This procedure generates Levey-Jennings control charts on single variables. The Levey-Jennings control chart is a special case of the common Shewart Xbar . The Levey-Jennings chart was created in the s to answer questions about the quality and consistency of measurement systems in the. The Levey-Jennings chart usually has the days of the month plotted on the X-axis and the control observations plotted on the Y-axis. On the right is the Gaussian.

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T he Levey-Jennings chart was created in the s to answer questions about the quality and consistency of measurement systems in the chemical and process industries.

This column will illustrate the fatal flaw in this technique and show a better way to track the consistency of your measurement systems. In addition it will describe how to quantify the actual resolution of your measurements.

For our example we will use data from page 20 of Walter A. These data were collected as part of a research project on measuring the resistivity in megohms of an electrical insulator. Since this test was destructive, these measurements were made on samples cut from the same sheet of material.

In this way the measurements were as close to multiple measurements of the same thing as jenhings tests jebnings be. The data are shown in figure 2.

## Basic QC Practices

The average for these 64 values is The Levey-Jennings chart plots these 64 values as a running record and adds a central line and two limits. The central line is generally taken to be the average value, although when testing a known standard, the central line may be set at the accepted value for the standard. The limits are then placed at a distance of three times the standard deviation statistic on either side of the central line.

Any point that falls outside these limits is taken as evidence of an inconsistency in the measurement process. Original Levey-Jennings chart for resistivity measurements of figure 2. The Levey-Jennings chart for our data is shown in figure 1. With no points outside the limits this measurement system is given a passing grade by the Levey-Jennings chart. However, with the values drifting around and with the sudden changes in level, the running record of figure 1 does not look like that of a consistent measurement process.

So, we might well conclude that the original Levey-Jennings chart did not always detect problems with the measurement process. To remedy this weakness the Levey-Jennings chart was modified in by the addition of some additional criteria for detecting problems.

The Westgard rules are used to identify potential signals of a change in the measurement process whenever the one of the following conditions exists on the Levey-Jennings chart: A point falls outside one of the three standard deviation limits; 2.

Two successive points fall outside one of the two standard deviation lines; 3. Four successive points fall outside one of the one standard deviation lines; 4.

Ten successive values all fall on the same side of the central line; or 5. Two successive values are on opposite sides of central line and are both beyond the two standard deviation lines. The modified Levey-Jennings chart is shown in figure 3 where rule four and then rule two indicate problems with these data.

Modified Levey-Jennings chart for resistivity measurements with Westgard rules. Thus, the Westgard rules do improve the ability of the Levey-Jennings chart to detect changes in the measurement system.

However, the whole process is still built on the global standard deviation statistic. As I explained in my columns for October and Decemberit is always inappropriate to use a global standard deviation statistic when oevey to separate potential signals from probable noise. Jenning you use a global standard deviation statistic you are making a very strong assumption that your data are homogeneous.

At the beginning of the 20th century we learned to avoid the use of global measures of dispersion when looking for potential signals within our data. This is why modern statistical techniques such as the analysis of variance, the analysis of means, and the process behavior chart all filter out the noise by using the within subgroup variation.

Thus, even though the Levey-Jennings chart was created in the s, it was built upon a 19th century approach to analysis that was known to be unsatisfactory at the time! In figure 4 we see the XmR chart for the jenbings resistivity measurements of figure 2. The average remains Thus, our three-sigma limits for the X chart are to and the upper limit for the range chart is XmR chart for resistivity measurements of figure 2.

Here, in addition to the long run above the central line, we find six points and three moving ranges outside their limits. When we include the points in the runs with the out-of-limits points we find 34 of the 64 values to be associated with changes in the measurement process. Thus, we not only know that this measurement system is not producing consistent results, but we also have clear indications about when the changes occurred.

So, while the original Levey-Jennings chart would mislead the researchers into feeling good about the jennnigs measurements, the XmR chart makes it clear that these measurements are subject to some dominant assignable cause that makes this measurement process into a rubber ruler.

As Shewhart reported regarding these data, the assignable cause was found and eliminated so that it could no longer take the measurement system on walkabout.

After making this change in the measurement process they proceeded jennnings collect an additional 64 measurements of the resistivity of this same insulating material. These data are given in figure 5. The XmR chart for these new data is shown in figure 6.

