Estimation of parameters of life from progressively censored data using Burr-XII model

• Published in: IEEE transactions on reliability Vol. 54; no. 1; pp. 34 - 42
• Main Author: Soliman, A.A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2005; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bayesian analysis; Computer simulation; Entropy; Estimates; Estimators; Fluid flow; Hazards; Insulation; Life estimation; Lifetime estimation; Mathematical analysis; Mathematical models; Maximum likelihood estimation; Numerical simulation; Parameter estimation; Shape; Testing
• ISSN: 0018-9529; 1558-1721
• DOI: 10.1109/TR.2004.842528

Based on progressively Type-II censored samples, the maximum likelihood, and Bayes estimators for some lifetime parameters (reliability, and hazard functions), as well as the parameters of the Burr-XII model, are derived. The Bayes estimators are obtained using both the symmetric (Squared Error, SE) loss function, and asymmetric (LINEX, and General Entropy, GE) loss functions. This was done with respect to the conjugate prior for the one shape parameter, and discrete prior for the other parameter of this model. Also the existence, uniqueness, and finiteness of the ML parameter estimates for this type of censoring are discussed. A practical example consisting of data from an accelerated test on insulating fluid reported by Nelson (1982) was used for illustration, and comparison. Finally, some numerical results using simulation study concerning different sample sizes, and progressive censoring schemes were reported.