Collecting accelerated degradation test (ADT) data can provide useful lifetime information for highly reliable products if there exists a product quality characteristic whose degradation over time can be related to reliability. However, conducting a constant-stress ADT is very costly. This is obviously not applicable for assessing the lifetime of a newly developed product because typically only a few test samples (prototypes) are available. To overcome this difficulty, we propose a step-stress accelerated degradation test (SSADT) in this paper. A case study of light emitting diodes data is used to illustrate the proposed procedure. It is seen that SSADT has several advantages over a constant-stress ADT. SSADT not only reduces the experimental cost significantly, but also provides the reliability analysts an efficient tool to assess the lifetime distribution of highly reliable products.
Keywords: Lifetime Data, Reliability
by Sheng-Tsaing Tseng and Zhi-Chih Wen, National Tsing-Hua University, Hsinchu, Taiwan
Today most manufacturing products are highly-reliable. Therefore it is not an easy task for reliability engineers to assess a products lifetime distribution within a reasonable life-testing time. Traditionally, accelerated life tests (ALTs) are often used to assess the lifetime information of the products. However, this approach may offer little help for highly reliable products which are not likely to fail during a rather short period of time. An alternative approach assumes that there is a product quality characteristic whose degradation over time can be related to reliability. This approach collects the degradation data at higher levels of stress and then use these data to predict the products lifetime at a use-stress. Such an experiment is called an accelerated degradation test (ADT).
Nelson (1990, Chapter 11) and Meeker and Escobar (1993) survey the literature on ADT. Carey and Koenig (1991) describe a data-analysis strategy and a model-fitting method to extract reliability information from observations on the degradation of integrated logic devices that are components in a new generation of submarine cables. Boulanger and Escobar (1994) address the problem of determining both the stress levels and sample size for each stress level under a pre-determined termination time. For conducting the tests more efficiently, Tseng and Yu (1997) and Yu and Tseng (1998) propose a stopping rule for terminating a degradation/accelerated degradation test.
Although ADT is an efficient life-test method, it is very expensive in general. For example, suppose we adopt three higher levels of stress, with 25 test units for each stress. We then need three ovens and 75 units to complete the test. Obviously, for a newly developed product, it is very difficult (or expensive) to have so many test units on hand. In addition, the selection of suitable stress levels for conducting an efficient ADT is not straightforward. If the selected stress levels are not appropriate (or are too low), the degradation will occur so slowly that the products lifetime cannot be precisely extrapolated. Thus, conducting a constant-stress ADT for a newly developed product may be impractical or impossible for the reliability analyst. To overcome the difficulties, an efficient step-stress accelerated degradation test (SSADT) procedure is proposed. By using a cumulative exposure (CE) model (Nelson (1990)), the products lifetime can be predicted quickly. In addition, the cost of conducting a degradation experiment can be reduced significantly.
The rest of the paper is organized as follows. First, we introduce a motivating example. Next a statistical model of SSADT is introduced, followed by a diagnostic check for the validity of the proposed model. Then the proposed procedure is applied to analyze the motivating example. We also perform a sensitivity analysis of the proposed method. Finally, some concluding remarks are given at the end of this paper. Note that we use an intuitive approach to address this problem. Thus some criteria used in our analysis may be ad hoc in nature. Some alternatives are proposed in the conclusion.
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