Reliability of a system under an accelerated life of step-stress with a progressive first failure sample of Burr distribution is investigated. The Burr distribution has an importance in applied engineering. Under normal circumstances, it is difficult to measure the lifetimes of the product to study the validity function. Failure rarely occurs, so we resort to the process of accelerating failure using accelerated life tests. Great results were scheduled in paper obtained using point-estimation methods such as the maximum likelihood estimator function (MLEs). Also, the mean square error (MSEs) is calculated from the estimated values. Confidence intervals were obtained with different confidence levels to study different cases of confidence intervals. The present paper asserts that the greater the size of the sample, the better and more specific the results are to the real values.