Effectively using Gage R&R and measurement systems variability.
Gage Repeatability and Reproducibility (Gage R&R) is a procedure frequently used to assess the statistical properties of a gage and the operators who use the gage. Typically, three operators will use one gage to make a total of three identical measurements on 10 identical parts. Using standard analysis procedures, the percent Gage R&R is calculated from the recorded data. A total of not more than 10% is considered acceptable and TABULAR DATA OMITTED 10-30% may be acceptable under certain conditions. The purpose of this article, however, is to point out that this procedure is the introduction to Multiple Systems Variability (MSV).
The MSV procedure is similar to Gage R&R with some notable differences. First, Gage R&R is a procedure for analyzing one gage using identical parts for nondestructive testing by different operators. MSV can be used for process evaluation of parts that are consumed by the test (destructive testing) by including part variation in the analysis.
Second, the collection of the data is basically the same for both procedures, but the analysis of the data is somewhat different.
Almost none of the tests performed in a foundry laboratory fit the criteria for GR&R. Because the physical metal tests (hardness, tensile, etc.), metal TABULAR DATA OMITTED chemistries (spectrographic or wet analysis) and sand tests, are destructive measurements, they cannot be repeated on the same sample. All of these tests are really processes rather than gage-type tests since they require multiple pieces of equipment or gages.
The AFS Sand Division's Basic Concepts Committee accepted the challenge of adapting the GR&R approach to destructive testing and capability of process controls using statistical controls. For a period of time the group attempted to use the GR&R technique even though the samples could not be retested. It did not take long to determine this was not a valid approach. The main problem was how to account for the variability of the individual parts or samples.
Other organizations, like quality control groups, and foundry customers, such as automotive companies, were contacted and literature surveys were conducted. These indicated that there was much interest in the idea, but no particular proposals given other than "we should show them how" to adapt GR&R to handle destructive testing.
The one common denominator throughout this process was the question "How can we account for sample or part variation?"
It was pointed out that part variation could not be added to the equipment and/or operator variation. The established GR&R calculation uses a factor from the equipment variation along with the operator variation to allow for part variation, but this did not seem to solve the problem. This same calculation correctly uses "the square root of the sum of the squares" of standard deviations to determine the GR&R value.
Based on the committee's investigations, it was decided the MSV value should be calculated the same way. Percent MSV would equal the square root of the sum of the squares of the percent equipment, operator and sample variations.
The validity of this idea was checked by referring to various text books as well as checking with professionals in the statistical and quality control fields. We did find some hesitation in getting a "yes" or "no" answer from these professionals, but they did support the idea.
Testing the Idea
In order to test our idea regarding the use of MSV, a series of tests were conducted on a variety of foundry and nonfoundry products and processes.
Shown in Table 1 is a copy of an analysis of an electronic balance scale which actually more closely fits GR&R but is also used for processes. In this case, different operators weighed 10 U.S. one-half dollar coins. The computer work sheet shows the data that was entered into sample columns for each of the operator's trials. The calculations were performed automatically by the software program.
Note that both the standard Gage R&R calculations and the proposed MSV are shown for comparison purposes, though the percent operator variation in the MSV calculation does not have the part correction that is shown for GR&R. As is demonstrated, this particular procedure does not speak very well for the Federal Mint's ability to hold half dollar weights, but does show how closely the two procedures reproduce GR&R. Also, the Cpk value is 1.33 for this data. It has been found that the Cpk will be about 1.3 when the MSV value is about 60%.
Another application for MSV is shown in Table 2. This example shows coded TABULAR DATA OMITTED Working Bond values from an automated sand system. Working bond is the mathematical relationship between green compression strength and compactibility, two unique processes. This analysis indicates the processes used for determining working bond for this automated sand system are viable because the MSV value is 78.7%. The committee noticed that if the MSV is over about 100%, the process is generally out of control. The calculations also point out that the equipment parts of these processes would be the best place to analyze for continuous improvement.
Table 3 also is for working bond data from a manual sand system. Again, the data tends to illustrate the possible advantages of automation. In this case, both the part and equipment variations are too high.
Figure 1 is a graph showing actual data of coded compactibility checks made with regular production checks on one sand system plotted sequentially. Each point represents about three hours of production time. Also shown are the upper and lower control limits (using the average +/- 3 sigma) and specification limits. The graph demonstrates that compactibility appears to be under control. The percent MSV also shows fairly good control while the GR&R is out of control as shown in Table 4. This also indicates a Cpk of 1.15 that, along TABULAR DATA OMITTED with the percent MSV, indicates improvement is needed.
These last illustrations using the coded compactibility data are shown to illustrate how changing the tolerance range or standard deviation affect both GR&R and MSV. The committee does not recommend tolerance changes unless absolutely necessary. However, reducing the standard deviation is a positive way to continuous improvement.
Casting requirements are becoming increasingly stringent each year. To keep up with the increasing demands for improved quality requires continuous improvement of the many processes involved in the manufacturing of a casting. For maintaining process control, many statistical techniques have been used.
First, average and range charts were instituted for graphical control of various processes. These were then supplemented with upper and lower control limits for improved control. The 6 sigma approach was then recommended until it was found that a process could meet the 6 sigma values but not be properly located within the specification limits. The Cpk statistic solved that problem by establishing +/- 3 sigma in relation to the average.
GR&R was used to determine if a gage was statistically capable of meeting the requirements imposed upon it. Foundries applying for certified supplier status were being asked if their laboratory tests would meet GR&R requirements. But because these tests are, in reality, processes that require multiple gages, and also are destructive which does not allow samples to be rechecked, it has become necessary to develop a new approach. MSV is this latest technique which shows how well the process is in control. It also points out weak areas of the test (equipment, operator or part variation) that require attention.
Casting quality does continuously improve as the control of the respective processes becomes tighter, and the use of MSV helps by indicating the weak parts of different processes.
In summary, the following are the variability benchmarks discussed in this article:
* MSV greater than 100% indicates the process is not viable and must be improved with the initial effort aimed at reducing the areas of greatest variation.
* MSV of less than 100% indicates the process is viable but action could be taken to improve the process.
* MSV of about 60% has data meeting a Cpk of about 1.3.
Independent of the work done by this AFS committee, a Reference Manual has been prepared by quality and supplier assessment staffs from Chrysler, Ford and General Motors working together through the Automotive Industry Action Group (AIAG). The AIAG is a member of the American Society for Quality Control (ASQC) Task Force charter to standardize reference manuals. This Reference Manual titled "Measurement Systems Analysis" is available from AIAG by calling 313/358-3570.
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|Title Annotation:||part 1; Gage Repeatability and Reproducibility|
|Author:||Volkmar, Alan P.|
|Date:||Nov 1, 1993|
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