Interval estimation of component failure rates based on data from series systems having differing numbers of components of various kinds is addressed. Complete, Type I, and Type II censored observations from exponential lifetime distributions are considered. The cuberoot normalizing transformation is used to derive approximate confidence intervals for the component failure rates. Exact results and a simulation study show that the proposed method performs better than the standard application of maximum likelihood and a method stemming from Miyamura (1982). In fact, the proposed method is shown to be as accurate as the Wilson–Hilferty normal approximation to the chi-squared distribution in a limiting case. A data set on air-conditioner life-test results is used for illustration and comparison.