Accelerated life tests under finite mixture models

Abstract

In this paper, the failure time of a device is observed under a higher stress subjected to a general class of stress-response model, when its distribution is a mixture of k components each of which represents a different cause of failure. The problem is studied when each of the components belongs to a general class of distributions which includes, among others, the Weibull, compound Weibull (or three-parameter Burr type XII), power function, Gompertz and compound Gompertz distributions. On the basis of the censored data, the maximum likelihood estimates of the unknown parameters involved under the general stress-response model are obtained. A special attention is paid to the power rule model applied to mixtures of two Weibull components. Mixtures of two exponentials, Rayleigh and Weibull components models are used as illustrative examples.

Keywords:

• Exponential
• Rayleigh and Weibull mixtures
• Accelerated life tests
• Power rule model
• Maximum likelihood estimation
• Simulation

Acknowledgements

The authors appreciate the comments and remarks of the Associate Editor and Referee.