Everybody wants to have good measurements. To this end, many recommend a regular schedule of recalibration. While this sounds reasonable, it can actually degrade the quality of the measurements.

The key to getting the most out of a measurement process is to know when to recalibrate and when to refrain from recalibrating. This was beautifully illustrated by two of my clients.

Plant A

Like all process industries, Plant A lived and died by the values delivered by the in-house lab. The lab director wanted to provide good values, so he followed the manufacturer’s recommendation and had the calibration of his key analytical instrument checked every day using a known industrial standard. When the value he obtained didn’t match the accepted value for the standard, he would adjust the instrument by an amount equal to the difference between the accepted value and the observed value. Because they ended up recalibrating more than 80% of the time, the lab director was convinced that these adjustments were both necessary and correct. Figure 1 shows the observed values for 100 consecutive tests of the known standard for Plant A.

Figure 1: XmR chart for 100 measurements of a known standard at Plant A

During these 100 days, the process was recalibrated 88 times. Since the accepted value for the known standard was 310, the lab director felt quite content that his lab was delivering unbiased, high-quality measurements to the plant.

And just how good were his measurements? Since Figure 1 shows repeated measurements of the same standard, the moving ranges may be used to characterize the uncertainties in these measurements. The average moving range is 2.96 units, so when we divide by the appropriate d2 bias correction factor of 1.128, we obtain an estimate of the standard deviation of the measurement system:

From this value, we can compute the probable error for a single reading:

Because these values are recorded to the nearest whole number, this latter value means that a value will err by plus or minus two units or more at least half the time. (In Figure 1, 54 of the 100 values err by two units or more.) Plant A’s values can only be interpreted as good to within plus or minus two units.

Plant B

Plant B was a competitor of Plant A. The in-house lab at Plant B had an analytical instrument that was precisely the same make and model as that used at Plant A. It also tested the same industrial standard every day, like Plant A. However, this was where the similarities ended. Rather than recalibrating based on each reading, the lab director at Plant B placed each observed value for the standard on a consistency chart.

A consistency chart for a known standard is an XmR chart where the central line for X is set at the accepted value for the known standard. As long as this chart shows no evidence that the analytical instrument is off target, no adjustments are needed—and so none are made. On those occasions when an observed value falls outside the limits on this X chart, an adjustment is appropriate.

Figure 2: XmR Chart for 100 measurements of a known standard at Plant B

Figure 2 illustrates 100 consecutive tests of the known standard at Plant B, during which no recalibration was required. The average of 310.1 units is essentially the same as the accepted value of 310. The average moving range of 2.00 units results in an estimate of the standard deviation of the measurement system of:

This probable error means that the observed values are essentially good to the nearest whole number. At least half the time, they will err by one unit or less. (Figure 2 has 60 out of 100 values within one unit of the accepted value.)

By filtering out the noise in the data, Plant B reduced the workload in the lab by avoiding all the recalibrations. At the same time, the lab delivered higher-quality data than Plant A using the same instrument. But the real payoff for the consistency chart wasn’t in the lab. In the words of the lab director for Plant B, “You don’t know how much grief you’ve saved us! When we started using the consistency chart for the standard, suddenly the whole plant started running better!”

Figure 3: The effect of needless recalibrations

The difference

At Plant A, every value was interpreted at face value. Values not equal to 310 were treated as evidence that the instrument was out of calibration. Consequently, the recalibrations took the instrument on walkabout, which increased the uncertainty in the measurements.

In their efforts to achieve perfection, Plant A created a rubber ruler. Almost every day, the production team at Plant A had to learn how to operate with the measurement system du jour.

But the chart for Plant A shows a predictable process. Isn’t that good? It would be good if Plant A weren’t creating excess variation. Here, the adjustments are so frequent that they are part of the routine variation. When the data are full of signals, the signals inflate the moving ranges, and the chart will look predictable when it isn’t operating up to its full potential. So although Plant A is consistent, it’s consistently failing to get the most out of its instrument.

Summary

You can’t cheat on the laws of rotational inertia. These laws dictate that any unnecessary recalibration of a measurement system will inevitably increase the variation in the measurements. Adjustments can only add variation—they can never reduce it.

At the same time, failing to make a needed recalibration will also degrade the measurements. So the trick is to know when to adjust and when to refrain from adjusting. And this is what a consistency chart will tell you.

Measurement systems operated using a consistency chart can operate up to their full potential. You’ll be able to produce measurements that are on target with minimum measurement error.

Measurement systems operated without consistency charts are likely to have more measurement error than is necessary. Efforts to keep the process calibrated that do not take variation into account will virtually guarantee excess measurement error.

If you try to interpret data at face value without first filtering out the noise, you may be working at Plant A without even knowing it.

Donald Wheeler’s complete “Understanding SPC” seminar may be streamed for free; for details, see spcpress.com.