BAYESIAN ESTIMATION OF COMPONENT RELIABILITY USING PROGRESSIVELY CENSORED MASKED SYSTEM LIFETIME DATA FROM RAYLEIGH DISTRIBUTION
Keywords:
Bayesian Estimation, Competing Risk, Gibbs Sampler, Masked Data, Maximum Likelihood Estimation, Rayleigh Distribution.Abstract
Progressive type-II censoring scheme is a very popular scheme adopted by contributors in the fields of reliability and life-testing. In this paper, we consider a problem when this scheme is applied to a life-testing experiment in which each unit under test is a series system and the investigator is interested in obtaining reliability estimates of individual components. Assuming the components lifetimes to be Rayleigh distribution, we present maximum likelihood and Bayesian approaches to estimate the reliability measures of individual components using masked system lifetime data. The Bayes estimates are evaluated using Lindley’s approximation and Gibbs Sampler. The results are illustrated with the help of simulation study.
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References
Balakrishana, N. (2007). Progressive censoring methodology: An appraisal (with
discussions), Test, 16, p. 211-296.
Balakrishanan, N. and Aggarwala, R. (2000). Progressively censoring: Theory,
Methods, and Application, Birkhauser, Boston, MA.
Balakrishnan, N., Kannan, N., Lin, C.T. and Ng, H.K.T. (2003). Point and
Interval estimation for Gaussian distribution, based on progressively censored
samples, IEEE Trans. Reliab., 52, p. 90–95.
L. Kuo and T. E. Yang. (2000). Bayesian reliability modeling for masked system
lifetimedata, Statist. Probab. Lett. , 47, p.229–241.
Lawless, J. F. (2003). Statistical models and methods for lifetime data, Wiley,
New York.
Lindley, D.V. (1980). Approximate Bayesian methods, Trabajos de Estadistica.,
, p. 223-237.
Mukhopadhyay, C. and Basu, A. P. (1997). Bayesian analysis of incomplete time
and cause of failure data, Jour. Stat. Plan. Infer., 59, p. 79-100.
Miyakawa, M. (1984). Analysis of incomplete data in competing risks model,
IEEE Trans. Reliability, 33, p. 293-296.
Nassar, M. M. and Eissa, F. H. (2005). Bayesian estimation for the exponentiated
weibull model, Communications in Statistics - Theory and Methods, 33(10), p.
-2362,
Ng, H. K. T., Chan, P. S. and Balakrishnan, N. (2005). Optimal progressive
censoring plans for the weibull distribution, Technometrics, 46, p. 470–481.
Reiser, B., Guttman, I., Lin, D.K.J., Guess, F.M. and Usher, J.S.(1995). Bayesian
inference for masked system lifetime data, Appl. Stat. 44, p. 79-90.
Sarhan, A.M. and El-Gohary, A. (2003). Estimations of parameters in Pareto
reliability model in the presence of masked data, Reliab. Eng. Syst. Safety, 82, p.
-83.
Singh, A.K. and Tomer, S.K. (2011). Maximum Likelihood Estimation of
component reliability using masked series system life time data, Cul. Stat. Assoc.
Bull., 63, p. 249-252.
Sinha, S.K. (1986). Reliability and Life Testing. Wiley Eastern Ltd., New Delhi.
Soliman, A. A. (2005). Estimation of parameters of life from progressively
censored data using Burr-XII model, IEEE Transactions on Reliability, 54(1), p.
-42.
Tan, Z. (2007). Estimation of exponential component reliability from uncertain
life data in series and parallel systems, Reliab. Eng. Syst. Safety, 92, p. 223-230.
Tomer, S. K., Singh, A. K. and Panwar, M. S. (2014). Bayesian analysis of
masked series system lifetime data from a family of lifetime distributions, Inter.
Jour. of System Assur. Engg. Mgmt., 5(4), p. 495-502.
Usher, J.S. and Hodgson, T.J. (1988). Maximum likelihood analysis of
component reliability using masked system life-test data, IEEE Trans. Reliab.,
R-37, p. 550-555.
Xu, A. and Tang, Y. (2009). Bayesian analysis of Pareto reliability with
dependent masked data, IEEE Trans. Reliab., 58(4), p. 583-588.
