Estimation Of The Join Point In A Heteroscedastic Regression Model Arising In Accelerated Life Tests

In certain accelerated life test experiments, when accelerating beyond certain values of the stress, a change in the basic failure mechanism occurs. Such situations call for the introduction of two or more submodels joined at what is known as a “join point.” In this paper we consider two continuous linear submodels, each applicable over a particular but unknown interval of the applied stress. We assume that the exponential model for failure times is valid for the entire range of the applied stress. We apply an iterative weighted least-squares procedure to data obtained from censored sample life tests conducted at different values of the applied stress. In this way we obtain (i) an estimator of the join point such that the residual sum of squares is minimized, and (ii) estimators of the parameters of each submodel. The techniques presented here are quite general and can be easily adapted to other problems of join point estimation, especially those involving heteroscedasticity. © 1974, Taylor & Francis Group, LLC. All rights reserved.