Introduction to Control Charts

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Run Charts vs. Control Charts

In order to understand how SPC control charts work, let’s compare a standard time series run chart to a control chart.

The chart below is a simple run chart. We’re all familiar with these. It’s a time-series chart that’s used to track a characteristic of interest over time. The x-axis represents date, time, sample, S/N, or any other time ordered measured observation.

The y-axis is the measurement of the characteristic of interest. Run charts are a very popular business tool and are used by almost all businesses.

Run Chart

Should The Process Be Adjusted?

Run charts alone will play tricks with your mind!

This is because whenever we see a downward trend in data our instinct is to interpret it as bad. Whenever we see an upward trend, we interpret it as improvement.

With a run chart it’s very difficult to understand when corrective action should be taken on the process.

In the run chart sample above there was a sharp downward trend in “length” after sample 13. Should the process be adjusted? Looking at only the run chart may lead you to answer “yes”?

Run Chart Risks

There are two risks or errors that can occur when interpreting run charts.

  • We erroneously interpret common-cause variation as special-cause variation and over adjust the processes,
  • Or, we incorrectly interpret special-cause variation as a common-cause and make no adjustments when we really should have.

But here’s the good news! By using SPC control charts, you can eliminate the limitations of run charts. To understand how it works we need to go back to Shewhart and the true “magic” of his discoveries.

Shewhart showed that if only common-cause variation exists within a process then 99.73% of the plotted data points will fall within +/- 3 standard deviation units from the mean performance.

The likelihood of getting a data point outside of these limits is 0.27%. Stated otherwise, very unlikely! Therefore, if we do see a data point outside of these limits we can conclude 99.73% certainty that something has indeed really changed in the process.

With SPC control limits are placed at +/- 3 standard deviation units from the mean (e.g UCL and LCL).

Control Chart with Control Limits

Common and Special Cause Variation

Control Charts - Common and Special-Cause Variation

Control Charts

Take a look at the chart below. It’s the same data from the “length” run chart above but is in control chart format.

Like the run chart, the control chart has an x-axis and y-axis. It has 3 additional lines as well. One of these lines is the “mean or average” value. In the control chart below the mean is 100.7 millimeters (mm).

A control chart also contains an upper control limit (UCL) and lower control limit (LCL). These control limits are +/- 3 standard deviations units from the mean/average.

Control Chart Example

Contro Chart with Control Limits

Control Chart w/Control Limits

In our length example the mean is 100.7 mm and the standard deviation is 9.4 (not shown on chart).

UCL=Xbar+3(std dev), 100.7+3(9.4) = 128.9

LCL=Xbar-3(std dev), 100.7-3(9.4) = 72.5

These control limits are +/– 3 standard deviation units (sigma) from the mean. If only common-cause variation exists within the process, which is true in the chart above, we can expect that almost all of our data points (99.73%) will fall within the calculated control limits.

Let’s return to our question from the original run chart. Should the process be adjusted based upon the downward trend in “length”?

You can see in the control chart above that none of the downward trend plotted data points go below the lower control limit (LCL) of 72.5 mm. We would therefore conclude that the variation is random and from common causes.It is not a signal to adjust the process.

Adjusting the process upward based upon the “eyeball test” of the run chart would have shifted future observations upward. Some percentage of future items would potentially violate the upper control limit and possibly the actual upper specification requirement.

Control Chart Benefits

  • They statistically determine when special-cause variation has entered the process,
  • They support data collection, process monitoring, and data based decision making,
  • They are easy to implement control method and the cost to do so is low,
  • They support process ownership,
  • They eliminate “fire fighting”,
  • They can be used for both process inputs and outputs.

Statistical Control

A process is in a “state of statistical control” when only common-cause variation is acting upon the process. It is out of statistical control when special-cause variation is acting upon the process.

For process in statistical control the following is true.

  • 68% of the measurements will fall within +/- 1 standard deviation unit of the mean,
  • 95% of the measurements will fall within +/- 2 standard deviation units from the mean,
  • and 99.74% - practically all of the measurements will fall within +/- 3 standard deviation units from the mean.

Control charts detect the presence of special-cause variation. They do this by detecting highly unlikely patterns in the data.

Below are the control chart signals that signify the likely presence of special-cause variation. These events are very unlikely to happen randomly.

Control Chart Rules

Control Chart Out Of Control Indicators

Control Chart - Out of Control Indications

Control Chart Zones

Control Chart Zones

Control Chart Zones - +/- 3 Sigma (Standard Deviations)

Statistical Process Control Basics

Statistical Process Control

Control Charts

Control Chart Selection

Control Limits

Capability Indices - Cpk, Etc.

Process Capability Study

Statistical Process Control Control Charts

Xbar & R (Range) Chart

Xbar & s (Standard Deviation) Chart

I (Individuals) & MR (Moving Range) Chart

p Chart

np Chart

u Chart

From Control Charts to Statistical Quality Control.

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