| Summary: | 碩士 === 國立清華大學 === 統計學研究所 === 91 === Rapid advances in technology, development of highly sophisticated products, intense global competition, and increasing customer expectations have put new pressures on manufacturers to produce high-quality products. Customers expect purchased products to be reliable and safe. In other words, customer expect products be able to perform their intended function under usual operating conditions, for some specified period of time. The problems that come along are how to obtain the information of product reliability. But, today, many products are designed and manufactured to function for a long period of time before they fail. The problem of obtaining failure data to apply traditional statistical tools to predict lifetime distribution becomes more difficult. An alternative is to use data on a quality characteristic (QC) whose degradation over time is highly correlated with product failure. If degradation paths can be modeled properly, and the product fails when the QC’s degradation path first passes a critical value, then predicting the product’s failure time or the lifetime can be made without actually observing the product’s failure. Instead one will obtain what will be termed as the initial data from the early stage of reliability testing. A Wiener process is typical for describing a degradation process since it allows non-constant variance and non-zero correlation among data collected over time. In this paper we first review how a Wiener process was used to describe the continuous degradation path of a quality characteristic of the product. We compare the MLES and UMVUES of the mean and variance of lifetime distribution of the product, all based on initial data. Next, we propose an estimator of the lifetime distribution and compare it with the corresponding MLE. Then using an example in the literature, we demonstrate that our proposed estimator of the lifetime distribution is better than the MLE. The example is about the light intensity of light emitting diodes (LEDs). The data we use to obtain various estimates are all collected only from the product’s initial observed degradation path.
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