# Specify the estimation methods for Parametric Distribution Analysis (Arbitrary Censoring)

Stat > Reliability/Survival > Distribution Analysis (Arbitrary Censoring) > Parametric Distribution Analysis > Estimate
Estimation Method
• Maximum Likelihood: Estimate the distribution parameters by maximizing the likelihood function.
• Least Squares (failure time(X) on rank(Y)): Estimate the distribution parameters by fitting a regression line to the points on a probability plot.

For more information on these two methods, go to Least squares estimation method and maximum likelihood estimation method.

Assume common shape (slope-Weibull) or scale (1/slope-other dists)
Select to estimate the parameters using a common shape or scale parameter for the distribution. For information on how this assumption affects the estimation method, go to Least squares estimation method and maximum likelihood estimation method and click "Assume common shape or scale parameters for parametric distribution analysis" .
Bayes Analysis
Set shape (slope-Weibull) or scale (1/slope-other dists) at
To estimate other model coefficients while keeping the shape or scale parameter fixed, enter one value to use as the shape or scale parameter for all the response variables, or enter a number of values that is equal to the number of response variables.
Set threshold at
To estimate other model coefficients while keeping the threshold parameter fixed, enter one value to use for the threshold parameter for all the variables, or enter a list of values that are equal to the number of response variables. If you do not provide values to use, Minitab estimates the threshold parameters.
Estimate percentiles for these additional percents
Enter the percents for which you want to estimate percentiles. A percent for a percentile is the percentage of items that are expected to fail by a particular time (percentile). Therefore, each value that you enter must be between 0 and 100 and should indicate the percentage of items that will fail. The nth percentile has n% of the observations below it, and (100 – n)% of observations above it.
Estimate probabilities for these times (values)
Enter one or more times or a column of times for which you want to calculate survival probabilities or cumulative failure probabilities.
• Estimate survival probabilities: Estimate the proportion of units that survive beyond a given time. Use these values to determine whether your product meets reliability requirements or to compare the reliability of two or more designs of a product. For more information, go to What is the survival probability?
• Estimate cumulative failure probabilities: Estimate the likelihood that units fail before a given time. The cumulative failure probability is 1 minus the survival probability.
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.

###### Note

You can only specify a confidence level and calculate confidence intervals when you select Maximum Likelihood from Estimation Method.

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