  Accelerated life-testing (ALT) is a very useful technique for examining the
reliability of highly reliable products. It allows testing the products at
higher than usual stress conditions to induce failures more quickly and
economically than under typical conditions. A special case of ALT are
step-stress tests that allow experimenter to increase the stress levels at
fixed times. This paper deals with the multiple step step-stress model under
the cumulative exposure model with lognormally distributed lifetimes in the
presence of Type-II and Progressive Type-II censoring. For this model, the
maximum likelihood estimates (MLE) of its parameters, as well as the
corresponding observed Fisher Information Matrix (FI), are derived. The
likelihood equations do not lead to closed-form expressions for the MLE, and
they need to be solved by means of an iterative procedure, such as the
Newton-Raphson method. We then evaluate the bias and mean square error of the
estimates and provide asymptotic and bootstrap confidence intervals. Finally,
in order to asses the performance of the confidence intervals, a Monte Carlo
simulation study is conducted.
