What does it mean if a single data point appears above the upper specification limit on a control chart?

Control limits distinguish control charts from a simple line graph or run chart. They are like traffic lanes that help you determine if your process is stable or not. Control limits are calculated from your data. Control limit formulas are complex and differ depending on the type of data you have.

Table of Contents Show

How do you calculate control limits?
Why are there so many formulas for sigma?
The secret formula to ignoring all other formulas. QI Macros SPC Software!
QI Macros Also Makes it Easy to Update Control Limit Calculations
Why Choose QI Macros Control Chart Software for Excel?
Fast and Easy to Use
Proven and Trusted
Affordable
When to Use a Control Chart
Basic Procedure
Create a control chart
Control Chart Resources
Case Studies

You can try and calculate control limits yourself, but ...

It will suck up a bunch of your time and you've got better things to do.
You'll probably make mistakes and get the wrong answer.
You will find your homegrown template hard to maintain.

In a stable process:
68.3% of the data points should fall between ± 1 sigma.
95.5% of the data points should fall between ± 2 sigma.
99.7% of the data points should fall between the UCL and LCL.

How do you calculate control limits?

First calculate the Center Line. The Center Line equals either the average or median of your data.
Second calculate sigma. The formula for sigma varies depending on the type of data you have.
Third, calculate the sigma lines. These are simply ± 1 sigma, ± 2 sigma and ± 3 sigma from the center line.
+ 3 sigma = Upper Control Limit (UCL)

- 3 sigma = Lower Control Limit (LCL)

Why are there so many formulas for sigma?

The formula for sigma depends on the type of data you have:

Is it continuous or discrete?
What is the sample size?
Is the sample size constant?

Each type of data has its own distinct formula for sigma and, therefore, its own type of control chart.

There are seven main types of control charts (c, p, u, np, individual moving range XmR, XbarR and XbarS.) Plus there are many more variations for special circumstances. As you might guess, this can get ugly. Here are some examples of control limit formulas:

p Chart formula

Individual Moving Range Chart formula

X bar R Chart formula

* "Introduction to Statistical Quality Control," Douglas C. Montgomery *

The secret formula to ignoring all other formulas. QI Macros SPC Software!

QI Macros is an easy to use add-in for Excel that installs a new tab on Excel's toolbar.

Just select your data and QI Macros does all of the calculations and draws the control chart for you.

QI Macros calculations are tested and accurate.

QI Macros built in code is smart enough to:

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QI Macros Also Makes it Easy to Update Control Limit Calculations

Once you create a control chart using QI Macros, you can easily update the control limits using the QI Macros Chart Tools menu. To access the menu, you must be on a chart or on a chart embedded in a worksheet.

Here's what you can do with the click of a button:

There are also options to easily re-run stability analysis after changing data or control limit calculations.

Why Choose QI Macros Control Chart Software for Excel?

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We often hear control limits and specification limits discussed as if they are interchangeable. But control limits and specification limits are completely different values and concepts. What is the relationship between control limits and specification limits? Usually there is no relationship whatsoever.

Control limits are calculated from process data for a particular control chart. An X-bar chart and an Individual measurements chart will have different limits.

Specification limits are chosen in numerous ways. They generally apply to the individual items being measured and appear on histograms, box plots, or probability plots.

The table below contrasts control limits and specification limits:

Control Limits	Specification Limits
Voice of the process	Voice of the customer
Calculated from Data	Defined by the customer
Appear on control charts	Appear on histograms
Apply to subgroups	Apply to items
Guide for process actions	Separate good items from bad
What the process is doing	What we want the process to do

Confusing control limits with specification limits leads to mistakes. The most common mistake is to use specification limit values instead of control limit values on an X-bar chart or an Individuals chart. Using specifications on an X-bar is the most egregious error: the specifications are in one unit (items) while the chart is in another (average of several items).

Even using specification limit values on an Individuals chart leads to problems. Unless the specification and control limit values are identical, one of two errors occurs:

The control limits are set too tightly. This leads to over-adjustment and tampering with the process. Tampering adds to process variation, resulting in lower quality and higher costs.
The control limits are set too loosely. Signals of process change are ignored and opportunities for process improvement are missed. The result is additional avoidable variation, lower quality, and higher costs.

