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In this paper, the optimal plans for k-level constant-stress accelerated life test are presented for Lindley failure data under complete sampling. According to the log-linear life-stress relationship, the optimal proportion of test units allocated to each stress level is determined under D- and C-optimality criteria. Moreover, two real data sets are analyzed to illustrate the proposed procedures. Furthermore, the real data sets are used to show that the Lindley distribution can be a better model than one based on the exponential distribution. In addition, numerical examples are used to compare between the D-optimal plan, C-optimal plan, and traditional plan through asymptotic variance of maximum likelihood estimators (MLEs). Finally, some interesting conclusions are obtained.