Mixture model of the power law

This paper deals with a new degradation model, a power-law mixture-model which extends the power law in accelerated life testing. Some types of insulation deteriorate at a rate determined by the stress. If the stresses are classified into distinct groups, a total degradation model could be a mixture or several degradation models. If the breakdown voltage (V_B) has a certain failure probability distribution and the degradation follows a power law, then a mixture model of the power law can be constructed. The cluster analysis is done by maximum likelihood estimation. For instance, by using the intermittently-inspected V_B test-data of electrical insulation removed from active power-lines, the remaining life of the insulation can be assessed based on this mixture model. Application of the model to the V_B data of cross-linked polyethylene insulated cables is demonstrated: the breakdown data are classified into groups using the Akaike Information Criterion and the generalized likelihood ratio test method. The remaining life of the insulation can be estimated with approximate standard deviation, for Japanese 22 kV and 33 kV insulation-class inspected cables, samples are clustered into 4 groups and a positive threshold stress is not found