Optimal degradation-based burn-in policy using Tweedie exponential-dispersion process model with measurement errors

In this paper, degradation-based burn-in for highly-reliable products subject to degradation is studied. Since the common degradation models for burn-in are usually established on the basis of a specific stochastic process, such as Wiener process and gamma process, it greatly restricts the scope of application. Moreover, measurement errors are often inevitable due to the imperfect inspection and environment disturbance. Hence, a Tweedie exponential-dispersion process with measurement errors (TEDPE) model is developed to describe the degradation paths of the population which includes weak units and normal units. The TEDPE model contains the common stochastic process models as special case by setting different forms of variance function. Then, a joint saddle-point approximation and expectation maximization algorithm is proposed for parameter estimation. To identity and eliminate weak units, the linear discriminant analysis method, which can make full use of the degradation sequence of observations, is used to develop classification criterion. The optimal burn-in policy involving the duration and cutoff point can be obtained by minimizing the total per-unit cost. Furthermore, considering the failure costs in field operation, a joint policy of burn-in and preventive maintenance is optimized. Finally, a case study based on an IRLED dataset is implemented to illustrate the proposed methods.