<p>In this work, a failure rate-based progressive first failure censored multiple-step-stress model is formulated where the stress-specific time-to-failure distributions of the test units conform to a proportional hazard (PH) family of distributions. With elevation in the stress levels, the mean times-to-failure of the test units get shortened resulting in a natural order restriction among the means of the stress-specific time-to-failure random variables. Order-restricted (constrained) inference becomes a natural alternative in this case and is addressed by employing the sophisticated generalized isotonic regression technique. The observed Fisher information matrix is used to compute the asymptotic confidence intervals (CIs) of the model parameters. Often, a non-trivial issue in designing a life testing experiment is to figure out the optimal censoring scheme. The variable neighborhood search (VNS), a meta-heuristic algorithm, is used to solve this problem for the suggested model. Extensive simulation experiments are conducted to investigate the efficacy of the proposed methodology. Although the problem of model misspecification is quite relevant in accelerated life testing (ALT) experiments, it has not been addressed in a multiple step-stress ALT framework. The relative bias (RB) and relative variability (RV) of the <i>p</i>-th quantile measure are used to evaluate the effects of model misspecification in the event that the true distribution is misspecified. For illustrative purposes, a real-world data example is thoroughly analyzed.</p>