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A control limit chart definition is made up of many parts. There are two control limits. The lower limit (LCL) is at the bottom, while the upper limit is at the top. The solid middle line represents the average of all the statistics being plotted. Natural process limits, are determined from historical data of how the process will run if undisturbed. The control limited are at the historical mean or target +/- 3 x the historical standard deviation.

The data plotted on the control charts is used to calculate the limits. They are +/-3 sigma from the average line.

They are used to indicate the limit beyond which a sample value can be considered a special cause of variation. These limits are used to determine the upper and the lower limits of common cause variation.

### Control limited have 3 benefits

Control limits definition are determined by the process data. Control limited accomplishes three things.

Specification limits and control limits do not require that you set limits. Control limits are based upon the process measurement and give you an accurate guideline of what to expect from the process.

#### 2.Be sure to take into consideration both the between and within sample variation

Consider, for example, a control diagram for the average or range. Five parts make up the sample. The control limited formula includes both the range (highest to lowest) and the average length of five parts. The sample variation is represented by the range and the average between them.

### 3.Determine the limits of variation that are predictable for the process measurement

When the process is stable, it provides a framework for common cause variation.

### What are the importance of control limited?

Control limits have existed for a long period of time. Walter Shewhart, a Bell Laboratories physicist, was the first to write about control limits. To improve the quality and reliability of telephone equipment, he created control charts.

Dr. Shewhart conducted many, many experiments over many years to simulate different production outputs.

Based on these results and Tchebycheff’s theorem Dr. Shewhart determined that control limits should be set at +/-3 sigma of an average, such as an average range, to reduce economic losses from both types of errors.

Technical Note: Tchebycheff’s theorem supports the +/-3 sigma limits. It says that 89% of all distributions (regardless their shape, center and spread) will fall within +/-3 sigma.

• Error 1: Using variation as a cause of special variation when it is actually a common reason. This can lead to wasted time and effort in chasing non-existent special reasons and/or making changes which might cause harm in unexpected ways.
• Second mistake: Using variation as a common cause, when it is a special cause. This leads to missed opportunities. There is a special, fleeting source of variation that can be added to the process. It will not be found.

### Three best practices for thinking about control limit

Keep in mind that control limits do not represent probability limits. They are placed at +/-3 sigma because they work best. One key to process improvement is control limits.

### 1. To calculate control limits, use the standard control limit formula or the control chart table

The control limit formula can vary depending on which statistic is being plotted (average, ranges, proportion, count). Make sure you’re using the correct formula

### 2. To determine if there is a particular cause, use the control limited

A special cause can be identified when a plotted point crosses the upper or lower limit. The manager/worker should take action to identify the cause of the special cause and follow the control plan directions for special causes.

### 3. To evaluate the spread of common cause variation, use the control limits

If the process is stable, it can be expected that the process measurement will fluctuate randomly between the upper or lower control limits.