Compound System Reliability Test Design Based on Bayesian Approach and Monte Carlo Method

Abstract

Analyzing the current lack of reliability test design and considering the producer’s risk and consumer’s risk, the reliability test design model for compound system (CSRTD) based on information fusion was constructed. Analyzing the requirements and constraint conditions of reliability test design, the information fusion technology between binomial distributed subsystems and their system was presented by means of Bayesian approach and Monte Carlo method. According to posteriori risk criteria, the formulas of producer’s risk and consumer’s risk were deduced. The solution of computing the optimum test plan was given by Matlab software. Finally, an example of missile launching installation was given to demonstrate the validity of the model. Introduction In the field of reliability test, the evaluation of the system reliability of product with high reliability and long life is one of the important problems, especially for the complex system such as aircrafts, missiles and satellites. Therefore, due to high cost and long test time, it is improper to perform reliability test by the traditional test method [1-3]. As the Bayesian theory has the advantage on reduce actual test numbers, it has been widely studied in the field of reliability test in recent years and gradually recognized by the international academic community. Belkacem et al [4] used the Bayesian network approach to formulate the reliability model of systems with uncertain structures. Sanku [5] obtained Bayes’ estimators for the unknown parameter of an Inverse Rayleigh distribution under symmetric and asymmetric linear exponential loss functions using a non-informative prior. Cai et al [6] developed a redundant software system for subsea blowout preventers by Bayesian networks. However, in many circumstance, the application of these methods may not give satisfactory result. The existing methods have at least the following problem:  When encountering complex compound system, we cannot obtain the prior distribution of system from the subsystems by analytic method, so the posterior distribution of system cannot be deduced by Bayesian theory.  The subsystems’ and system’s test cost should be totally taken into consideration, but the current researches pay fewer attentions on the total cost of reliability test. According to the above shortcomings, this paper presents a subsystem-to-system information fusion method for compound system by means of Bayesian approach and Monte Carlo method. And CSRTD (the reliability test design model for compound system) is built to figure out the minimum cost of the compound system when considering the constraints. At last, one numerical example is used to demonstrate the validity of the model.