# Table of mean cumulative 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 function: The cumulative number of failures (or repairs) averaged over systems. If you enter a cost column, then Minitab calculates cumulative repair costs averaged over systems.
• Standard error: The standard error of the mean cumulative function.
• 95% Normal CI: The lower and upper limits of the 95% confidence interval for the mean cumulative function.

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

## Example output

### Results for Type = 1

System: ID Nonparametric Estimates
Table of Mean Cumulative Function Mean Cumulative Standard 95% Normal CI Time Function Error Lower Upper System 33 0.07143 0.068830 0.01081 0.47218 179 88 0.14286 0.093522 0.03960 0.51540 132 250 0.21429 0.109664 0.07859 0.58426 128 272 0.28571 0.120736 0.12481 0.65408 137 287 0.35714 0.128060 0.17686 0.72120 181 302 0.42857 0.132260 0.23407 0.78471 119 317 0.50000 0.133631 0.29613 0.84423 182 364 0.57143 0.132260 0.36303 0.89945 112 367 0.64286 0.128060 0.43506 0.94990 167 391 0.71429 0.157421 0.46374 1.10019 112 402 0.78571 0.149098 0.54168 1.13970 175 421 0.85714 0.170747 0.58008 1.26653 137 431 0.92857 0.158574 0.66444 1.29771 155 444 1.00000 0.174964 0.70969 1.40906 119 462 1.07143 0.158574 0.80165 1.43200 101 481 1.14286 0.137661 0.90253 1.44718 145 498 1.21429 0.149098 0.95456 1.54468 182 500 1.28571 0.187044 0.96675 1.70992 119 500 1.35714 0.191853 1.02872 1.79042 128 548 1.42857 0.219328 1.05735 1.93013 112 552 1.50000 0.242226 1.09304 2.05848 137 625 1.57143 0.280566 1.10744 2.22982 137 635 1.64286 0.259653 1.20522 2.23940 169 650 1.71429 0.256120 1.27912 2.29750 169 657 1.78571 0.270649 1.32679 2.40338 182 687 1.86264 0.266655 1.40692 2.46596 179 687 1.93956 0.260862 1.49012 2.52456 181 700 2.03047 0.254826 1.58771 2.59671 175 708 2.13047 0.274527 1.65498 2.74258 169 710 2.24158 0.268755 1.77214 2.83537 145 710 2.35269 0.257586 1.89833 2.91581 155 710 2.46380 0.240267 2.03516 2.98273 167 719 2.63047 0.347216 2.03084 3.40714 137 724 2.83047 0.425594 2.10800 3.80055 112 724 3.03047 0.443994 2.27405 4.03849 128 724 3.23047 0.410559 2.51818 4.14424 132 730 3.73047 0.471307 2.91221 4.77864 101 730 4.23047 0.410559 3.49769 5.11677 119

### Results for Type = 2

System: ID Nonparametric Estimates
Table of Mean Cumulative Function Mean Cumulative Standard 95% Normal CI Time Function Error Lower Upper System 19 0.06667 0.064406 0.01004 0.44284 228 22 0.13333 0.087771 0.03670 0.48447 212 39 0.20000 0.103280 0.07269 0.55029 192 54 0.26667 0.114180 0.11521 0.61721 214 61 0.33333 0.121716 0.16295 0.68186 219 91 0.40000 0.157762 0.18465 0.86652 192 93 0.46667 0.159629 0.23869 0.91237 243 119 0.53333 0.207989 0.24834 1.14538 192 148 0.60000 0.263312 0.25386 1.41809 192 173 0.66667 0.261052 0.30945 1.43622 190 185 0.73333 0.274334 0.35227 1.52661 228 187 0.80000 0.269979 0.41289 1.55006 235 192 0.86667 0.264435 0.47658 1.57604 205 194 0.93333 0.257624 0.54335 1.60321 216 203 1.00000 0.249444 0.61330 1.63052 183 205 1.06667 0.257624 0.66442 1.71243 243 211 1.13333 0.264435 0.71738 1.79046 183 242 1.20000 0.269979 0.77210 1.86504 190 250 1.26667 0.257624 0.85023 1.88706 204 264 1.33333 0.277555 0.88664 2.00507 243 277 1.40000 0.295146 0.92615 2.11630 183 293 1.46667 0.280740 1.00786 2.13434 184 306 1.53333 0.324779 1.01238 2.32237 192 369 1.60000 0.309839 1.09468 2.33859 206 373 1.66667 0.335548 1.12325 2.47298 183 382 1.73333 0.319258 1.20810 2.48693 200 415 1.80000 0.342540 1.23962 2.61370 243 416 1.87143 0.340512 1.31007 2.67333 235 419 1.94835 0.338097 1.38662 2.73764 219 419 2.02527 0.349310 1.44435 2.83985 228 432 2.11618 0.347441 1.53391 2.91948 216 434 2.21618 0.345034 1.63337 3.00696 204 441 2.32729 0.341839 1.74512 3.10369 214 447 2.45229 0.337430 1.87262 3.21141 212 448 2.59515 0.331033 2.02109 3.33227 205 448 2.73801 0.315398 2.18466 3.43152 206 460 2.93801 0.298009 2.40832 3.58420 200 461 3.18801 0.449834 2.41776 4.20364 192 464 3.52134 0.511478 2.64893 4.68108 190 503 4.02134 0.535360 3.09778 5.22025 184 511 5.02134 0.535360 4.07443 6.18831 183

## Interpretation

For the type 1 brake component, the mean cumulative function is 1.00000 at 444 days. That is, by 444 days, the average number of repairs needed for a single system is 1. The engineer can be 95% confident that the average number of repairs by 444 days falls within the interval of 0.70969 and 1.40906.

When all systems with the type 1 brake component have retired at 730 days, an average of 4.23047 repairs have been made on each system. The engineer can be 95% confident that the true average number of repairs for a system before retirement at 730 days falls within the interval 3.49769 and 5.11677.

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