When you estimate parameters for one of Minitab's distribution analyses in Reliability/Survival, Minitab uses the Newton-Raphson algorithm to calculate maximum likelihood estimates of the parameters that define the distribution. All resulting functions are calculated from that distribution. Messages that indicate that the algorithm stopped searching for a solution occur because Minitab is far from the true solution. This means that the function is not optimal or that the actual estimates continue to change.
An option to consider when the Newton-Raphson algorithm diverges or does not converge is to fit a regression line through the data. This estimation method is not algorithmic.