A Method for Quantitatively Describing Fuzzy Prior Information in Bayesian Estimation

Abstract:

In order to precisely evaluate reliability under small sample size, prior information such as expert judgment is needed in Bayesian reliability estimation. General Bayesian method cannot deal with expert judgment when it is fuzzy. With a quantitative description method of fuzzy prior distribution for microphone selectors introduced, based on fuzzy membership functions, experts’ prior information can be effectively merged with test data with Bayes method. Reliability evaluation shows that, the precision can be enhanced notably for data with small samples by using Bayes estimation with fuzzy prior distributions. Furthermore, triangle fuzzy prior distributions can be used to enhance the precision when the bandwidth of the fuzzy prior distributions are wide. And normal distributions are applicable to the circumstance when the fuzzy prior distributions are narrow.

Key words:fuzzy prior information; Bayes method; reliability evaluation; small samples