The least squares estimation method for model parameters under failure step-stress accelerated life tests is studied and a numerical example will be given to illustrate the proposed inferential procedures under the compound linear plans proposed as an alternative to the optimal quadratic plan, assuming that the exponential distribution with a quadratic relationship between stress and log-mean lifetime. The proposed compound linear plan for constant stress accelerated life tests and 4:2:1 plan are compared for various situations. Even though the compound linear plan was proposed under constant stress accelerated life tests, we found that this plan did well relatively in failure step-stress accelerated life tests.