Accelerated life tests are vital in reliability studies, especially as new technologies create highly reliable products to meet market demand and competition. Progressive stress accelerated life test (PSALT) allows continual stress adjustments. For reliability and survival analysis in accelerated life studies, generalized progressive hybrid censoring (GPHC) is very important. The research on GPHC in PSALT models is lacking despite its growing importance. Binomial elimination and generalized progressive hybrid censoring augment PSALT in this investigation. This research examines PSALT under the Generalized Kavya–Manoharan exponential distribution based on the GPHC scheme. Using gamma prior, maximum likelihood, and Bayesian techniques, estimate model parameters. Squared error and entropy loss functions yield Bayesian estimators using informational priors in simulation and non-informative priors in application. Various censoring schemes are calculated using Monte Carlo simulation. The methodology is demonstrated using two real-world accelerated life test data sets.