This paper presents new compromise ALT plan which is applied to situations that true relationship between stress and parameters is not known exactly. The assumed failure distribution of this study is one of location-scale family, i. e., exponential, Weibull, and lognormal distributions which have been ones of the popular choices of failure distributions. The method of applying the stress is constant, and the censoring mechanism is Type I censoring. Compared with existing compromise plans under true simple linear model in terms of statistical efficiency, the efficiency of new compromise plan is better than the corresponding other compromise ones in most cases. For case when true model is quadratic, this plan can be used without any severe loss in statistical efficiency. The proposed new compromise ALT plan is illustrated with a numerical example and sensitivity analyses are conducted to study effects of pre-estimates of design parameters.