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.

There are two options when the Newton-Raphson algorithm diverges or does not converge after X iterations:
  • You can enter different starting estimates for Minitab to use.
  • You can fit a regression line through the data so convergence is not a problem.

Enter starting estimates for Minitab to use

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.

  1. Enter estimates for your parameters in an empty column of the worksheet containing your data. Different distributions require different parameters. You should enter your shape, location, or mean parameter estimate in the top row, your scale parameter estimate in the second row, and your threshold parameter estimate in the third row. If your chosen distribution has fewer than three parameters, leave the second and third rows blank, as appropriate.

    For the 2-parameter exponential distribution, enter your threshold parameter estimate in the second row.

  2. Choose Stat > Reliability/Survival > Distribution Analysis (Right Censoring) or Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis.
  3. Click Options. Enter the column that contains your starting estimates for the parameters in Use starting estimates.

Fit a regression line so convergence is not a problem

  1. Choose one of the distribution analysis commands that estimates parameters:
    • Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Distribution ID Plot
    • Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Distribution Overview Plot
    • Stat > Reliability/Survival > Distribution Analysis (Right Censoring) > Parametric Distribution Analysis
    • Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Distribution ID Plot
    • Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Distribution Overview Plot
    • Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis
  2. Click the button that lets you choose the estimation method.
    • For Distribution ID Plot and Distribution Overview Plot commands, click Options.
    • For Parametric Distribution Analysis commands, click Estimate.
  3. Under Estimation Method, choose Least Squares (failure time(X) on rank(Y)).
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