Mean Cumulative Function and Nelson-Aalen Plot
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Use the mean cumulative function and Nelson - Aalen plot to determine whether your system is improving, deteriorating, or staying constant.

The plot consists of:

·    The Nelson-Aalen plot, which is a plot of 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 plot, which is a plot of the mean cumulative function based on the estimated shape and scale. 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 down. For a homogeneous Poisson process, the failure rate is constant, resulting in a straight line.

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 chose. The mean cumulative function plot, however, differs depending on your model.

The plot provides information about the pattern of system failures:

·    A straight line pattern indicates that system failures are remaining constant over time - your system is stable

·    A concave down pattern indicates that the time between failures is increasing over time - your system reliability is improving

·    A concave up pattern indicates that the time between failures is decreasing over time - your system reliability is deteriorating

Below are examples of mean cumulative function plots for improving, stable, and deteriorating systems.