Statistical inference in Burr type XII lifetime model based on progressive randomly censored data

Abstract

Censoring commonly occurs in real-world scenarios, either intentionally or unintentionally. Unintentional (or accidental) censoring usually happens randomly, i.e., it is out of the experimenters’ control, such as broken equipment, lack of follow-up, etc. Experimenters typically use intentional censoring to save experimental time and cost. In this article, we develop frequentist and Bayesian statistical inferential procedures for the parameters and reliability characteristics of the Burr type XII lifetime model under the Koziol-Green model based on progressive randomly censored data. For the frequentist approach, maximum likelihood methods for point and interval estimation are developed. For the Bayesian approach, the Bayes estimates under the squared error loss function (SELF) are evaluated using the Markov Chain Monte Carlo (MCMC) and Tierney-Kadane (T-K) approximation techniques. A Monte Carlo simulation study is used to assess the performance of the proposed estimation procedures. A real data analysis is performed to illustrate the proposed methods. Moreover, obtaining progressive censoring schemes for experimental planning purposes is also discussed.

Keywords:

• Bayesian estimation
• Koziol-Green model
• Markov chain Monte Carlo method
• maximum likelihood estimation
• progressively Type-II censoring

Acknowledgements

The authors would like to thank the guest editor and two anonymous reviewers for their positive remarks and useful comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Rajni Goel

Dr. Rajni Goel is an assistant professor in the Department of Mathematics, Chandigarh University, Mohali, Punjab, India. She is M.Sc., M.Phil., and Ph. D. in Statistics. She has published Seven research papers in international journals. She is working in the field of Censoring in Survival analysis, Classical & Bayesian inference, and Computational Statistics.

Kapil Kumar

Dr. Kapil Kumar is an Associate Professor and Head of the Department of Statistics, Central University of Haryana, Mahendergarh, India. He received his Ph.D. in Statistics from Ch. Charan Singh University, Meerut, India in 2011. He has ab out 12 years of teaching experience. His areas of research are Reliability and Life Testing, Classical Estimation, Bayesian Estimation, Survival analysis and Censored data. He has published 30 research papers and has reviewed more than a hundred research papers for different journals.

Hon Keung Tony Ng

Hon Keung Tony Ng is a Professor at the Department of Mathematical Sciences, Bentley University, Waltham, MA, USA. He received a Ph.D. degree in mathematics from McMaster University, Hamilton, ON, Canada, in 2002. His research interests include reliability, censoring methodology, ordered data analysis, nonparametric methods, and statistical inference. Dr. Ng is an Associate Editor for Communications in Statistics, Computational Statistics, IEEE Transactions on Reliability, Journal of Statistical Computation and Simulation, Naval Research Logistics, Sequential Analysis, and Statistics & Probability Letters. He is a Fellow of the American Statistical Association and an Elected Member of the International Statistical Institute.

Indrajeet Kumar

Dr. Indrajeet Kumar is an Assistant Professor in the Department of Mathematics at Kalasalingam Academy of Research and Education, Krishnankovil, Tamilnadu, India. He received his Ph.D. in Statistics from the Central University of Haryana, Mahendergarh, India in 2022. He has about one year of Data Scientist and two years of teaching experience. His areas of research are Reliability and Life Testing, Classical Estimation, Bayesian Estimation, Survival Analysis, Quality Control, Data Science and Censored data. He has published 07 research papers and also reviewed several research papers for different journals.