The average value is and ejnnings average moving range is Thus Sigma X is XmR chart for additional resistivity measurements of figure 5. Now their measurement system is not only consistent but it is also operating with less measurement error than before. Levey-Jennings chart for additional resistivity measurements of figure 5. The Levey-Jennings chart for the data of figure 5 is shown in figure 7.

### The Levey-Jennings Chart | Quality Digest

The global standard deviation statistic lvey figure 5 is With a consistent and predictable measurement system the Levey-Jennings chart will mimic the XmR chart. But when the measurement system is inconsistent the Levey-Jennings chart will be handicapped by the use of the global standard deviation statistic.

This use of the global standard deviation statistic is the inherent and fatal flaw in the Levey-Jennings chart. It cchart both primitive and naive. As a result the Levey-Jennings chart will only work with a good measurement process.

## Levey Jennings Control Chart

Since it does not reliably detect problems with your measurement process the Levey-Jennings chart should not be used in practice. How good are your measurements? How many digits should you record? To answer these questions we need to recap some lefey the history surrounding the problem of measurement error.

InGauss proposed using a normal distribution as a model for the errors of measurement. The middle 50 percent of a normal distribution defines the probable error. Think of the mean of the distribution in figure 8 as the value of an item being measured, and let the distribution represent a series of repeated measurements of that item. Here the standard deviation will characterize the measurement error. Half the time the measurements will be in the central region of figure jebnings and half the time they will fall in one of the two tails.

While we typically do not know the value of the item to be measured, we can still think about the error of a single measurement as the difference between that measurement and the value of the item.

Putting all the elements of figure 8 together, we can say that half the time a measurement will err by more than one probable error, and half the time a measurement will err by less than one probable error. Thus, the probable error defines the median error of a measurement. And if we are going to err by one probable error jjennings more half the time, it does not pay to interpret a measurement more precisely than plus or minus one probable error.

Thus, the probable error of a measurement system defines the effective and demonstrated resolution of the measurements.

In figure 6 the average moving range for the measurement system was The probable error of this measurement process is then estimated by multiplying by the conversion factor of 0. While the data in figure 5 are recorded to the nearest 5 megohms, they are only good to the nearest megohms. Half the time these measurements will err by megohms or less, and half the time these measurements will err by megohms or more.

These measurements jennongs a demonstrated resolution of megohms. This is the essential uncertainty attached to every measurement of resistivity in figure 5. When the measurement increment is appreciably larger than megohms, the round-off will degrade the measurements.

### Levey-Jennings Quality Control Charts – , Laboratory Continuing Education

When, as is the case here, the measurement increment is substantially smaller than megohms, then the users will be writing down pure noise in the last digit. A guideline for writing down the appropriate number of digits is to use a measurement increment that falls somewhere between the smallest effective measurement increment and cart largest effective measurement increment, where: In this case they should use a measurement increment somewhere between 23 megohms and megohms.

So while they recorded these resistivities to the nearest 5 megohms, they could have rounded them off to the nearest megohms without any serious degradation. To illustrate this, the data of figure 5 have lvey rounded to the nearest megohms in figure The resulting XmR chart is shown in figure 9. XmR chart for additional resistivity measurements rounded to nearest megohms.

Chqrt 9 shows the XmR chart for the rounded resistivities of figure In addition it also shows the running records for the data of figure 5 in red. While the average moving range is slightly larger in figure 9 than in figure 6, both XmR charts tell the same story. These measurements are good to the nearest megohms, and rounding to the nearest megohms does not degrade the quality of the information they contain.

So, while the Levey-Jennings chart will work with good data, it fails to work when the measurement system is operating inconsistently. It will not reliably tell you how to improve a measurement system that is not being operated up to its full potential.

While the Westgard rules do help the Levey-Jennings chart to some degree, they cannot overcome the inherent fatal flaw of using a global measure of dispersion. For this lecey, you should always avoid using a Levey-Jennings chart.

If you want to get the most out of your measurement processes you will need to use an XmR chart for repeated measurements of the same thing. Chary a chart is known as a consistency chart.

It will allow you to determine when extraneous factors influence your measurement process, so that you can identify them and control for their effects. And if increased sensitivity is desired for this consistency jennkngs, the standard Western Electric zone tests may always be used. In addition, by using the within subgroup variation, the XmR consistency chart will provide you with a better estimate jenninsg the inherent measurement jenninsg than you can obtain from a Levey-Jennings chart where the global standard deviation will be inflated by any inconsistencies in the measurement process.