In industrial engineering reliability studies the Mean-Time-To-Failure (MTTF) is an accepted indication of the expected time to failure by the post-processing of the failure probability density function (PDF) data. Usually, the data of the failure PDF are fitted with Weibull, Lognormal or Gaussian distributions under assumptions of normality, with either chi-square or Maximum Likelihood Estimation (MLE) methods, however it is rarely the case that the uncertainty of the MTTF is also calculated due to the complexity of the analysis. In this paper the estimate of the uncertainty of the PDF parameters is formulated as a nonlinear regression problem and utilized as inputs into a corresponding measurement uncertainty equation for the MTTF that incorporates correlation effects in order to determine the nominal value and associated uncertainty of the MTTF for reported failure data of lithium-ion batteries with numerical experiments. Results demonstrate that the combination of the expected value and uncertainty for the MTTF can quantitatively estimate appropriate statistical lower and upper bounds for the MTTF to offer superior functionality and accuracy for reliability engineering applications.