Time Transformation Function Research Articles

Nonparametric inferences for ramp stress tests under random censoring

This paper considers nonparametric estimation of lifetime distribution of a product under ramp stress accelerated life tests in which the stress on an item increases linearly with time and observations are randomly censored. Assuming that a cumulative exposure model holds, the lifetime distribution of an item under ramp stress is derived. Three nonparametric estimators of the lifetime distribution at use condition stress are obtained for the situation where the time transformation function relating stress to lifetime distributions of a test item is a version of the inverse power law. The proposed estimators are robust to underlying lifetime distribution and are computed in closed form. They are compared with maximum likelihood estimator for small samples under exponential lifetime distribution. The method is extended to the case of competing risks.

A nonparametric approach to progressive stress accelerated life testing

Progressive-stress accelerated life testing in which the stress on an unfailed item increases linearly with test time when the time transformation function is a version of the inverse power law is considered. The approach is nonparametric in that not many assumptions are made about life distribution. A testing pattern is introduced, and it is explained how to draw inferences from progressive stress tests. An estimator of life distribution at the usual stress level is proposed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Bayes estimation of hazard and acceleration in accelerated testing

In accelerated life testing, the time transformation function theta (t) is often unknown, even if that function is assumed to be linear. If theta (t) is known, data in the accelerated condition can be adjusted to provide information about the failure time distribution in the use condition. If theta (t) is unknown, the usual estimation procedures require data from the use condition as well as data from the acceleration condition. In this work it is assumed that the uncertainty about theta can be modeled by a prior distribution, chosen from the truncated Pareto family of distributions, and that the uncertainty in lambda , the failure rate, can be modeled by a prior distribution from the gamma family. Under these assumptions, the posterior distributions and their first two moments are provided for both lambda and theta . Thus, this complete Bayes approach to accelerated life testing with the assumed model allows the adjustment of data taken in the accelerated condition to provide the user with the important estimates in the use condition. The results are illustrated by examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Inference from Accelerated Life Tests Using Filtering in Coloured Noise

SUMMARY We present a new approach for inference from accelerated life tests. Our approach formulates such problems as inference under Kalman filter models with correlated observation errors. We restrict attention to exponential life distributions, and the power rule as a time transformation function. Extensions to other time transformation functions are straightforward; however, extensions to other distributions involve nonlinear filtering and are not considered. The advantages of our formulation are that we are able to incorporate uncertainty in the time transformation function and also are able to allow it to change with the stress. to validate our approach we consider some simulated data; to give it a sense of reality we apply it to actual data.

Nonparametric Estimation and Goodness-of-Fit Testing of Hypotheses for Distributions in Accelerated Life Testing

This paper presents a nonparametric approach to accelerated life testing by deleting the requirement that the common parametric family of life distributions under all the stresses be specified in advance. The requirement that the time transformation function be specified is retained, and a version of the familiar inverse power law is considered. A s-consistent estimate of the failure distribution at use stress, and a test of the hypothesis that the underlying failure distribution belongs to a specified family are given. Approximate s-confidence bounds for the failure distribution at use stress are obtained. The approach is illustrated in an example using real data.

Testing of Hypotheses for Distributions in Accelerated Life Tests

Abstract In this paper we consider the problem of inference from accelerated life tests in which a common parametric family of life distributions at the different stress levels is not specified in advance. By assuming a time transformation function, which is a version of the familiar inverse power law, we give a procedure for testing hypotheses that the unknown distributions are specified members of a location-scale family. The behavior of the test procedure is indicated by some simulations. We illustrate the methodology with some real-life data.

Testing of Hypotheses for Distributions in Accelerated Life Tests

Abstract In this paper we consider the problem of inference from accelerated life tests in which a common parametric family of life distributions at the different stress levels is not specified in advance. By assuming a time transformation function, which is a version of the familiar inverse power law, we give a procedure for testing hypotheses that the unknown distributions are specified members of a location-scale family. The behavior of the test procedure is indicated by some simulations. We illustrate the methodology with some real-life data.