MSA for continuous variables.

I will describe the case for continuous variables, i.e. dimensions, times, masses, etc. Another important note: I will only talk about the case of characteristics that can be measured repeatedly without fear that this characteristic changes from measurement to measurement. The opposite case (not being the subject of this article) are tests, where the measurement means either the destruction of the measured element or the irreversible change of characteristics, e.g.:

1. Measurement of tensile strength destroys the sample.
2. Measurement of the screw tightening torque does not damage the connection, but each loosening and tightening changes the connection characteristics. Repetition of the measurement is not possible.

Another important note: preparing an element for measurement may damage it, while the measurement can be performed many times without affecting the measured characteristics, e.g. measuring the length of a weld requires making a cross-section, but a sample can be measured many times.

Let us imagine, for example, that we have a problem with a varnish coat, the thickness of which should be in the range of 0.3-0.4 mm. The varnish layer is created in a process that uses the phenomenon of electrophoresis, in which water-thinnable paint covers the painted object, which is connected to a suitable electrode.

Before you start improving the process, check how well you can measure the thickness of this coating. First you have to prove that you measure correctly and only then you can correct the painting process if you really need to. A minimum of 10 parts (there may be more) should be selected, however the parts should be not collected one after another. Part selection should probably take several days as parts must cover the full range of tolerance and in addition approximately 20% of parts should be outside the upper and lower specification limits.

Sample data below. It can be seen that there were 3 operators, 10 parts and 3 repetitions. The table contains structured data, but of course the parts were measured in a randomized manner.

Tab. 1 MSA data for self-analysis.

Data analysis will be performed in Minitab 18. You can analyze the data yourself in the program. Just copy the data and follow the steps.

The data should be copied in that way that the header is on the first, unnumbered, gray line (see Fig. 1).

Then select "Gage R&R Study Crossed" from the menu as shown in Fig. 2.

In this box you need to determine which data column indicates Part, Operator and Measure (see Fig. 3) and then select the "Options" button to enter the tolerances for the measured characteristic (part). After pressing the button, another window will appear (see Fig. 4), where you should enter the tolerance range. In this case, 0.3 and 0.4, while the decimal separator depends on the system settings and therefore in the window you can see the numbers 0.3 and 0.4 (this is what I use for my own settings).

That is all. Minitab will do the rest for us. There is still an interpretation of the results left. I will analyze the individual diagrams numbered from (1) to (6) in Fig. 5:

1. Components of Variation. The 3 left bars labeled "Gage R&R". The brown is 42 tall, the yellow is 110 tall. Both should be as short as possible. The same numbers are also in the table Tab. 1. marked as (1) and (2). 42 is Gage R&R, 110 is SV/Toler, called P/T.
2. R Chart by Operator. There are 3 sections - each is for one operator. Each point is the difference between the maximum and minimum measurement value of the selected Sample Range for the operator. These values should be kept to a minimum. Also, all points should be within the control limits marked in red ULC and LCL. If some points were not within the limits, it would mean serious measurement errors, e.g. a typing error.
3. Xbar Chart by Operator. There are 3 sections - each is for one operator. This time one point is the average value of all measurements of the selected part by the selected operator. All 3 sections should present the same variability.
4. Grubość powłoki by Część (means Coating Thickness by Part). This is Individual Value Plot, where each part is represented by a group of points. Additionally, you can see the average of all measurements of a given part, marked as a blue circle with a cross. Ideally, all points should be close to the mean values. On this chart, you can see if any part caused exceptional problems, i.e. for which the spread was greater than for the rest. This would indicate that this part is difficult to measure. This could be a tip for improving your routine or training.
5. Grubość powłoki by Operator (means Coating thickness by Operator). This is a boxplot by operator. In addition, in each box you can see the average of all measurements for a given operator, which is marked with a circle with a cross. Ideally, the line connecting all averages should be horizontal. The deviation of the line from the horizontal indicates a systematic error from the operator. A typical example is the parallax error for each operator. Additionally, all boxplots should be similar, which would indicate that each operator observes the same variability.
6. Część * Operator Interaction (means Part * Operator Interaction). If you imagine cutting the "Xbar Chart by Operator" chart into 3 sections, which you then overlap, you will get the Interaction chart. There should be no intersecting lines in this chart. If they appeared, it would mean that one operator read the results for the selected part differently than others. This would indicate a lack of training.

Minitab creates several tables of results. The first 2 sections are the ANOVA table. For you, the most important numbers are marked with (1), (2), (3). Look carefully at the "Gage Evaluation" table at the end. I explain the meaning of the selected points:

1. It is wanted Gage R&R = 42.75%. It includes repeatability (Repeatability row, one row below) = 35.64% and reproducibility (Reproducibility row, two rows below) = 23.61%. Why is Gage R&R not the sum of Repeatability and Reproducibility? Probably because standard deviations are not additive ;-). The R&R gage should be within [0%, 10%], but the gauge may be conditionally used when the R&R Gage is within [10%, 30%]. If it is above 30%, then the Measurement System should definitely be improved first.
2. This is a ratio known as P/T (Precision of the Measurement System / Tolerance). Study Variation = 0.11012 we refer to 0.1 (tolerance range), which gives 110.12%. P/T should be in the range [0%, 10%], but the measuring instrument may be conditionally used when P/T is in the range [10%, 30%]. If it is above 30%, then the Measurement System should definitely be improved first.
3. Number of Distinct Categories. In simple terms, it could be compared to the resolution. The higher the number the better. According to Automotive Industry Action Group (AIAG), the factor should be 5 or higher. What to do when it is smaller? One should think about the selection of parts. Perhaps they did not represent the entire spectrum of tolerance?

I am aware that I have not exhausted the topic of MSA. Nothing can replace training and contact with an experienced person. And even better, if an experienced person could advise you in your case. Feel free to contact me. At this point, we are doing training conducted by people working in the positions of Black Belt or Master Black Belt in manufacturing or service companies. We know the difference between theory and practice and we know how to apply theory to practice.

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Author: Adam Cetera (LeanSigma.pl)
Creation date: 2018-09-17
Modification date: 2018-09-17

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