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.
You can enter starting estimates for the parameters. If these estimates are close to the true solution, then the algorithm might converge even though the algorithm did not converge before.
For the 2-parameter exponential distribution, enter your threshold parameter estimate in the second row.