STATISTICAL ANALYSIS OF TWO-PARAMETER BATHTUB- SHAPED LIFETIME DISTRIBUTION UNDER PROGRESSIVE CENSORING WITH BINOMIAL REMOVALS

Year 2016, Volume: 29 Issue: 4, 783 - 792, 19.12.2016

Akram Kohansal

Abstract

The estimation of unknown parameters of two-parameter bathtub-shaped lifetime distribution based on Type-II progressive censoring with binomial removals is studied. Maximum likelihood estimators are evaluated and using Fisher information matrix, asymptotic confidence intervals are provided. By applying Markov Chain Monte Carlo techniques, Bayes estimators, and corresponding highest posterior density confidence intervals of parameters are obtained. The expected time required to complete the life test under this censoring scheme is investigated. Monte Carlo simulations are performed to compare the performances of the different methods,
and one data set is analyzed for illustrative purposes.

References

• Balakrishnan, N., "Progressive censoring methodology: an appraisal (with discussions)", TEST, 16, 211-296, (2007).
• Balakrishnan, N., Aggarwala, R., Progressive censoring: theory, methods and applications, Birkhauser, Boston, (2000).
• Cohen, A.C., "Progressively censored samples in life testing, Technometrics", 5, 327-339, (1976).
• Viveros, R., Balakrishnan, N., "Interval estemation of parameters of life from progressive censoring data", Technometrics, 36, 84-91, (1994).
• Hashemi, R., Amiri, L., "Analysis of progressive Type-II censoring in the Weibull model for competing risks data with binomial removals", Applied Mathematical Sciences, 5, 1073-1087, (2011).
• Yan, W., Shi, Y., Song, B., Mao, Z., "Statistical analysis of generalized exponential distribution under progressive censoring with binomial removals", Journal of Systems Engineering and Electronics, 22, 707-714, (2011).
• Mubarak, M., "Parameter estimation based on the Fréchet progressive Type-II censored data with binomial removals", International Journal of Quality, Statistics, and Reliability, Accepted, (2012).
• Azimi, R., Yaghmaei, F., "Bayesian estimation based on Rayleigh progressive Type-II censored data with binomial removals", Journal of Quality and Reliability Engineering, Accepted, (2013).
• Dey, S., Dey, T., "Statistical Inference for the Rayleigh distribution under progressively Type-II censoring with binomial removal", Applied Mathematical Modelling, 38, 974-982, (2014).
• Azimi, R., Fasihi, B., Sarikhanbaglu, F. A., "Statistical inference for generalized Pareto distribution based on progressive Type-II censored data with random removals", International Journal of Scientific World, 2, 1-9, (2014).
• Soliman, A.A., Abd Ellah, A.H., Abou-Elheggag, N.A., El-Sagheer, R.M., "Inferences using type-II progressively censored data with binomial removals", Arabian Journal of Mathematics, 4, 127-139, (2015).
• Asgharzadeh, A., Abdi, M., Wu, S.J., "Interval estimation for the two-parameter Bathtub-shaped life time distribution based on records", Hacettepe Journal of Mathematics and Statistics, 44, 399-416, (2015).
• Sarhan, A.M., Hamilton, D.C., Smith, B., "Parameter estimation for a two-parameter bathtub-shaped lifetime distribution", Applied Mathematical Modelling, 36, 5380-5392, (2012).
• Selim, M.A., "Bayesian estimations from the two-parameter bathtub-shaped lifetime distribution based on record values", Pakistan Journal of Statistics and Operation Research, 8, 155-165, (2012).
• Rastogi, M.K., Tripathi, Y.M., "Estimation using hybrid censored data from a two-parameter distribution with bathtub shape", Computational Statistics and Data Analysis, 67, 268-281, (2013).
• Rastogi, M.K., Tripathi, Y.M., Wu, S.J., "Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring", Journal of Applied Statistics, 39, 2389-2411, (2012).
• Ahmed, E.A., "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach", Journal of Applied Statistics, 41, 752-768, (2014).
• Shoaee, S., Khorram, E., "Stress-strength reliability of a two-parameter bathtub-shaped lifetime distribution based on progressively censored samples", Communications in Statistics - Theory and Methods, 44, 5306-5328, (2015).
• Chen, Z., "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function", Statistics & Probability Letters, 49, 155-161, (2000).
• Tse, S.K., Yang, C.Y., Yuen, H.K., "Statistical analysis of Weibull distributed lifetime data under type II progressive censoring with binomial removals", Journal of Applied Statistics, 27, 1033-1043, (2000).
• Lieblein, J., Zelen, M., "Statistical investigation of the fatigue life of deep-groove ball bearings", Journal of Research of the National Bureau of Standards, 57, 273-316, (1956).
• Raqab, M.Z., "Inference for generalized exponential distribution based on record statistics", Journal of Statistical Planning and Inference, 104, 339-350, (2002).
• Kim, C., Han, K., "Estimation of the scale parameter of the Rayleigh distribution under general progressive censoring", Journal of the Korean Statistical Society, 38, 239-246, (2009).