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The customers' hopes are having great superiority reliable goods on period and reasonable costs. Then, researchers spend accelerated life testing that allows rapidly them reduction the examination period and keep a group of manpower, money and material sources. The major aim of this paper is to study the constant stress time censoring accelerated life tests. It is supposed that the lifetime of a test unit monitors an exponentiated lomax distribution. The estimators of maximum likelihood are developed when the parameters are unknown. The shape parameter of the lifetime distribution at constant stress stages is adopted to be a log linear model. Furthermore, confidence limits of intervals for the parameters, reliability, hazard functions are formed. Moreover, optimum constant acceleration life testing plan is studied through the asymptotic generalized variance of the maximum likelihood estimators of the parameters is minimized. Monte Carlo simulation and two real data are approved to indicate the theoretical results.