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In this paper, step-stress partially accelerated life tests SSPALTare applied when the lifetime of a product under design stress follows a 3-parameter compound Weibull-gamma distribution based on type-I censored samples. Maximum likelihood estimators MLEs for the considered parameters obtained for the distribution parameter and acceleration factor. Also, asymptotic variance and covariance matrix of the estimators given. Furthermore, confidence intervals of the estimators presented. Bayes estimators for the parameters are carried out based on (a) non-informative prior NIP for each parameter represented, (b) both symmetric loss (squared error loss) function and asymmetric LINEX loss function. The Bayes estimates cannot be obtained in explicit form, so we propose to use MCMC algorithm. Analysis of a simulated data set presented for illustrative purposes. Finally, a Monte Carlo simulation study is carried out to investigate the precision of the Bayes estimates with MLEs and to compare the performance of different corresponding confidence intervals considered.

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