Control charts for variables are classified according to the subgroup summary statistic plotted on the chart:
• The IR selection provides additional chart types:
– Individual Measurement charts display individual measurements. These charts are appropriate when only one measurement is available for each subgroup sample.
– Moving Range charts display moving ranges of two or more successive measurements. See Moving Range (Average) Charts.
• XBar charts display subgroup means (averages). This selection provides additional chart types:
– R charts display subgroup ranges (maximum – minimum).
– S charts display subgroup standard deviations.
For quality characteristics measured on a continuous scale, a typical analysis shows both the process mean and its variability with a mean chart aligned above its corresponding R or S chart.
• Runs Chart displays data as a connected series of points. Runs charts can also plot the group means when the Sample Label role is used, either on the window or through a script.
• Levey-Jennings charts show a process mean with control limits based on a long-term sigma. The control limits are placed at 3s distance from the center line. The standard deviation, s, for the Levey-Jennings chart is calculated the same way standard deviation is in the Distribution platform.
• Presummarize charts display subgroup means and standard deviations. See Presummarize Charts.
• CUSUM charts show cumulative sums of subgroup or individual measurements from a target value. See V-Mask CUSUM Control Charts.
• UWMA charts show a uniformly weighted moving average of a specified number of measurements. See Uniformly Weighted Moving Average Charts.
• EWMA charts show an exponentially weighted moving average of all measurements with a specified weight. See Exponentially Weighted Moving Average Charts.
In a Moving Average chart, the quantities that are averaged can be individual observations instead of subgroup means. However, a Moving Average chart for individual measurements is not the same as a control chart for individual measurements or moving ranges with individual measurements plotted.
Moving Range (Average) charts display moving ranges of two or more successive measurements. Moving ranges are computed for the number of consecutive measurements that you enter in the Range Span box. The default range span is 2. Because moving ranges are correlated, these charts should be interpreted with care.
A Median Moving Range chart is also available. If you choose a Median Moving Range chart and an Individual Measurement chart, the limits on the Individual Measurement chart use the Median Moving Range as the sigma, rather than the Average Moving Range.
If your data consist of repeated measurements of the same process unit, you can combine these into one measurement for the unit. Pre-summarizing is not recommended unless the data have repeated measurements on each process or measurement unit.
Presummarize summarizes the process column into sample means or standard deviations, based either on the sample size or sample label chosen. Then it charts the summarized data based on the options chosen in the launch window. You can also append a capability analysis by checking the appropriate box in the launch window.
The Presummarize launch window has the following options for chart types:
• Individual on Group Means
• Individual on Group Std Devs
• Moving Range on Group Means
• Moving Range on Group Std Devs
• Median Moving Range on Group Means
• Median Moving Range on Group Std Devs
There is also an option for setting the range span that is used for the moving range chart types.
V-Mask Cumulative Sum (CUSUM) control charts show cumulative sums of subgroup or individual measurements from a target value. V-Mask CUSUM charts can help you decide whether a process is in a state of statistical control by detecting small, sustained shifts in the process mean. In comparison, standard Shewhart control charts can detect sudden and large changes in measurement, such as a two or three sigma shift, but they are less effective at spotting smaller changes, such as a one sigma shift.
The CUSUM menu selection has options for V-mask cumulative sum charts. In addition to KSigma, you also specify:
• The vertical distance h between the origin for the V-mask and the upper or lower arm of the V-mask for a two-sided chart. For a one-sided chart, H is the decision interval. Choose H as a multiple of the standard error.
• The reference value k, where k is greater than zero.
Another form of a cumulative sum control chart is the tabular CUSUM chart. To create a tabular CUSUM chart, see “CUSUM Control Charts”. The tabular CUSUM chart is recommended over the V-mask chart for a variety of reasons, including the following:
• The V-mask must be moved with each observation, not simply placed on the last observation.
• The cumulative sums in the V-mask procedure can end up a long way from the center of the graph, even for an on-target process.
Caution: Montgomery (2013) strongly “advises against using the V-mask procedure.”
Each point on a Uniformly Weighted Moving Average (UWMA) chart is the average of the w most recent subgroup means, including the present subgroup mean. When you obtain a new subgroup sample, the next moving average is computed by dropping the oldest of the previous w subgroup means and including the newest subgroup mean. The constant, w, is called the span of the moving average.
In addition to KSigma and Alpha, in the UWMA launch window you also specify:
• The Moving Average Span, or w, which indicates how many subgroups to include to form the moving average. The larger the Moving Average Span (w), the smoother the UWMA line, and the less it reflects the magnitude of shifts. This means that larger values of w guard against smaller shifts. See Control Limits for UWMA Charts.
Each point on an Exponentially Weighted Moving Average (EWMA) chart is the weighted average of all the previous subgroup means, including the mean of the present subgroup sample. The weights decrease exponentially going backward in time.
Note: An Exponentially Weighted Moving Average (EWMA) chart can also be called a Geometric Moving Average (GMA) chart.
In addition to KSigma and Alpha, in the EWMA launch window you also specify:
• A Weight parameter, which is the weight (0 < weight ≤ 1) assigned to the present subgroup sample mean. Small values of Weight are used to guard against small shifts. See Control Limits for EWMA Charts.
Tip: See “EWMA Control Charts” for the newer EWMA Control Charts platform.