Maximum Likelihood Estimation (MLE)

This is most popularly used term in reliability studies in which the probability of the sample is obtained by multiplying the density function evaluated at each data point. The product containing the data points and the unknown parameter is called the likelihood function. By finding the value of parameter that maximizes this expression, we make the set of data observed "more likely". In other words we choose parameter values that are more consistent with our data by maximizing the likelihood of the sample. Thus the MLE method is equivalent to maximizing the equation of several variables.

If the assumption of independently and identically distributed (IID) is not contradicted for Time Between Failures (TBFs), the MLE method provides fairly good estimate of the parameter of the theoretical distribution. This method requires computer programs to do the calculations efficiently and rapidly.  Further, there are some more methods available in literature for plotting TTT transforms such as Kaplan-Meier (KME) or Product Limit Estimates, Piecewise Exponential Estimates (PEXE).