A Method to Estimate the Weibull Parameters for Progressively Censored Tests

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.