Journal Article10.1109/TR.1987.5222306
A Method to Estimate the Weibull Parameters for Progressively Censored Tests
M. Cacciari,Gian Carlo Montanari +1 more
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TL;DR: In this article, a statistical procedure is presented which makes it possible to obtain satisfactory estimates of the parameters and percentiles of a 2-parameter Weibull distribution, as well as of their confidence intervals, in the presence of life tests of the progressivelycensored type.
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Abstract: The paper treats a statistical method which allows estimation of Weibull parameters and their confidence limits for progressively-censored aging tests. Estimate of shape and scale parameters is based on a procedure which establishes a relation of the progressively-censored tests performed on a set of specimens with an equivalent singly-censored test, so that the Blom estimator can be used and the later failures of the aging test, which are pertinent to really-aged specimens, acquire a greater weight. Statistical confidence limits of time-to-failure percentiles are calculated by a method derived from Bain & Engelhardt. A statistical procedure is presented which makes it possible to obtain satisfactory estimates of the parameters and percentiles of a 2-parameter Weibull distribution, as well as of their confidence intervals, in the presence of life tests of the progressively-censored type. The comparison of the results for various samples, drawn from literature and statistically different as to the size, degree of censoring, material and aging conditions, exhibit the goodness of the proposed procedure. In particular, one notes an intrinsic characteristic of the method, that is, of weighting the later failures to a greater extend. Hence, the proposed method is useful in the statistical treatment of life tests, where moderately-large samples are often used and the later failures, those of really-aged specimens, are particularly important in order to characterize aging.
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Citations
Progressive censoring methodology: an appraisal
TL;DR: In this article, the authors provide an overview of various developments that have taken place in this direction and also suggest some potential problems of interest for further research, including the potential problem of missing information.
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Estimation of parameters of life from progressively censored data using Burr-XII model
TL;DR: Based on progressively Type-II censored samples, the maximum likelihood, and Bayes estimators for some lifetime parameters (reliability, and hazard functions), as well as the parameters of the Burr-XII model, are derived.
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Progressive interval censoring: some mathematical results with applications to inference
TL;DR: Aggarwala et al. as discussed by the authors introduced a union of two methods of collecting Type-I censored data, namely interval censoring and progressive censoring, and called the resulting sample a progressively type-I interval censored sample.
129
Estimations of the parameters of the weibull distribution with progressively censored data
TL;DR: In this article, a progressively type-II censored sample from a two-parameter Weibull distribution was used to derive the point estimators of the parameters and the exact confidence interval and an exact joint confidence region for the parameters were constructed.
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Statistical inference based on progressively censored samples with random removals from the Burr type XII distribution
TL;DR: In this article, the estimation problems for the Burr type XII distribution based on progressive type II censoring with random removals, where the number of units removed at each failure time has a discrete uniform distribution, were studied.
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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.
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