Journal ArticleDOI
Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach
Reads0
Chats0
TLDR
In this paper, a systematic approach using the Monte Carlo method has been taken to determine the optimal probability estimators for unbiased estimation of m (mean, median and mode) using the general equation F = ( i − a ) / ( N + b ) whilst simultaneously minimising the coefficient of variation for each of the average values.Abstract:
The wide applicability of the Weibull distribution to fields such as hydrology and materials science has led to a large number of probability estimators being proposed, in particular for the widely used technique of obtaining the Weibull modulus, m, using unweighted linear least squares (LLS) analysis. In this work a systematic approach using the Monte Carlo method has been taken to determining the optimal probability estimators for unbiased estimation of m (mean, median and mode) using the general equation F = ( i − a ) / ( N + b ) whilst simultaneously minimising the coefficient of variation for each of the average values. A wide range of a and b values were investigated within the region 0 ≤ a ≤ 1 and 1 ≤ b ≤ 1000 with the form of F = ( i − a ) / ( N + 1 ) being chosen as the recommend probability estimator equation due to its simplicity and relatively small coefficient of variation. Values of a as a function of N were presented for the mean, median and mode m values.read more
Citations
More filters
Journal ArticleDOI
Is a three-parameter Weibull function really necessary for the characterization of the statistical variation of the strength of brittle ceramics?
TL;DR: In this article, it was shown that two-parameter Weibull function is sufficient for the description of the statistical variation of the conventionally adopted small strength sample, regardless of whether the strength follows a twoparameter or a threeparameter weibull distribution.
Journal ArticleDOI
Determination of the Weibull parameters from the mean value and the coefficient of variation of the measured strength for brittle ceramics
Bin Deng,Danyu Jiang +1 more
TL;DR: In this article, an unbiased estimation for Weibull modulus can be derived directly from the coefficient of variation of the considered strength sample, and the scale parameter σ0 can also be estimated accurately.
Journal ArticleDOI
Confidence interval estimation of Weibull lower percentiles in small samples via Bayesian inference
Meryem Yalçinkaya,Burak Birgören +1 more
TL;DR: In this article, the authors proposed the Bayesian Weibull Method as an alternative using the information that ceramic and composite materials have increasing failure rates, which requires the weibull shape parameter to be at least 1.
Journal ArticleDOI
Confidence limits for Weibull parameters estimated using linear least squares analysis
TL;DR: In this article, a Monte Carlo procedure was used to obtain probability distributions for unbiased estimates of Weibull modulus, m, and scale parameter, S o, as a function of total specimen number.
Journal ArticleDOI
Minimum lifetime of ZERODUR® structures based on the breakage stress threshold model: a review
TL;DR: In this paper, the authors used the Weibull distribution of ground surfaces to calculate the minimum lifetime of glass ceramic ZERODUR® for optical elements with high mechanical loads, which is equivalent to a minimum strength below which breakage probability is zero.
References
More filters
Journal ArticleDOI
A Statistical Distribution Function of Wide Applicability
TL;DR: In this article, the applicability of statistics to a wide field of problems is discussed, and examples of simple and complex distributions are given, as well as a discussion of the application of statistics in a wide range of problems.
Journal ArticleDOI
The Future of Data Analysis
TL;DR: For a long time I have thought I was a statistician, interested in inferences from the particular to the general as mentioned in this paper. But as I have watched mathematical statistics evolve, I have had cause to wonder and to doubt.
Journal ArticleDOI
The Probability Plot Correlation Coefficient Test for Normality
TL;DR: In this paper, the normal probability plot correlation coefficient (NPC) was used as a test statistic for the composite hypothesis of normality, and the proposed test statistic is conceptnally simple, is compntationally convenient, and is readily extendible to testing non-normal distributional hypotheses.
Journal ArticleDOI
A plotting rule for extreme probability paper
TL;DR: In this paper, a plotting rule for the ith of n ordered observations from a double exponential distribution is obtained as i = (i − 044)/(n + 012), where n is the number of observations, i is the order of the observation from the smallest, and i is an estimate of the cumulative frequency of the term.