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Quality Scan: About Control Charts

Jeff DePuy







Variation is a result of common causes and special causes. Common causes are random and built into the process. Because no one event triggers them, common causes can't be controlled. Special causes interfere with the process so it creates an irregular output.They can be triggered by such events as human error and equipment malfunction, and can be removed from the process.

Shewhart control charts were designed to signal special causes of variation. If there aren't any statistical signals on the control chart, the process is in control. That doesn't mean we're happy with the way the process is performing; it only means the process is stable and not changing. If the process is unstable, we can't make a prediction about the next group of production samples.

How do we confidently make predictions when a change in the process is signaled? For most purposes, 20–25 samples are sufficient. After obtaining the samples, calculate their averages, ranges, and control limits. Control limits are estimates of how far the process can deviate from the prediction and still have variance caused by sampling rather than process changes.The control limits apply to these samples. If there aren't any signs of out-of-control behavior, we have enough evidence that the prediction about the next group of samples will be accurate. When designing the control chart, extend the control limits well past these samples to create a snapshot of the process over time.

SPC software calculates control limits so we don't have to get involved in manual computations. It also computes the sample averages (Xbar), the ranges (R), the scale of the chart, automatically draws the Xbar and R control chart, and flags out-of-control points in real time.With such feedback, we can adjust the process and reverse corrective actions that don't work.

SPC software should provide four ways to calculate control limits.The method chosen depends on statistical guidance from process engineering staff and/or customer quality requirements.

Option 1: Estimated Sigma—This calculation uses the formula


Equation 1


where the d2 denominator comes from a Standard Table of Constants for Control Charts, and is based on the sample size.

Option 2: Calculated Sigma—The appropriate formula is


Equation 2


where n represents total observations.

Option 3: Target Calculate—Uses the Estimated Sigma formula as mentioned above, but gets the target (nominal) value from the specification limit for the center line of the Xbar chart.

Option 4: User-defined Control Limits—Software should also allow the user to determine their own control limits, if the situation calls for it: for example, if carrying over previously established limits from a manual control chart. Users should exercise caution when employing this method. Using an incorrect mean, standard deviation, or sample size produces invalid results, and leads to incorrect predictions.

When we create a new control chart, there's no way to be sure the initial data doesn't include special-cause variation. We consider this first set of control limits as trial limits. If the trial limits aren't right for the process, they shouldn't be discarded. Doing so would change the prediction of what to expect in the future. Trial data should be maintained as a historical record.

There will always be occasions when the process evolves, and the control limits no longer apply. If this is the case, it's time to establish new control limits. The software should allow you to maintain multiple sets of control limits to monitor process fluctuations, or to observe ongoing process improvement.

When to recalculate control limits is one of the most misunderstood SPC concepts. A popular—but incorrect—practice urges operators to recalculate control limits every time they observe an out-of-control point. This procedure diminishes the ability of a control chart to distinguish special causes from common causes. Recalculate control limits only when a process change is indicated by an undesirable process trend or drift. Constantly manipulating control limits will widen or narrow the data distribution, resulting in data points that provide false conclusions about process performance. Data points that appear to be within acceptable limits may actually be out-of-control, and vice versa.

Out-of-control conditions can be a good thing. If the process is never out of control, there will never be a reason to adjust the process, and the level of quality will never improve. If we monitor the process, remove special causes, and maintain positive changes to the process, quality, productivity, and costs will improve.


This article was first published in the May 2009 edition of Manufacturing Engineering magazine. 

Published Date : 5/1/2009

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