Estimation Method of Weibull Distribution Parameters Based on Logarithmic Transformation of Distribution Function

A technique of Weibull distribution and distribution function, applied in the field of reliability statistics, can solve the problem of "overestimation of distribution parameters", and achieve the effect of simplifying calculation and ensuring accuracy

Active Publication Date: 2019-03-22
NAT UNIV OF DEFENSE TECH
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Problems solved by technology

[0018] Since the maximum likelihood estimation method is likely to cause "overestimation" of the distribution parameters, the distribution curve fitting method should be used

Method used

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  • Estimation Method of Weibull Distribution Parameters Based on Logarithmic Transformation of Distribution Function
  • Estimation Method of Weibull Distribution Parameters Based on Logarithmic Transformation of Distribution Function
  • Estimation Method of Weibull Distribution Parameters Based on Logarithmic Transformation of Distribution Function

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Embodiment Construction

[0039] The present invention will be described in further detail below in conjunction with examples.

[0040] This example utilizes the time-to-failure data of a group of 9 sample products, and the time-to-failure 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), concrete method of the present invention as follows:

[0041] 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. Then according to formula (4), the corresponding failure probability estimated values ​​of each failure time data are estimated to be 0.0745, 0.1809, 0.2872, 0.3936, 0.5, 0.6064, 0.7128, 0.8191 and 0.9255.

[0042] In the second step, the Weibull distribution function is logarithmically transformed using formula (5), and then let where i=1,...,9.

[0043] Finally, according to formula (6), the point estimate of the Weibull distribution parameter is obt...

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Abstract

The invention belongs to the technical field of reliability statistics, and discloses a Weibull distribution parameter estimation method based on logarithmic transformation of distribution function, which firstly calculates failure probability point estimation at each sample data, then takes logarithmic transformation of Weibull distribution function, then fits the transformed function according to distribution curve fitting method, and provides an estimation method of Weibull distribution parameter. By logarithmic transformation of the Weibull distribution function, the invention can convertthe Weibull distribution function into a linear form, thereby simplifying the calculation of the Weibull distribution parameter estimation. In addition, when fitting the distribution curve, it is considered that the abscissa in the axis is not changed, therefore, instead of using the common principle of minimizing the error of ordinate fitting in coordinate axis, the principle of minimizing the error of abscissa fitting in coordinate axis is used to ensure the accuracy of Weibull distribution parameter estimation.

Description

technical field [0001] The invention mainly relates to the field of reliability statistics, in particular to a Weibull distribution parameter estimation method based on logarithmic transformation of distribution functions. 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, which generally refers to the point estimation of parameters. [0003] The Weibull distribution is widely used to describe the life T of the product, and the distribution function of the Weibull distribution is [0004] [0005] Correspondingly, the probability density function of the Weibull distribution is [0006] [0007] m and η are the two distribution parameters of the Weibull distribution, where m is the shape parameter and η is the scale parameter. [0008] When the product life obeys the Weibull d...

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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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