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

A technology of Bayesian theory and lower confidence limit, which is applied in the direction of complex mathematical operations, can solve problems such as unfavorable engineering applications and time-consuming, and achieve the effect of convenient calculation

Pending Publication Date: 2019-04-12
NAT UNIV OF DEFENSE TECH
View PDF4 Cites 2 Cited by
  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

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

Method used

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
View more

Image

Smart Image Click on the blue labels to locate them in the text.
Viewing Examples
Smart Image
  • Reliability confidence lower limit construction method based on the Bayesian theory and linear fitting
  • Reliability confidence lower limit construction method based on the Bayesian theory and linear fitting
  • Reliability confidence lower limit construction method based on the Bayesian theory and linear fitting

Examples

Experimental program
Comparison scheme
Effect test

Embodiment Construction

[0045] The present invention will be described in further detail below in conjunction with examples.

[0046] This example utilizes the failure data of a group of 9 sample products, and the failure time of these 9 sample products is respectively 96.9,100.3,100.8,122.6,103.3,103.4,105.4,151.3 and 162.4 (hours), and the concrete method of the present invention is as follows Shown:

[0047] Firstly, the failure times of the nine sample products are arranged in ascending order as 96.9, 100.3, 100.8, 103.3, 103.4, 105.4, 122.6, 151.3 and 162.4.

[0048] Then, based on the failure probability p i The posterior distribution Beta(p i ; 1.5,n-i+0.5), giving the failure probability p at the confidence level of 0.9 i The upper confidence limit for estimated value of where i=1,...,9. The upper confidence limits of the failure probabilities at the failure times of the nine sample products arranged in ascending order are 0.2631, 0.2871, 0.3158, 0.3509, 0.3944, 0.45, 0.523, 0.6218 an...

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to view more

PUM

No PUM Login to view more

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)...

Claims

the structure of the environmentally friendly knitted fabric provided by the present invention; figure 2 Flow chart of the yarn wrapping machine for environmentally friendly knitted fabrics and storage devices; image 3 Is the parameter map of the yarn covering machine
Login to view more

Application Information

Patent Timeline
no application Login to view more
IPC IPC(8): G06F17/18
CPCG06F17/18
Inventor 贾祥程志君郭波
Owner NAT UNIV OF DEFENSE TECH
Who we serve
  • R&D Engineer
  • R&D Manager
  • IP Professional
Why Eureka
  • Industry Leading Data Capabilities
  • Powerful AI technology
  • Patent DNA Extraction
Social media
Try Eureka
PatSnap group products

Browse by: Latest US Patents, China's latest patents, Technical Efficacy Thesaurus, Application Domain, Technology Topic.

© 2024 PatSnap. All rights reserved.Legal|Privacy policy|Modern Slavery Act Transparency Statement|Sitemap