Journal ArticleDOI
Inferences on the Parameters of the Weibull Distribution
TLDR
The problems of estimation and testing hypotheses regarding the parameters in the Weibull distribution are considered in this paper, where exact confidence intervals for the parameters based upon maximum likelihood estimators are presented.Abstract:
The problems of estimation and testing hypotheses regarding the parameters in the Weibull distribution are considered in this paper. The following results are given: 1. Exact confidence intervals for the parameters based upon maximum likelihood estimators are presented. 2. A table of unbiasing factors (depending upon sample size) for the maximum likelihood estimator of the shape parameter is given. 3. Tests of hypotheses regarding the parameters and the power of the test regarding the shape parameter are developed and presented. 4. Sample sizes at which large sample theory may be useful are presented.read more
Citations
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Journal ArticleDOI
A practical and systematic review of Weibull statistics for reporting strengths of dental materials
Janet B. Quinn,George D. Quinn +1 more
TL;DR: Weibull analysis has a strong theoretical basis and can be of particular value in dental applications, primarily because of test specimen size limitations and the use of different test configurations.
Journal ArticleDOI
On estimating the Weibull modulus for a brittle material
K. Trustrum,A. De S. Jayatilaka +1 more
TL;DR: In this paper, the authors surveyed common methods of estimating the Weibull modulus and their respective adjustment factors, for a range of experimentally feasible sample sizes, are given.
Journal ArticleDOI
The Weibull Distribution: A New Method of Summarizing Survivorship Data
TL;DR: The shape parameter controls the rate of change of the age- specific mortality rate and, therefore, the general form of the survivorship curve.
Journal ArticleDOI
Synchronizing shared abstract types
TL;DR: The analysis indicates a significant difference between the models based on the exponential distribution and those based onThe decreasing hazard rate Weibull distribution, which means system designers should be aware of these differences.
Journal ArticleDOI
Strength Measurement of Optical Fibers by Bending
TL;DR: A bending technique for the strength measurement of glass fibers is described and an analysis is presented which determines the effective tested length as a function of the statistical parameters which describe the fracture properties of the fiber as discussed by the authors.
References
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Journal ArticleDOI
Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples
TL;DR: In this paper, maximum likelihood equations are derived for estimating the distribution parameters from (i) complete samples, (ii) singly censored samples and (iii) progressively (multiple) censored samples.
Journal ArticleDOI
Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings
J. Lieblein,M. Zelen +1 more
TL;DR: This paper summarizes the principal results of the analyses undertaken by the National Bureau of Standards, and describes the statistical procedures used in the investigation.
Journal ArticleDOI
Estimation of the Shape and Scale Parameters of the Weibull Distribution
TL;DR: In this article, the shape parameter c and the scale parameter b of the Weibull distribution on the assumption that the location parameter is known were estimated by first finding an estimate of 1/c, and then setting ĉ = 1/.