Models with bathtub-shaped failure rate function are useful in reliability analysis and particularly in reliability related decision making and cost analysis. A modified Weibull distribution (MWD) was recently proposed by Lai et al.(2003) as a generalization of the two-parameter Weibull distribution. This distribution has both the two-parameter Weibull and the type I extreme value distributions as special cases. This lifetime distribution is able to model data with bathtub-shaped hazard rate, which is an important feature for engineering reliability analysis. Parameter estimation is crucial for the model to be built and is often a difficult problem, especially for distributions with more than 2 parameters. In this book, maximum likelihood estimation (MLE) is studied in detail. Several techniques regarding this estimation method are proposed to simplify computation. Another estimation method called Bayesian is used to estimate the parameters as well as some life parameters (reliability and hazard functions). We consider estimation of the modified Weibull parameters based on progressively Type II censored data, an adapptive progressively Type II censored data and upper record values.

The main object of this book is to make statistical inferences (recurrence relations, estimation and prediction) for inverse Weibull model using generalized order statistics. This book has been organized and presented in six Chapters. Basic concepts and some other definitions and notations are given. A review of some of the work done concerning the generalized order statistics (progressive censored data, ordinary order statistics and lower k-record values) on the recurrence relations, the Bayesian and non- Bayesian approaches are given. We are concerned with the problem of estimation of the parameters and the reliability function of inverse Weibull model based on generalized order statistics. For this purpose, the maximum likelihood and Bayes estimators are used. Bayes estimators with respect to balanced squared error loss function and Balanced LINEX loss function are obtained. This was done under assumption of discrete-continuous mixture prior for the unknown model parameters. A Bayesian approach using Markov chain Monte Carlo techniques to generate from the posterior distributions is also developed. Our results are specialized to Progressively Type-II censored data.

In the statistical literature R = P(Y

The discovery of asymptotic freedom in the theory of the strong interaction has initiated the high-energy heavy-ion collisions program. It is expected such collisions to produce a deconfined phase of quarks and gluons. The prediction of the phase transition to occur in the vicinity of non-pQCD regime increase the challenges at the theoretical and experimental levels. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory was constructed to explore the QGP-hadronic matter phase transition.