On the maximum likelihood estimation for progressively censored lifetimes from constant-stress and step-stress accelerated tests

In order to gather the information about the lifetime distribution of a product, a standard life testing method at normal operating conditions is not practical when the product has an extremely long lifespan. Accelerated life testing solves this difficult issue by subjecting the test units at higher stress levels than normal for quicker and more failure data. The lifetime at the design stress is then estimated through extrapolation using an appropriate regression model. Estimation of the regression parameters based on exponentially distributed lifetimes from accelerated life tests has been considered by a number of authors using numerical methods but without systematic or analytical validation. In this article, we propose an alternative approach based on a simple and easy-to-apply graphical method, which also establishes the existence and uniqueness of the maximum likelihood estimates for constant-stress and step-stress accelerated life tests under progressive censorings.