Thesis (Ph.D.) - Cairo University - Insitute of Statistical Studies and Research - Department of Mathematical Statistics

When the life times of items are relatively large or the sample size is large, it is often necessary to terminate the test before all observations are failed, in this case the results will be happening in a censored test. In this thesis we analyze the life time data in the case of more than one cause of failures based on two censoring scheme namely, adaptive type-I and adaptive type-II progressive censoring schemes. We investigate the maximum likelihood and Bayesian estimation methods to obtain the estimates of the unknown parameters for some life time distributions. The Bayes estimates of the unknown parameters are obtained based on squared error and LINEX loss functions. The new results are reported in chapter IV and V. in chapter IV, we introduce the adaptive type-I progressive censoring schemes in the presence of competing risks. Based on the proposed model and assumed the lifetimes of the latent failure times have exponential distributions, the maximum likelihood and Bayesian estimators of the parameters are obtained. We also proposed the Weibull distributions with the same shape parameter as a lifetimes of the latent failure times. We investigate the maximum likelihood and Bayesian estimation of the parameters and the corresponding confidence intervals.

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