# Viz - Control Chart (Shewhart)

The purpose of control charts is to allow simple detection of events that are indicative of actual process change.

Control charts attempt to differentiate “assignable” (“special”) sources of variation from “common” sources.

Control charts, also known as Shewhart charts (after Walter A. Shewhart) or process-behavior charts, are a statistical process control tool used to determine if a process (manufacturing, business, computer ?) is in a state of control.

A process that is stable but operating outside desired limits (Example: SLO: Service Level Objectives) needs to be improved through a deliberate effort to understand the causes of current performance.

Control charts are typically used for time-series data.

The goal is to reduce variation in a the process.

## 3 - Structure

A control chart consists of:

• Points representing a statistic (e.g., a mean, range, proportion) of measurements of a quality characteristic in samples taken from the process at different times (i.e., the data)
• The mean of this statistic using all the samples is calculated (e.g., the mean of the means, mean of the ranges, mean of the proportions)
• A center line is drawn at the value of the mean of the statistic
• The standard deviation of the statistic

## 4 - State

### 4.1 - Control

Under control means stable, with variation only coming from sources common to the process.

If the process is in control (and the process statistic is normal), 99.7300% of all the points will fall between the control limits.

When the process does not trigger any of the control chart “detection rules” for the control chart, it is said to be “stable”.

Instead of immediately launching a process improvement effort to determine whether special causes are present, the Quality Engineer may temporarily increase the rate at which samples are taken from the process output.

False There is approximately a 0.27% probability of a point exceeding 3-sigma control limits. For a Shewhart control chart using 3-sigma limits, this false alarm occurs on average once every 1/0.0027 or 370.4 observations. Therefore, the number of points that must be plotted before an out of control condition (also known as average run length - ARL) is 370.4.

Investigation

## 5 - Limit

A control chart has:

• Upper and lower control limits (sometimes called “natural process limits”) that indicate the threshold at which the process output is considered statistically 'unlikely' and are drawn typically at 3 standard deviations from the center line.
• Upper and lower warning or control limits, drawn as separate lines, typically two standard deviations above and below the center line.

With:

• a three-sigma warning levels, common-cause variations result in signals:
• less than once out of every twenty-two points for skewed processes
• and about once out of every three hundred seventy (1/370.4 or 0.002 percentage ) points for normally distributed processes.
• a two-sigma warning levels. This level will be reached about once for every twenty-two (1/21.98) plotted points in normally distributed data.

More see Control_chart#Choice_of_limits