Abstract
AbstractIn step-stress experiments, test units are successively exposed to higher usually increasing levels of stress to cause earlier failures and to shorten the duration of the experiment. When parameters are associated with the stress levels, one problem is to estimate the parameter corresponding to normal operating conditions based on failure data obtained under higher stress levels. For this purpose, a link function connecting parameters and stress levels is usually assumed, the validity of which is often at the discretion of the experimenter. In a general step-stress model based on multiple samples of sequential order statistics, we provide exact statistical tests to decide whether the assumption of some link function is adequate. The null hypothesis of a proportional, linear, power or log-linear link function is considered in detail, and associated inferential results are stated. In any case, except for the linear link function, the test statistics derived are shown to have only one distribution under the null hypothesis, which simplifies the computation of (exact) critical values. Asymptotic results are addressed, and a power study is performed for testing on a log-linear link function. Some improvements of the tests in terms of power are discussed.
Highlights
In accelerated life testing, step-stress models are applied to lifetime experiments with highly reliable products, where under normal operating conditions the number of observed failures is expected to be low; see Bagdonavicius and Nikulin (2001), Meeker and Escobar (1998) & Nelson (2004)
From which the formula for W is obtained by inserting for u1, . . . , um, v1, . . . , vm and replacing θ by θ. As it is the case for the likelihood ratio and Rao score statistic shown in Lemma 2, simulations indicate that the Wald statistic for testing the linear link function assumption does not have a single null distribution
In step-stress experiments, where test units are exposed to higher stress levels to cause earlier failures, some additional assumption such as a link function connecting parameters and stress levels is usually required to infer on the lifetime distribution under normal operating conditions
Summary
Step-stress models are applied to lifetime experiments with highly reliable products, where under normal operating conditions the number of observed failures is expected to be low; see Bagdonavicius and Nikulin (2001), Meeker and Escobar (1998) & Nelson (2004). Maximum likelihood estimation of the parameters associated with the stress levels turns out to be simple in this model, and various estimators along with their properties are shown. For the aforementioned general multi-sample step-stress model based on SOSs, the present work provides statistical tests to check for the validity of some link function assumption. A data-based statistical test may help to assess the accuracy of the model assumptions, to detect significant deviations, and with it to prevent the use of unsuitable estimates of θ0, the parameter corresponding to normal operating conditions.
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