### What is the upper control limit (UCL) of a vehicle?

The control chart is composed of multiple parts. The control chart has two control limits and an average line. The dashed bottom line is the Lower Control Limit (LCL). The solid middle line represents the average statistic. The upper dashed line represents the upper control level (UCL).

The upper limit of the control chart is calculated based on the data plotted. The average line is 3 sigmas away from it.

The upper control level is used to indicate the point at which a sample is considered a cause of variation. The upper control limit is used to determine the upper limit for the common cause of variation.

### Three benefits of the upper limit control

The actual process data determine the upper limit of control. The upper control limit is based on the process data itself.

#### 1. It gives you an idea of what’s really going on in your process

The upper control limit does not have to be met, as is the case with an upper specification level. The UCL is based upon the process measure and gives you a realistic expectation of what to expect.

#### 2. The sample variation is taken into account, both within and between samples

Consider, for instance, a control graph for the range and average. Five-part lengths are used in a sample. The UCL formula includes both the range (highest to lowest part lengths) and the average of all 5 parts. The range is the variation between samples and the average within the sample.

#### 3. Sets the limits of variation (alongside the lower control limit), for the process measure

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

### Why is it important to understand the upper limit of control?

Control limits are not new. Walter Shewhart wrote the first article on control limits in 1924. He created control charts to improve the quality and reliability of telephone equipment.

Dr. Shewhart has spent many years conducting research and many experiments in order to simulate different production outputs.

In order to minimize economic losses from two types of errors, Dr. Shewhart used the Tchebycheff theorem and the results of the experiments to determine the control limits: +/-3 sigma for an average (such as an average or range). Technical note: Tchebycheff’s theorem is statistically supported by the +/-3 sigma limit. It states that +/-3 sigma will cover 89% of all distributions (regardless to shape, center, and spread).

**Error 1:**When referring to variation as a particular reason for the variation, when in fact it is a common reason for the variation. This leads to wasted time and energy, chasing after non-existent special reasons and making unhelpful changes.**Mistake #2:**Calling a variation common cause, when in fact it is a special cause variation. It results in missed opportunities. There is a special and temporary source of variation in the process that will not be found.

Consider Dr. Shewhart’s dilemma!

We would almost never make a mistake No. if the control limits are very large, such as +/- 8 sigma. 1.

We would almost never make a mistake No. if they were narrower, say +/-0.1 sigma. 2.

The 3-sigma limit balances the probabilities of both mistakes. Shewhart chose 3-sigma limitations for these reasons.

### Three best practices for thinking about the UCL

Remember that the upper limit of control is not a limit on probability; it’s set at +3 sigma because it works best there! The upper control limits are a key element in process improvement.

#### 1. Calculate the UCL using the UCL standard formula and control chart table

The formula for the upper limit will differ depending on which statistic is being plotted (average, ranges, proportions, counts). Use the correct formula!

#### 2. Use the UCL as a tool to determine if there are any special causes on the high side

A plotted point that exceeds the upper control limit can be deemed a special cause. The manager/worker must act to determine the cause of the UCL special causes or follow the direction in the control plan.

#### 3. Use the UCL along with the LCL to evaluate the predicted distribution of common cause variations.

The process measure will fluctuate randomly between upper and lower control limits when the process is stable.