Due to technological advance and high expectation from consumers, many products are now expected to function for a long time before failure. However, during design and manufacturing stages, managers and engineers need failure data much sooner to estimate the lifetime distributions of their products. Accelerated life testing and step-stress life testing, where products are subject to higher-than-normal stresses to accelerate their failures, are standard methods of obtaining timely failure data. In a different approach, one will study the degradation/accumulated decay of a quality characteristic (QC) in case where the product will fail when its QC’s sample degradation path first passes the failure threshold. One advantage is that, if one can model the degradation sample path by, for example, a stochastic process, then it is possible to predict/estimate the lifetime without testing till failure of the product. When assuming a Wiener process with a constant or linear failure threshold, the lifetime distribution is an inverse Gaussian distribution and estimation procedures based on failure data are available. However, since we have a time-continuous degradation process, it is possible to obtain intermediate data before product’s failure and these data may be useful for lifetime estimation and model verification. In this paper, we first propose a simple way of obtaining intermediate data, which are basically boundary-crossing times of the degradation process but over certain boundaries before failure and hence are not actual failure times. Then we obtain various estimators of the lifetime distribution and its parameters based on these intermediate data, with or without the actual failure data. The results for cases without failure data are particularly useful for products that are highly reliable since lifetime could be too long or costly to obtain. In addition to the standard maximum likelihood estimators, we also obtain the uniformly minimum variance unbiased (UMVU) estimators, or mixtures of the two, for various quantities of interest. An example of an electronic product, namely the contact image scanner (CIS), is used to illustrate the proposed method.

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