## ABSTRACT

Failures of highly-reliable units are rare and failure time data can be very scarce. Two ways of obtaining additional information about reliability of units can be used. One way is to use higher levels of experimental factors or stresses to increase the number of failures, and, hence, to obtain reliability information quickly. Another way is to measure some parameters characterizing degradation (aging) of the product in time. Both methods can be combined: degradation and failure time data can be obtained at higher levels of stress, (see, for example, Meeker, Escobar and Lu (1998), Singpurwalla (1995)). Analysis of such data is possible if accelerated degradation models relating degradation and failure times to the accelerating factors (stresses) are well chosen. Degradation models with the explanatory variables may also be used to esti-

mate reliability when the environment is dynamic (see, Singpurwalla (1995)). The explanatory variables may be uncontrollable by an experimenter in such a case. For example, tire wear rate and failure times depend on quality of roads, temperature, and other factors. Accelerated degradation models can be used when optimal values of ex-

planatory variables are needed to maximize the reliability of the product, are needed. For example, degradation of light emitting diodes is characterized by their decreasing luminosity, and the rate of degradation depends on such factors as type of silver, epoxy coating, epoxy lens material, initial curing temperature, and curing duration, (see, Hamada (1995), Chiao and Hamada (1996)). Modeling accelerated degradation one must keep in mind that an unit may

be treated as failed when its degradation reaches a critical level (non-traumatic failure) or when a traumatic event occurs. The probability of the traumatic event may depend on the degradation level and on the explanatory variables. For example, a puncture of a tire is more probable if thickness of the tire protector (degradation measure) is smaller and the load (the explanatory variable) is heavier. Thus, in the most general situations an accelerated degradation model must

include: 1. The stochastic process describing changing of the degradation level in

time; 2. Dependence of degradation process parameters on the explanatory vari-

events; 4. Dependence of this process on degradation and the explanatory variables.

3.2 Degradation models