FEATURED ARTICLE

Hybrid SPC Charts in Statistical Process Control

The BIS.Net Team BIS.Net Team

Background

SPC Charts were introduced by Dr. Walter Shewhart in the 1920s, based on six years of an investigation to “develop a scientific basis for attaining economic control of quality of manufactured product through the establishment of control limits to indicate at every stage in the production process from raw material to finished product when the quality of product is varying more than is economically desirable”. Shewhart particularly used the control chart to identify assignable causes which are economically undesirable. Shewhart and his engineers realized that reacting to common causes that are inherent to the process is a futile process that can increase variation, not reduce it.

Over the years since, many others such as Dr. W.E. Deming popularized the use of SPC charts to reduce variation and improve processes. Almost one hundred years since the technology remains virtually unchanged in a ‘time capsule’. Even though today's processes are far more complicated than in the limited environment of Bell Laboratories and Western Electrical Company, from early this century, statistical process control has not kept up with the times.

Problems with classical Shewhart Control Charts

There are several issues with the shewhart control chart.

The Shewhart control chart is not as robust to non-normality as is often thought. Shewhart in his book ‘Economic Control of Quality of Manufactured Product’ alleges that even for a sample size of 4 the distribution of averages is normal.

For many non-normal distributions this has not been substantiated by our research and can be verified with simulations. Depending on the degree of non-normality and sub-group size a Shewhart Chart applied to a moderate or high level of non-normality may have an excessive number of false alarms, discrediting the chart through the frustration of searching for assignable causes when there are none.

An example of the problem is shown in Figure 1 below for both the X-bar and Range Chart, based on a sub-group size of 5 and for an in-control non-normal process. Even though the process is in-control, even though Shewhart X-bar charts are supposed to be robust to non-normality the number of out-of-control points is unacceptable.

Hybrid SPC Charts - X-bar chart applied to a non-normal process Figure 1a: X-bar chart applied to a non-normal process
Hybrid SPC Charts - Range chart applied to a non-normal process Figure 1b: Range chart applied to a non-normal process

SPC Charts are essentially a plot of points within two lines strategically placed to ensure that the there is no overreaction to inherent process variability. Although easy to use, this technology, originating at a time, where there was no modern computing power, is insensitive to changes and does not reliably pinpoint the onset of changes and measure the duration of a change.

The example in Figure 2 shows no out-of-control point and no warning limit violation (2 consecutive points). A runs test would show some problems, but it is an established fact that a runs test will increase false alarms and cause problems with in-control processes.

Hybrid SPC Charts - X-bar chart without out-of-control points Figure 2: X-bar chart without out-of-control points

Hybrid SPC Charts as shown in Figure 3 uses Change Analysis Dynamic Plateau Charts which clearly shows that the process was out of-control. It was above target until 30th of May and below target after.

Hybrid SPC Charts - Hybrid X-bar Chart Figure 3: Hybrid X-bar Chart

Hybrid SPC Charts

As briefly shown above, Hybrid SPC charts combines old technology with modern machine powered technology to provide greater insights into the process than possible with either technology alone. It also helps the analyst, who is reluctant to move away from established technology, to accept more modern technology.

Hybrid SPC combines control charts with Change Analysis with an option of Classical Shewhart or Distribution Optimized SPC Charts.

This section will explain the concept by first comparing classically calculated limits with distribution optimized limits.

The chart in Figure 4 (repeated from above) shows the ineffectiveness of the Shewhart Chart applied to skewed non-normal data.

Hybrid SPC Charts - Standard SPC Chart applied to an in-control non-normal process Figure 4: Standard SPC Chart applied to an in-control non-normal process

Figure 5 shows how a distribution optimized SPC chart has more realistic control limits for the same in-control data.

Hybrid SPC Charts - Distribution Optimized SPC Chart applied to the same data above Figure 5: Distribution Optimized SPC Chart applied to the same data above

Figure 6 shows a standard Shewhart X-bar chart applied to an out-of-control non-normal process

Hybrid SPC Charts - Shewhart Control Chart applied to an out-of-control non-normal process Figure 6: Shewhart Control Chart applied to an out-of-control non-normal process

Figure 7 shows a Hybrid SPC Chart using a classical x-bar chart, augmented with a Dynamic Plateau Chart using machine powered change analysis. Changes in the process are clearly indicated.

