Specify estimation options for Parametric Growth Curve

Stat > Reliability/Survival > Repairable System Analysis > Parametric Growth Curve > Estimate

Estimation method

Select a method to estimate the distribution parameters.
Maximum Likelihood
Estimate the distribution parameters by maximizing the likelihood function.
Conditional ML
Estimate the distribution parameters by maximizing the conditional likelihood function. If you use this method, Minitab provides estimates for standard error and confidence interval for the shape value only.
Least Squares
Estimate the distribution parameters by fitting a regression line to the points on a probability plot. If you use this method, Minitab does not provide estimates for standard error and confidence intervals.
Note

For more information on the results that you can obtain using each estimation method, go to Estimating parameters for growth curves.

Process model

Select a process model based on whether a trend exists in the failure/repair rate.
  • Power-Law process: Select this option to model the data using a power-law process. Use a power-law process to model failure/repair times that have an increasing, decreasing, or constant rate. The repair rate for a power-law process is a function of time.
    Note

    If you use the maximum likelihood estimation method (default), the power-law model is also referred to as the AMSAA model or Crow-AMSAA model. If you use the least squares estimation method, the power-law model estimation method is also called the Duane model. For more information, go to Methods and formulas for parametric models in Parametric Growth Curve.

    • Estimate shape parameter: Select to have Minitab estimate the shape parameter from the sample data.
    • Set shape parameter: Select this option to specify the value of the shape parameter. Then enter a positive numeric constant. The value you enter might be based on a distribution analysis or historical process knowledge.
  • Poisson process: Select this option to model the data using a Poisson process. Use to model failure/repair times that remain stable over time. The Poisson process is the simplest statistical model for describing the failure rate of a repairable system. However, it is only appropriate for a system that does not improve or deteriorate, an assumption that is difficult to meet in practice.

Confidence intervals

Confidence level

Enter a confidence level between 0 and 100. Usually a confidence level of 95% works well. A 95% confidence level indicates that you can be 95% confident that the interval contains the true population parameter. That is, if you collected 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the actual value for the population parameter (if all the data could be collected and analyzed).

A lower confidence level, such as 90%, produces a narrower confidence interval and may reduce the sample size or testing time that is required. However, the likelihood that the confidence interval contains the population parameter decreases.

A higher confidence level, such as 99%, increases the likelihood that the confidence interval contains the population parameter. However, the test may require a larger sample size or a longer testing time to obtain a confidence interval that is narrow enough to be useful.

Confidence intervals

From the drop-down list, indicate whether you want Minitab to display a two-sided confidence interval (Two-sided) or a one-sided confidence interval (Lower bound or Upper bound). A one-sided interval generally requires fewer observations and less testing time to be statistically confident about the conclusion. Many reliability standards are defined in terms of the worst-case scenario, which is represented by a lower bound.

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