Measurement Plan Optimization for Degradation Test Design based on the Bivariate Wiener Process

This article concerns the optimization of measurement plans in the design of bivariate degradation tests for bivariate Wiener processes. After describing an unbalanced measurement scheme for bivariate degradation tests, we derive the likelihood function and provide a method for estimating the model parameters that is based on maximum likelihood and least squares. From the corresponding Fisher information matrix, we deduce an important insight, namely that longer degradation tests and longer intervals between measurements in the test design result in more precise parameter estimates. We introduce a model for optimizing the degradation test measurement plan that incorporates practical constraints and objectives in the test design framework. We also present a search‐based algorithm to identify the optimal test measurement plan that is based on the aforementioned measurement rule. Via a simulation study and a case study involving the Rubidium Atomic Frequency Standard, we demonstrate the characteristics of optimal measurement plans for bivariate degradation test design and show the superiority of longer duration tests involving fewer samples compared to alternative designs that specify testing more samples over shorter periods of time.