Statistical Inference for the Reliability Functions of a Family of Lifetime Distributions based on Progressive Type II Right Censoring
DOI:
https://doi.org/10.6092/issn.1973-2201/7494Keywords:
Progressive type II right censoring, Uniformly minimum variance unbiased estimation, Maximum likelihood estimation, Invariantly optimal estimator, Testing proceduresAbstract
In this article, a general family of lifetime distributions is considered under progressive type II right censoring. The classical point estimation and testing procedures are developed for reliability function and stress-strength reliability. The uniformly minimum variance unbiased, maximum likelihood and invariantly optimal estimators are considered. Testing procedures are developed for the hypotheses related to scale parameter, reliability and stress-strength reliability functions. A Monte Carlo simulation study is performed for comparison of various estimators developed. Finally, the use of proposed estimators is shown in an illustrative example.
References
A. M. AWAD, M. K. GHARRAF (1986). Estimation of P(Y
N. BALAKRISHNAN, R. AGGARWALA (2000). Progressive Censoring-Theory, Methods and Applications. Birkhäuser Publishers, Boston.
N. BALAKRISHNAN, R. A. SANDHU (1995). A simple simulation algorithm for generating progressive type-II censored samples. American Statistician, 49, no. 2, pp. 229–230.
A. CHATURVEDI, S. KUMAR (1999). Further remarks on estimating the reliability function of exponential distribution under type-I and type-II censorings. Brazilian Journal of Probability and Statistics, 13, pp. 29–39.
A.CHATURVEDI, T.KUMARI (2015). Estimation and testing procedures for the reliability functions of a family of lifetime distributions. URL interstat.statjournals.net/YEAR/ 2015/abstracts/ 1306001.php.
A. CHATURVEDI, K. G. SINGH (2006). Bayesian estimation procedures for a family of lifetime distributions under squared-error and entropy losses. Metron, 64, no. 2, pp. 179–198.
A. CHATURVEDI, S. K. TOMER (2002). Classical and Bayesian reliability estimation of the negative binomial distribution. Journal of Applied Statistical Science, 11, pp. 33–43.
A. CHATURVEDI, S. VYAS (2017a). Estimation and testing procedures for the reliability functions of exponentiated distributions under censorings. Statistica, 77, no. 1, pp. 13–31.
A. CHATURVEDI, S. VYAS (2017b). Estimation and testing procedures for the reliability functions of three parameter BURR distribution under censorings. Statistica, 77, no. 3, pp. 207–235.
A. C. COHEN (1963). Progressively censored sample in life testing. Technometrics, 5, pp. 327–339.
J. HURT, W. WERTZ (1983). Asymptotic properties of the invariantly optimal estimator of reliability in the exponential case. Statistics and Decisions, 1, pp. 197–204.
G. D. KELLY, J. A. KELLY,W. R. SCHUCANY (1976). Efficient estimation of P(Y
S. KOTZ, Y. LUMELSKII, M. PENSKY (2003). The Stress-Strength Model and its Generalization: Theory and Applications. World Scientific Press, Singapore.
H. KRISHNA, K. KUMAR (2011). Reliability estimation in Lindley distribution with progressively type II right censored sample. Mathematics and Computers in Simulation, 82, no. 2, pp. 281–294.
H. KRISHNA, K. KUMAR (2013). Reliability estimation in generalized inverted exponential distribution with progressively type-II censored sample. Journal of Statistical Computation and Simulation, 83, no. 6, pp. 1007–1019.
K. KUMAR, R. GARG, H. KRISHNA (2017). Nakagami distribution as a reliability model under progressive censoring. International Journal of System Assurance Engineering and Management, 8, no. 1, pp. 109–122.
E. L. PUGH (1963). The best estimate of reliability in the exponential case. Operations Research, 11, pp. 57–61.
M. K. RASTOGI, Y. M. TRIPATHI (2014). Parameter and reliability estimation for an exponentiated half-logistic distribution under progressive type-II censoring. Journal of Statistical Computation and Simulation, 84, no. 8, pp. 1711–1727.
H. TONG (1974). A note on the estimation of P(Y
R. K. TYAGI, S. K. BHATTACHARYA (1989). A note on the MVU estimation of reliability for the Maxwell failure distribution. Estadistica, 41, pp. 73–79.
R.VALIOLLAHI, M. Z. RAQAB, A.ASGHARZADEH, F.ALQALLAF (2018). Estimation and prediction for power Lindley distribution under progressively type II right censored samples. Mathematics and Computers in Simulation, 149, pp. 32 – 47.
Z. P.XIA, J. Y. YU, L. D. CHENG, L. F. LIU,W. M.WANG (2009). Study on the breaking strength of jute fibres using modified Weibull distribution. Composites: Part A, 40, pp. 54–59.
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