# Control charts

Control charts determine if a process is in a state of statistical control.

A control chart plots a quality characteristic statistic in a time-ordered sequence. A center line indicates the process average, and two other horizontal lines called the lower and upper control limits represent process variation.

All processes have some natural degree of variation. A control chart for a process that is in-control has points randomly distributed within the control limits. That is it has variation only from sources common to the process (called common-cause variation). An out-of-control process has points falling outside the control limits or non-random patterns of points (called special-cause variation).

If the process is in-control, no corrections or changes to the process are needed.

If the process is out-of-control, the control chart can help determine the sources of variation in need of further investigation. It is appropriate to determine if the results with the special-cause are better than or worse than results from common causes alone. If worse, then that cause should be eliminated if possible. If better, it may be appropriate to investigate the system further as it may lead to improvements in the process.

Typically control limits are defined as a multiple of the process sigma. For a Shewhart control chart with 3-sigma control limits and assuming normality, the probability of exceeding the upper control limit is 0.00135 and the probability of falling below the lower control limit is also 0.00135. Their sum is 0.0027 (0.27%). Therefore the probability of a point between the control limits for an in-control process is 0.9973 (99.73%). An alternative is to define the control limits as probability limits based on a specified distribution rather than assuming a normal distribution.

Another way to look at the performance of a control chart is the average run length (ARL). An average in control run length is the number of observations when a process is in-control before a false alarm occurs. An average out of control run length is the number of observations that a process is out-of-control before a shift is detected, and depends on the size of the shift to be detected. The Shewhart control chart described above has an ARL = 1/0.0027 = 370.37. That is, when a process is in control, you should expect a false alarm out-of-control signal approximately once every 371 runs.

Although most examples of control charts show quality characteristics that are of interest to the end-user (such as length, diameter, or weight) they are most beneficial applied to process variables further upstream (such as the temperature of the furnace or content of tin in the raw material).

**Shewhart control charts**

A Shewhart control chart detects changes in a process.**Time-weighted control charts**

A time-weighted control chart detects small shifts in a process mean.

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Version 6.15

Published 18-Apr-2023