I chart

An I-chart is a type of control chart used to monitor the process mean when measuring individuals at regular intervals from a process.

It is typical to use individual observations instead of rational subgroups when there is no basis for forming subgroups, when there is a long interval between observations becoming available, when testing is destructive or expensive, or for many other reasons. Other charts such as the exponentially weighted moving average and cumulative sum may be more appropriate to detect smaller shifts more quickly.

Each point on the chart represents the value of an individual observation.

The center line is the process mean. If unspecified, the process mean is the mean of the individual observations.

The control limits are either:
  • A multiple (k) of sigma above and below the center line. Default k=3.
  • Probability limits, defined as the probability (alpha) of a point exceeding the limits. Default alpha=0.27%.
If unspecified, the process sigma is the standard deviation of the individual observations, unless the chart is combined with an MR-chart where it is estimated as described for the respective chart. For an in-control process, both estimators are unbiased, and the standard deviation is a more efficient estimator. For a process with special causes of variation, both estimators are biased, and it may be preferable to use the median moving range estimator.

The observations are assumed to be independent and normally distributed. If the process shows a moderate departure from normality, it may be preferable to transform the variable so that it is approximately normally distributed.

It is important to ensure process variability is in a state of statistical control before using the I-chart to investigate if the process mean is in control. Therefore an I-chart is often combined with an MR-chart to monitor process variability, although some authors question the benefit of an additional MR-chart.