Hybrid SPC Chart applied to the same data using a Classical Shewhart Control Chart Figure 7: Hybrid SPC Chart applied to the same data using a Classical Shewhart Control Chart

Figure 8 is a distribution optimized Hybrid SPC Chart which is then compared to the standard X-bar Hybrid control chart shown in Figure 7.

Hybrid SPC Chart applied to the same data using a distribution optimized chart. Figure 8: Hybrid SPC Chart applied to the same data using a distribution optimized chart.

The classical Shewhart Hybrid SPC Chart shown in Figure 7, indicates out-of-control points above the upper control limit, contrary to the distribution optimized Hybrid chart, shown in Figure 8, which has out-of-control points below the lower limit.

The distribution optimized x-bar chart is correct. The distribution was known to be heavily skewed to the higher values and should thus be less concentrated near the upper limit, with less if not zero, out of-control-points. Figure 7 contradicts reality. Comparing the magnitude of changes with the centreline it is evident that the drop in mean where the control points of the distribution optimized chart (Figure 8) indicates a problem is larger than the increase above the centreline where the standard Shewhart Chart (Figure 7) indicates there is a problem. The standard Shewhart Hybrid chart is not indicating the worst situation. The distribution optimized Hybrid chart is.. The changes are shown in Figure 9

Magnitude of Changes Figure 9: Magnitude of Changes

The standard Hybrid chart indicates out-of-control at a lesser magnitude of change than the Distribution Optimized Hybrid chart shows.

Limits

Control limits should only become fixed for Phase II SPC, once the process is in-control. The examples above are for processes out-of-control.

Classical limits are based on within sub-group variation, which is in effect mathematically removing the effect of time-to-time variation from an out-of-control process. This technology cannot be applied to non-normal x-bar data. Instead the effect of time-to time variation is removed by a different but highly effective process relying on the dynamic plateaus.

Ideally, fixed limits should be established only after bringing a process into control i.e. the process is a flat liner as shown in Figure 10

Hybrid SPC Chart - A flat liner Figure 10: A flat liner

Until this is the case control limits calculated should only be used as a guide.

Which to choose - Classical? Classical Hybrid SPC? Distribution optimized Hybrid?

Since distribution optimized Hybrid SPC Charts use standard Shewhart Control Charts, if the underlying distribution is normal, it makes sense to use distribution optimized charts. If the data is non-normal, then the analyst can be confident that correct control limits for the data will be determined. If it is normal, then conventional Shewhart Control charts are used.

Since either type of hybrid charts provide more information than classical control charts alone, Hybrid SPC Charts are recommended. However, the final choice depends on the analyst and the data. If a choice does not appear correct, try another choice.

Change Analysis versus Hybrid

The above examples showed problems with Control Charts. This begs the question, why not just use Change Analysis using the BIS.Net Change Analysis App. That choice is up to analysts. Hybrid SPC charts were introduced for the analyst to become comfortable with Change Analysis and to provide the best of both worlds. Hybrid SPC charts may show outliers, which Change Analysis has not been designed to do.

Augmented with Deviation from Target charts

These are almost identical to the dynamic plateau charts. The only difference is that if a plateau is statistically different to the target, within a reasonable tolerance, then the plateau is coloured red and green otherwise and the value of the plateau is set to the defined target if insignificant.

Hybrid SPC Chart with augmented Deviation from Target Charts

Attributes

Similar comments to those above apply to Hybrid SPC Charts, However, distribution optimized control charts are not optimized in the same sense as X-bar and Individual charts are. Instead Control limits are based on exact methods, instead of approximations used in classical technology.

EWMA and MA

These are based on smoothing algorithms which are inappropriate for augmentation. The Hybrid SPC Charts described above provide more information with similar sensitivity

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