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Estimation Method of Confidence Interval of Weibull Distribution Parameters Based on Nonlinear Fitting

A technology of Weibull distribution and nonlinear fitting, applied in the field of reliability statistics, can solve the problem that the confidence interval estimation of Weibull distribution parameters cannot be given, etc.

Active Publication Date: 2020-08-07
NAT UNIV OF DEFENSE TECH
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Problems solved by technology

Through the above nonlinear fitting method, a point estimate of the parameters of the Weibull distribution can be given, but a confidence interval estimate of the parameters of the Weibull distribution cannot be given

Method used

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  • Estimation Method of Confidence Interval of Weibull Distribution Parameters Based on Nonlinear Fitting
  • Estimation Method of Confidence Interval of Weibull Distribution Parameters Based on Nonlinear Fitting
  • Estimation Method of Confidence Interval of Weibull Distribution Parameters Based on Nonlinear Fitting

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Embodiment Construction

[0037] The present invention will be described in further detail below in conjunction with examples.

[0038] This example utilizes the failure time data of a group of 9 sample products, and the failure times of these 9 sample products are respectively 96.9, 100.3, 100.8, 122.6, 103.3, 103.4, 105.4, 151.3 and 162.4 (hours), the specific method of the present invention as follows:

[0039] In the first step, the nine failure time data 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. Next, according to That is, formula (4) estimates that the corresponding failure probability estimates of each failure time data are 0.0745, 0.1809, 0.2872, 0.3936, 0.5, 0.6064, 0.7128, 0.8191 and 0.9255, and then use the error function, namely formula (3), based on the trust region The point estimate of the Weibull distribution parameters obtained by the reflection method is and .

[0040] In the second step, let the Weibull distribution fu...

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Abstract

The invention belongs to the technical field of reliability statistics, the invention discloses a confidence interval estimation method of Weibull distribution parameter based on nonlinear fitting. Firstly, according to the Weibull distribution parameter point estimation based on nonlinear fitting method, and then using the Weibull distribution parameter point estimation based on nonlinear fittingmethod under the specific Weibull distribution, the confidence interval estimation method of Weibull distribution parameter is given. The invention solves the problem of confidence interval estimation of Weibull distribution parameters under nonlinear fitting through the steps. Because the point estimation and confidence interval of Weibull distribution parameters are obtained simultaneously based on nonlinear fitting method, the consistency of the two methods is ensured. The key formulas for constructing confidence intervals are derived from pivot quantities, which can construct accurate confidence intervals of Weibull distribution parameters.

Description

technical field [0001] The invention relates to the field of reliability statistics, in particular to a method for estimating confidence intervals of Weibull distribution parameters based on nonlinear fitting. Background technique [0002] In the field of reliability statistics, the evaluation of product reliability is often involved. The key is to use the sample data of product life test to estimate the parameters in the distribution of product life, including point estimation and confidence interval estimation of parameters. [0003] The Weibull distribution is widely used to describe the lifetime of a product , whose distribution function is [0004] (1) [0005] The corresponding probability density function is [0006] (2) [0007] , are the two distribution parameters of the Weibull distribution, where is the shape parameter, is the scale parameter. [0008] When the product life obeys the Weibull distribution, for the estimation of the parameters o...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/18
CPCG06F17/18
Inventor 贾祥程志君郭波
Owner NAT UNIV OF DEFENSE TECH
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