Inferences for the Exponentiated Weibull Distribution Based on Record Statistics

The Weibull distribution is a very popular distribution. It is called after Waladdi Weibull, a Swedish physicist. He used it in 1939 to analyze the breaking strength of materials. Since then it has been widely used for modelling phenomena with monotone failure rates. It is not useful for modelling phenomena with non monotone failure rates. The Weibull distribution has been shown to be useful for modelling and analyzing of life time data in medical, biological and engineering sciences. Some applications of the Weibull distribution in forestry are given in Green et al. (1994). A great deal of research has been done on estimating the parameters of the Weibull distribution using both classical and Bayesian techniques. A good summary of this work can be found in Johnson et al. (1994). Recently, Hossain and Zimmer (2003) have discussed some comparisons of estimation methods for Weibull parameters using complete and censored samples. Record values and the associated statistics are of interest and important in many real life applications. In industry many products fail under stress. For example, a wooden beam breaks when sufficient perpendicular force is applied to it, an electronic component ceases to function in an environment of too high temperature, and a battery dies under the stress of time. But the precise breaking stress or failure point varies even among identical items. Hence, in such experiments, measurements may be made sequentially and only the record values are observed. Thus, the number of measurements made is considerably smaller than the complete sample size. This “measurement