# Mean cumulative function for Parametric Growth Curve

The mean cumulative function (MCF) plot displays the mean cumulative function versus time. Use this plot to determine whether your system is improving, deteriorating, or remaining constant.

The plot consists of the following:
• Plot points calculated using the Nelson-Aalen method for the empirical mean cumulative function. The plot points do not assume a particular model. When you have interval data, Minitab estimates failure times by evenly distributing the number of occurrences in each interval and plotting the appropriate points.
• The mean cumulative function based on the estimated shape and scale of the distribution. For a power-law process, the rate of system failures can increase, decrease, or remain constant. The resulting graph can be straight or a curve that is either concave up or concave down. For a homogeneous Poisson process, the failure rate is constant, resulting in a straight line.

To assess the fit of the distribution model, examine how closely the plotted points follow the line or curve. If the points closely follow the line or curve, the distribution provides a good fit.

The MCF plot also provides information about the pattern of system failures:
• A straight line indicates that system failures are constant over time—your system is stable.
• A curve that is concave down indicates that the time between failures is increasing over time—your system reliability is improving.
• A curve that is concave up indicates that the time between failures is decreasing over time—your system reliability is deteriorating.
You may want to set the minimum value of the X-scale to the time of the first failure to more easily view the failure rate.
###### Note

Because the Nelson-Aalen plot does not depend on the model, the plot points are the same, regardless of which estimation method and model type you select The mean cumulative function plot, however, differs depending on the model.

## Interpretation

For the air conditioning data, the estimate of the mean cumulative function is approximately linear, which indicates that the rate of system failures is relatively constant.

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