Goodness-of-fit tests for progressively Type-II censored data: Application to the engineering reliability data from continuous distribution

Abstract

This study proposes two new methods of goodness-of-fit (GOF) tests for progressively Type-II censored data from any continuous distribution. For the first method, we transform the original censored sample into an approximately independent and identically distributed normality complete sample, and perform a complete sample GOF test for normality thereafter based on the empirical cumulative distribution function (ECDF). This method merely requires one table of critical values for all the distributions. For the second method, we propose a parametric bootstrap GOF test based on test statistics proposed by Pakyari and Balakrishnan. This method does not require data transformation, but directly uses the observed censored sample to the GOF test. This proposed approach does not require some tables for critical values, which are constructed using parametric bootstrap samples. We estimate the power of the two proposed methods for several well-known parameter distributions, and compare the power of parametric bootstrap method with that of Pakyari and Balakrishnan through various censoring schemes. Simulation results reveal that two new methods both possess good power properties in detecting departure from the null distribution, and the parametric bootstrap method provides as good or better power than the method of Pakyari and Balakrishnan. Lastly, the proposed methods are applied to two real data sets from engineering reliability aspect to prove their practical versatility.

Keywords:

• ECDF
• progressively Type-II censored data
• data transformation
• parametric bootstrap
• Monte-Carlo simulation

Acknowledgments

The author would like to thank the reviewers and the editors who helped to substantially improve the paper.

Additional information

Funding

The research work is supported by Natural Science Foundation of Inner Mongolia (2020MS01001).

Notes on contributors

Tiefeng Zhu

T. F. Zhu is an Associate Professor with the School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot, China. His research interests include quality control, survival analysis and reliability.