Table of mean cumulative difference function for Nonparametric Growth Curve

Minitab displays nonparametric growth information in a table that includes the following:
  • Time: The successive failure (or repair) times.
  • Mean cumulative difference function: The difference between groups in the number of failures (or repairs) averaged over systems. If you enter a cost column, then Minitab calculates the difference between groups in the cumulative repair costs averaged over systems.
  • Standard error: The standard error of the mean cumulative difference function.
  • 95% Normal CI: The lower and upper limits of the 95% confidence interval for the mean cumulative difference function.

With a nonparametric estimation procedure, the value of the mean cumulative difference function changes only when a failure occurs.

Example output

Comparison: (Type = 1) - (Type = 2)

Table of Mean Cumulative Difference Function


Mean Cumulative
Difference
Function




Standard
Error
95% Normal CI
TimeLowerUpper
19-0.066670.064406-0.192900.05957
22-0.133330.087771-0.305360.03869
33-0.061900.111541-0.280520.15671
39-0.128570.124114-0.371830.11469
54-0.195240.133322-0.456540.06607
61-0.261900.139830-0.535970.01216
88-0.190480.153496-0.491320.11037
91-0.257140.183399-0.616600.10231
93-0.323810.185008-0.686420.03880
119-0.390480.228047-0.837440.05649
148-0.457140.279427-1.004810.09052
173-0.523810.277299-1.067300.01969
185-0.590480.289837-1.15855-0.02241
187-0.657140.285719-1.21714-0.09714
192-0.723810.280486-1.27355-0.17407
194-0.790480.274074-1.32765-0.25330
203-0.857140.266399-1.37928-0.33501
205-0.923810.274074-1.46099-0.38663
211-0.990480.280486-1.54022-0.44073
242-1.057140.285719-1.61714-0.49714
250-1.052380.279994-1.60116-0.50360
264-1.119050.298435-1.70397-0.53413
272-1.047620.302679-1.64086-0.45438
277-1.114290.318886-1.73929-0.48928
287-1.042860.321731-1.67344-0.41228
293-1.109520.308568-1.71431-0.50474
302-1.038100.310335-1.64634-0.42985
306-1.104760.350677-1.79208-0.41745
317-1.033330.351196-1.72166-0.34500
364-0.961900.350677-1.64922-0.27459
367-0.890480.349114-1.57473-0.20622
369-0.957140.335260-1.61424-0.30004
373-1.023810.359155-1.72774-0.31988
382-1.090480.343985-1.76467-0.41628
391-1.019050.355960-1.71672-0.32138
402-0.947620.352358-1.63823-0.25701
415-1.014290.373582-1.74649-0.28208
416-1.085710.371724-1.81428-0.35715
419-1.239560.379800-1.98395-0.49517
421-1.168130.388808-1.93018-0.40608
431-1.096700.383618-1.84858-0.34482
432-1.187610.381917-1.93616-0.43907
434-1.287610.379729-2.03187-0.54336
441-1.398720.376828-2.13729-0.66015
444-1.327290.384013-2.07995-0.57464
447-1.452290.380094-2.19726-0.70733
448-1.738010.360677-2.44492-1.03109
460-1.938010.345574-2.61532-1.26070
461-2.188010.482663-3.13401-1.24201
462-2.116580.476966-3.05142-1.18174
464-2.449910.535496-3.49947-1.40036
481-2.378490.529680-3.41664-1.34033
498-2.307060.532767-3.35126-1.26285
500-2.164200.546276-3.23488-1.09352
503-2.664200.568698-3.77883-1.54957
511-3.664200.568698-4.77883-2.54957
548-3.592770.578546-4.72670-2.45884
552-3.521340.587608-4.67303-2.36965
625-3.449910.604423-4.63456-2.26527
635-3.378490.595004-4.54467-2.21230
650-3.307060.593471-4.47024-2.14387
657-3.235630.599884-4.41138-2.05988
687-3.081780.595533-4.24900-1.91456
700-2.990870.592914-4.15296-1.82878
708-2.890870.601644-4.07007-1.71167
710-2.557540.586803-3.70765-1.40743
719-2.390870.638098-3.64152-1.14022
724-1.790870.674662-3.11319-0.46856
730-0.790870.674662-2.113190.53144

Interpretation

For the brake reliability data, the mean cumulative difference function is −0.99048 at 211 days. That is, the average number of repairs needed for a single system by 211 days is nearly 1 more for the type 2 brake component than for the type 1 brake component. The engineer can be 95% confident that this difference falls within the interval of −1.54022 and −0.44073.

For these data, all systems were retired for the type 2 brake component at 511 days and for the type 1 brake component at 730 days. At 511 days, the difference between the average number of repairs on each system for the two types of brake components is −3.66420. The engineer can be 95% confident that the true difference in the average number of repairs falls within the interval of −4.77883 and −2.54957. Because the confidence interval does not contain 0, a significant difference exists between the two types of brake components in the average number of repairs that are needed by the time all the systems have retired for the type 2 component at 511 days.