Statistical Inference of Two-Parameter Weibull Distribution under Progressive Type-II Censoring with Random Removals
Year: 2022
Type: article
Abstract: distribution.Wherein the time distance between consecutive failure times depends on the type of lifetime distribution and the number of units that will be removed after each failure are proportional to a root function of the difference between two last failure times divided by the time of the first failure.The joint probability mass functions of random removals are also derived.The estimations of parameters are derived using different estimation procedures such as the maximum likelihood , maximum product spacing, and least-squares methods .The proposed random removal schemes are compared to the discrete Uniform and the Binomial removal schemes via a Monte Carlo simulation study in terms of their biases ; root mean squared errors of estimators, expected total test times and the Ratio of the Expected Experiment Time (REET) values.Finally, an innovative technique is introduced for deriving progressive type II censoring samples from a real data set. Results and DiscussionFrom comparing the REET values, it is evident that a slight reduction in expected experiment time occurs when a large number of units are tested for lifetimes under Uniform and Binomial distributions with a considerable probability, p, especially for cases with decreasing failure rate β > 1.Although the Binomial distribution with p < 0.5 has relatively acceptable performance, two proposed approaches have smaller REET values, which decreases significantly as the sample size n increases.However, binomial removals perform better than uniform removals in terms of E(X m:m:n ).Still, the expected test time depends very much on the value of removal probability p. ConclusionIt is shown that the expected total time under the random coefficients has the most negligible value concerning other approaches and reduces the expected full time on the test.
Source: Journal of Statistical Sciences
Authors: Masumeh Ghahramani, Maryam Sharafi, Reza Hashemi
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4290803335