Optimal Classification Policy and Comparisons for Highly Reliable Products

Abstract

In the current competitive marketplace, manufacturers need to classify products in a short period of time, according to market demand. Hence, it is a challenge for manufacturers to implement a classification test that can distinguish the different grades of a product quickly and efficiently. For highly reliable products, if quality characteristics exist whose degradation over time can be related to the lifetime of the product, the degradation model can then be constructed based on the degradation data. In this study, we propose a general degradation model using a Gaussian mixture process that simultaneously considers unit-to-unit variability, within-unit variability and measurement error. Then, by adopting the concept of linear discriminant analysis, we propose a three-step classification policy to determine the optimal coefficients, the optimal cutoff points and the optimal test stopping time. In addition, we use an analytic approach to compare the efficiency of our proposed procedure with the methods that are reported in the previous literature under small-sample cases. Analytical comparisons provide functional equations under different assumptions. The solutions are found to elucidate the foundation between different methods proposed in recent studies. Finally, several data sets are used to illustrate the proposed classification procedure.