For the setting of interval censoring case 2, a nonparametric two‐sample test, based on a smooth functional of the nonparametric maximum pseudolikelihood estimator, is developed to compare the failure functions of two populations. Monte Carlo simulation studies on Weibull distributions show that this test performs quite well in many situations in comparison with the parametric likelihood ratio test. A real dataset from an study is used to illustrate the new test.

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