Summarized Guide to Variable Control Chart Selection

By Dave Harrold, CONTROL ENGINEERING March 1, 1999

Generally, selection of a control chart and rational subgroup must be balanced between needs, costs, and acceptable risks. Larger sample sizes may make the chart more sensitive in detecting changes, but usually will cost more to operate. X-bar & R charts are usually effective, but in some situations they are not as effective as other chart types. The following table may be used as a guideline in evaluating control charts for a variety of situations.

Summarized Guide to Variable Control Chart Selection

Chart type
Purpose
Usage
Subgroup size
Remarks

Average(X-bar)
Monitor the average of a process or product characteristic across time.
Moderate to high volume continuous production when a sample of more than three units can be selected every few hours.
n > 3
Insensitive to shifts smaller than 2 sigma when n = 4 to 6. Do not use test runs if data is autocorrelated.

Range (R)
Monitor the variability of a process or product characteristic across time.
Used with a X-bar chart when sample size is 10 or smaller.
3 & n & 11
Sampling distribution is not symmetric. Do not use test runs. Insensitive to small shifts.

Standard deviation (S)
Monitor the variability of a process or product characteristic across time.
Used together with X-bar charts when sample size is more than 10.
n > 10
Increased sensitivity due to increased sample size. Recommended when tighter control of a process is necessary and/or when sampling cost is not a factor. Do not use test runs.

Z-bar & W
Similar to X-bar & R charts.
These are standardized X-bar & R charts, used to monitor the same characteristic of several similar, but not identical, products.
3 & n & 11
Very useful for batch processes or short production runs when one machine is used for several similar products. This is a technique to combine several batches of data into one single set of charts instead of using one set of X-bar & R charts for each data type.

Individual and moving range (X & MR)
Monitor the variability of a process or product characteristic across time. Assumes past and present data are equally important.
Low-volume production that requires long periods of time to obtain a single sample, or when only a single sample is meaningful, or for a batch process with excess batch-to-batch variation.
n = 1
Underlying distribution of the X chart must be tested to make sure the normal distribution assumption is reasonably satisfied.

Exponentially weighed moving average (EWMA)
Monitor small shifts in the process average when conventional Shewhart charts are not sensitive enough.
Extremely useful in processes where rational subgroup is n = 1, or when it is important to detect small shifts in high capability and stable process, or when normal distribution assumptions are not satisfied.
n > 1
Non-Shewhart chart. Sensitive to small shifts in order of 0.5 to 1.5 Sigma. Does not react to large shifts as quickly as Shewhart X-bar chart. Able to forecast the process mean at the end of the next period.

Cumulative-sum (CUSUM)
Similar to EWMA chart.
Similar to EWMA chart, but difficult for manual charting. Recommended only when computerized charting is available.
n > 1
Non-Shewhart chart. As sensitive to small shifts as EWMA charts, but slower to react to large shifts.

Source: Control Engineering with data from Motorola