How about showing specifications on the control charts in addition to the control limits? The leading SPC solutions allow this, but it's generally not a good idea. Additional limits risk confusing customer demands with process behavior. The additional limits void the wonderful ability of control charts to give clear guidance. The only good use of specification limits on a control chart that I've seen is to make a point when the process is operating nowhere near the specifications.

Concerning specifications appearing on an X-bar chart, the X-bar chart below illustrates the problem. The subgroup size is two, and the Target and Specifications (rather than Center Line and Control Limits) have been added to the chart. All of the subgroup averages (the "O"s) are within the specifications. But all of the measurements making up the subgroups (the "+"s) are outside the specifications. The items are all either too large or too small; but on the average they're just right!

In summary, use only control limits on control charts; specification limits belong on histograms, box plots, and probability plots.

Info Center Collateral Types

Quality Glossary Definition: Control chart

Also called: Shewhart chart, statistical process control chart

The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. These lines are determined from historical data. By comparing current data to these lines, you can draw conclusions about whether the process variation is consistent (in control) or is unpredictable (out of control, affected by special causes of variation). This versatile data collection and analysis tool can be used by a variety of industries and is considered one of the seven basic quality tools.

Control charts for variable data are used in pairs. The top chart monitors the average, or the centering of the distribution of data from the process. The bottom chart monitors the range, or the width of the distribution. If your data were shots in target practice, the average is where the shots are clustering, and the range is how tightly they are clustered. Control charts for attribute data are used singly.

Control Chart Example

When to Use a Control Chart

When controlling ongoing processes by finding and correcting problems as they occur
When predicting the expected range of outcomes from a process
When determining whether a process is stable (in statistical control)
When analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process)
When determining whether your quality improvement project should aim to prevent specific problems or to make fundamental changes to the process

Basic Procedure

Choose the appropriate control chart for your data.
Determine the appropriate time period for collecting and plotting data.
Collect data, construct your chart and analyze the data.
Look for "out-of-control signals" on the control chart. When one is identified, mark it on the chart and investigate the cause. Document how you investigated, what you learned, the cause and how it was corrected.
- A single point outside the control limits. In Figure 1, point sixteen is above the UCL (upper control limit).
- Two out of three successive points are on the same side of the centerline and farther than 2 σ from it. In Figure 1, point 4 sends that signal.
- Four out of five successive points are on the same side of the centerline and farther than 1 σ from it. In Figure 1, point 11 sends that signal.
- A run of eight in a row are on the same side of the centerline. Or 10 out of 11, 12 out of 14, or 16 out of 20. In Figure 1, point 21 is eighth in a row above the centerline.
- Obvious consistent or persistent patterns that suggest something unusual about your data and your process.
Continue to plot data as they are generated. As each new data point is plotted, check for new out-of-control signals.
When you start a new control chart, the process may be out of control. If so, the control limits calculated from the first 20 points are conditional limits. When you have at least 20 sequential points from a period when the process is operating in control, recalculate control limits.

Create a control chart

See a sample control chart and create your own with the control chart template (Excel).

Control Chart Resources

You can also search articles, case studies, and publications for control chart resources.

Books

The Quality Toolbox

Innovative Control Charting

Improving Healthcare With Control Charts

Case Studies

Using Control Charts In A Healthcare Setting (PDF) This teaching case study features characters, hospitals, and healthcare data that are all fictional. Upon use of the case study in classrooms or organizations, readers should be able to create a control chart and interpret its results, and identify situations that would be appropriate for control chart analysis.

Quality Quandaries: Interpretation Of Signals From Runs Rules In Shewhart Control Charts (Quality Engineering) The example of Douwe Egberts, a Dutch tea and coffee manufacturer/distributor, demonstrates how run rules and a Shewhart control chart can be used as an effective statistical process control tool.

Articles

Spatial Control Charts For The Mean (Journal of Quality Technology) The properties of this control chart for the means of a spatial process are explored with simulated data and the method is illustrated with an example using ultrasonic technology to obtain nondestructive measurements of bottle thickness.

A Robust Standard Deviation Control Chart (Technometrics) Most robust estimators in the literature are robust against either diffuse disturbances or localized disturbances but not both. The authors propose an intuitive algorithm that is robust against both types of disturbance and has better overall performance than existing estimators.