Doubly censoring scheme, which includes left as well as right censored observations, is frequently observed in practical studies. In this paper we introduce a new interval say tracking interval for comparing the two rival models when the data are doubly censored. We obtain the asymptotic properties of maximum likelihood estimator under doubly censored data and drive a statistic for testing the null hypothesis that the proposed non-nested models are equally close to the true model against the alternative hypothesis that one model is closer when we are faced with an experimental situation. Monte Carlo simulations are performed to observe the behavior of the theoretical results, and the proposed methodology is illustrated with data from spreading of the micro plasma droplets. We also perform the statistical analysis of these data using the probability models including Weibull, Burr type XII, Burr type III and inverse Weibull distributions. One important result of this study is that the Burr type XII distribution, in contrast to inverse Weibull distribution, may describe more closely to Weibull distribution for spread factor data under doubly censored sample.