Test for equal shape (or scale or MTBF) parameters for Parametric Growth Curve

When your failure/repair data are from more than one system, Minitab provides a test for equal shape (or scale or mean-time-between failures) parameters.

The hypotheses for this test are as follows:
  • H0: All the shapes (or scales or MTBFs) are equal
  • H1: At least one of the shapes (or scales or MTBFs) is different
A chi-square test can determine whether the shape parameters for the different systems are significantly different from each other. Compare the p-value with your pre-determined α-value.
  • If the p-value is less than or equal to the α-value, you can conclude that the parameter for at least one system is significantly different.
  • If the p-value is greater than the α-value, you cannot conclude that the parameters are significantly different.

When estimating a parametric growth curve, Minitab assumes that all systems within a single column are from identical processes. Minitab produces a single growth curve for all the data from identical processes. If you reject the null hypothesis and conclude that the shapes (or scales or MTBF) are unequal, you cannot make this assumption. In this case, you should analyze the data from different systems separately.

When the data are from an identical process and you use a system variable, Minitab uses Bartlett's modified likelihood-ratio test. When the data are from different processes and you use a By (grouping) variable, Minitab uses a likelihood ratio chi-square test.

These tests are not available for interval data.

Example output

Test for Equal Shape Parameters Bartlett’s Modified Likelihood Ratio Chi-Square Test Statistic 10.88 P-Value 0.539 DF 12


For the air conditioning data, the p-value of 0.539 is greater than the α-value of 0.05. Therefore, the engineer cannot conclude that the shape parameters for the different systems are significantly different.

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