Optimal Classification Policy for Highly Reliable Products

• Activity Number: 425
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Chien-Yu Peng*+
• Companies: Institute of Statistical Science, Academia Sinica
• Keywords: degradation model ; functional equation ; highly reliable products ; linear discriminant analysis ; Gaussian mixture process

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 products 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, time-dependent error structure and measurement error. Then, by adopting the concept of linear discriminant analysis, we propose a three-step classification policy to determine optimal vector of coefficients, optimal cutoff points and 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 previous literature. Finally, several data sets are used to illustrate the proposed classification procedure.