers are willing to pay a higher price only if they can be assured about product reliability. Product warranty is one such tool to signal reliability with a longer warranty period indicating better reliability. Better warranty terms result in increased sales and also higher expected warranty servicing costs. Warranty costs are reduced by improvements in product reliability. Learning effects result in the unit manufacturing cost decreasing with total sales volume and this in turn impacts on the sale price. As such, reliability, price and warranty decisions need to be considered jointly. The paper develops a model to determine the optimal product reliability, price and warranty strategy that achieve the biggest total integrated profit for a general repairable product sold under a free replacement-repair warranty strategy in a market and looks at two scenarios for the pricing and warranty of the product. The model assumes that the sale rate increases as the warranty period increases and decreases as the price increases. The maximum principle method is used to obtain optimal solutions for dynamic price and warranty situations. Finally, numerical examples are given to illustrate the proposed model.

Probabilistic Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty

A probabilistic Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs operating under uncertainty is developed. The framework incorporates the overall uncertainties appearing in a structural integrity assessment. A comprehensive uncertainty quantification (UQ) procedure is presented to quantify multiple types of uncertainty using multiplicative and additive UQ methods. In addition, the factors that contribute the most to the resulting output uncertainty are investigated and identified for uncertainty reduction in decision-making. A high prediction accuracy of the proposed framework is validated through a comparison of model predictions to the experimental results of GH4133 superalloy and full-scale tests of aero engine high-pressure turbine discs.

Inverse Gaussian process models for degradation analysis: A Bayesian perspective

This paper conducts a Bayesian analysis of inverse Gaussian process models for degradation modeling and inference. Novel features of the Bayesian analysis are the natural manners for incorporating subjective information, pooling of random effects information among product population, and a straightforward way of coping with evolving data sets for on-line prediction. A general Bayesian framework is proposed for degradation analysis with inverse Gaussian process models. A simple inverse Gaussian process model and three inverse Gaussian process models with random effects are investigated using Bayesian method. In addition, a comprehensive sensitivity analysis of prior distributions and sample sizes is carried out through simulation. Finally, a classic example is presented to demonstrate the applicability of the Bayesian method for degradation analysis with the inverse Gaussian process models.

An Approach to Reliability Assessment Under Degradation and Shock Process

Product performance usually degrades with time. When shocks exist, the degradation could be more rapid. This research investigates the reliability analysis when typical degradation and shocks are involved. Three failure modes are considered: catastrophic (binary state) failure, degradation (continuous processes), and failure due to shocks (impulse processes). The overall reliability equation with three failure modes is derived. The effects of shocks on performance are classified into two types: a sudden increase in the failure rate after a shock, and a direct random change in the degradation after the occurrence of a shock. Two shock scenarios are considered. In the first scenario, shocks occur with a fixed time period; while in the second scenario, shocks occur with varying time periods. An engineering example is given to demonstrate the proposed methods.

An interactive fuzzy multi-objective optimization method for engineering design

Abstract The coupling of performance functions due to common design variables and uncertainties in an engineering design process will result in difficulties in optimization design problems, such as poor collaboration among design objectives and poor resolution of design conflicts. To handle these problems, a fuzzy interactive multi-objective optimization model is developed based on Pareto solutions, where the metric function and some additional constraints are added to ensure the collaboration among design objectives. The trade-off matrix at the Pareto solutions was developed, and the method for selecting weighting coefficients of optimization objectives is also provided. The proposed method can generate a Pareto optimal set with the maximum satisfaction degree and the minimum distance from ideal solution. The favorable optimal solution can be then selected from the Pareto optimal set by analyzing the trade-off matrix and collaborative sensitivity. Two examples are presented to illustrate the proposed method.

Grid Service Reliability Modeling and Optimal Task Scheduling Considering Fault Recovery

There has been quite some research on the development of tools and techniques for grid systems, yet some important issues, e.g., grid service reliability and task scheduling in the grid, have not been sufficiently studied. For some grid services which have large subtasks requiring time-consuming computation, the reliability of grid service could be rather low. To resolve this problem, this paper introduces Local Node Fault Recovery (LNFR) mechanism into grid systems, and presents an in-depth study on grid service reliability modeling and analysis with this kind of fault recovery. To make LNFR mechanism practical, some constraints, i.e. the life times of subtasks, and the numbers of recoveries performed in grid nodes, are introduced; and grid service reliability models under these practical constraints are developed. Based on the proposed grid service reliability model, a multi-objective task scheduling optimization model is presented, and an ant colony optimization (ACO) algorithm is developed to solve it effectively. A numerical example is given to illustrate the influence of fault recovery on grid service reliability, and show a high efficiency of ACO in solving the grid task scheduling problem.

Intelligent interactive multiobjective optimization method and its application to reliability optimization

In most practical situations involving reliability optimization, there are several mutually conflicting goals such as maximizing the system reliability and minimizing the cost, weight and volume. This paper develops an effective multiobjective optimization method, the Intelligent Interactive Multiobjective Optimization Method (IIMOM). In IIMOM, the general concept of the model parameter vector is proposed. From a practical point of view, a designers preference structure model is built using Artificial Neural Networks (ANNs) with the model parameter vector as the input and the preference information articulated by the designer over representative samples from the Pareto frontier as the desired output. Then with the ANN model of the designers preference structure as the objective, an optimization problem is solved to search for improved solutions and guide the interactive optimization process intelligently. IIMOM is applied to the reliability optimization problem of a multi-stage mixed system with five different value functions simulating the designer in the solution evaluation process. The results illustrate that IIMOM is effective in capturing different kinds of preference structures of the designer, and it provides a complete and effective solution for medium- and small-scale multiobjective optimization problems.

Genetic-algorithm-based optimal apportionment of reliability and redundancy under multiple objectives

When solving multi-objective optimization problems subject to constraints in reliability-based design, it is desirable for the decision maker to have a sufficient number of solutions available for selection. However, many existing approaches either combine multiple objectives into a single objective or treat the objectives as penalties. This results in fewer optimal solutions than would be provided by a multi-objective approach. For such cases, a niched Pareto Genetic Algorithm (GA) may be a viable alternative. Unfortunately, it is often difficult to set penalty parameters that are required in these algorithms. In this paper, a multi-objective optimization algorithm is proposed that combines a niched Pareto GA with a constraint handling method that does not need penalty parameters. The proposed algorithm is based on Pareto tournament and equivalence sharing, and involves the following components: search for feasible solutions, selection of non-dominated solutions and maintenance of diversified solutions. It deals with multiple objectives by incorporating the concept of Pareto dominance in its selection operator while applying a niching pressure to spread the population along the Pareto frontier. To demonstrate the performance of the proposed algorithm, a test problem is presented and the solution distributions in three different generations of the algorithm are illustrated. The optimal solutions obtained with the proposed algorithm for a practical reliability problem are compared with those obtained by a single-objective optimization method, a multi-objective GA method, and a hybrid GA method.