A method for parameter estimation of Mixed Weibull distribution

Many mechanical components exhibit more than one failure mode; and not all components under study have been exposed to similar operating conditions. For example, components may have been used in different operating environments or there may be differences in design and/or material. In these cases, life time data of components would not fall on a straight line on a Weibull probability paper (WPP), that is, the standard 2-parameter Weibull distribution is not an appropriate model. It has been recognized that Mixed Weibull distribution can be used to fit such data properly. However, a mixed Weibull distribution involves more unknown parameters; and due to the difficulty of estimation of these parameters, mixed models have not been widely used. In this paper, a mixed model involving two Weibull distributions is considered. We establish parameter estimation methods for the mixed Weibull model using nonlinear least squares (NLS) theory; and quasi-Newton method is used to solve the optimization problem. A numerical example is given to compare the proposed method with the conventional graphical method.