Reliability confidence lower limit construction method based on the Bayesian theory and linear fitting

Abstract

The invention belongs to the technical field of reliability statistics. The invention discloses a reliability confidence lower limit construction method based on the Bayesian theory and linear fitting, and the method comprises the steps: calculating the confidence upper limit of the failure probability of each sample product life test data according to the Bayesian theory for each given sample product life test data, namely the failure time of each sample product; converting the Weibull distribution function into a linear function; and finally, constructing a confidence lower limit curve of the Weibull distribution reliability based on linear fitting. Through the steps, the construction problem of the lower confidence limit of the Weibull reliability is well solved. In each step of the method, a determination form of a corresponding mathematical expression is given, and the whole process is convenient to calculate, so that the method is very suitable for application in engineering practice.

Description

technical field [0001] The invention relates to the technical field of reliability statistics, in particular to a reliability confidence lower limit construction method based on Bayesian theory and linear fitting in Weibull distribution occasions. Background technique [0002] In the field of reliability statistics, it often involves evaluating product reliability based on product life test data, and the lower confidence limit of reliability is an important indicator. The Weibull distribution is widely used to describe the life T of a product, and its probability density function is [0003] [0004] The corresponding distribution function is [0005] [0006] The reliability function is [0007] [0008] m and η are the two distribution parameters of the Weibull distribution, where m is the shape parameter and η is the scale parameter. Under a given confidence level (1-α), the lower confidence limit R of the reliability R(t) L (t) meet [0009] P[R(t)≥R L (t)...

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Problems solved by technology

[0016] 2. It can be seen from the above process that Thoman et al [Reference 1: Thoman, D.R., Bain, L.J., Antle, C.E. Maximum likelihood estimation, exact confidence intervals for reliability, and tolerance limits in the Weibull distribution. Technometrics, 1970, 12( 2): 363-371.] The core of the proposed method is the reliability point estimation in formula (5) However, in the process of constructing the lower confidence limit of the reliability, the maximum likelihood estimation and Monte Carlo simulation operation of the Weibull distribution parameters in the calculation formula (4) are involved, and it is difficult to give the extreme The definite expression of the large likelihood estimation, and the Monte Carlo simulation operation takes a lot of time, so the method proposed by Thoman et al. is not conducive to engineering applications

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