A study of Weibull shape parameter: Properties and significance

The two-parameter Weibull distribution has been widely used for modelling the lifetime of products and components. In this paper we study the effect of the shape parameter on the failure rate and three variables of importance in the context of maintenance and reliability improvement. These variables are (i) time to failure, (ii) age at replacement based on risk and (iii) residual life. We propose a classification scheme for the distribution based on the shape parameter and discuss the application of the results.