Methods and formulas for individual curve in Nonparametric Growth Curve

Mean cumulative function (MCF)

The mean cumulative function is the average cumulative number of failures or the average cumulative cost over all systems. Use this measure of the cumulative failures (or the cumulative cost) to determine whether repairs (or repair costs) are increasing, decreasing, or remaining constant.

For information on how to calculate the mean cumulative function, see Meeker and Escobar1 and Nelson2.

Standard error of mean cumulative function (MCF)

The standard errors are the standard deviations of the MCF. The standard error is a measure of the variability in the estimate.

For information on how to calculate the standard error of the mean cumulative function, see Meeker and Escobar1 and Nelson2.

Confidence limits for mean cumulative function (MCF)

When the MCF is positive, the confidence limits for MCF are calculated as follows:

Notation

TermDescription
estimated mean cumulative function
estimated standard error of the mean cumulative function
zα the (1 + α) / 2 percentile of a standard normal distribution where 100α % is the confidence level
1 W.Q. Meeker and L.A. Escobar (1998). Statistical Methods for Reliability Data. John Wiley & Sons, Inc.
2 W. Nelson (1982). Applied Life Data Analysis. John Wiley & Sons.
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