"Interaction" is originally a term of experimental design, which means that when two or more factors act at the same time, the superposition effect of a single factor will increase or decrease, that is,1+1>; 2 or 1+ 1
Next, let's introduce another commonly used tool, which is well-known analysis of variance (ANOVA). Analysis of variance itself can be regarded as experimental design (DOE), but it is usually used as a data analysis tool for experimental design, which can mainly help us to do the following things: 1. Significance test of differences between different levels of elements. 2. Separate the related factors and estimate their contribution rate to the total variation. 3. Analyze whether the interaction between elements is significant.
The repeatability and reproducibility analysis of the measurement system can actually be regarded as a special experimental design, which includes two factors, namely, the part (level 5 or 10) and the operator (level 2 or 3), while the repeatability is random error or intra-group variation, and the output is the measured value of a certain product characteristic. When we do repeatability and reproducibility analysis, we only use ANOVA's data analysis ability, and the expected results are different from the experimental design, which must be clear. Regarding the analysis of variance (ANOVA), I personally strongly recommend that you understand it. It's simple but important.
Through analysis of variance (ANOVA) report and GRR report, we can get the following information: 1. Is the difference between operators obvious? 2. Whether there is significant interaction between parts and operators; 3. Is the contribution rate of random error (EV/ repeatability) too large? 4. Repeatability (EV)%; 5. Reproducibility (AV)%; 6.GRR %； 7. Interaction between operator and parts%.
Usually, people will directly look at GRR%, and we often wonder whether GRR% meets the requirements of 10% or 30%. It is wrong to meet the requirements and everything will be fine. In fact, we need to know what problems exist in the whole measurement process and measurement system through variance analysis report and GRR report.
First, let's see if the random error (repeatability /EV) is too large. There is no uniform standard for this. According to my experience, if the EV exceeds 7%, it is necessary to analyze the reasons.
Second, if the difference between operators is significant, no matter what the GRR% is, it is necessary to analyze the reasons. Generally speaking, if there are significant differences between operators, GRR% will not meet the requirements of 10%, but may meet the requirements of 30%. What we need to do is to find ways to eliminate the differences between operators.
Third, if the interaction is significant, the cause must be found and eliminated before the next step.
Let's discuss the reasons for data representation and the interaction between parts and operators. The interaction form of GRR is that the measured value of one or two operators is much larger or smaller than that of other operators, that is, the data distribution mode is different. If the measured values of all parts are too large or too small as a whole, the error between operators will be displayed. As can be seen from the distribution of the average measurement value shown in the figure below, the measurement data pattern of operator # 1 is completely different from that of the other two people. In this case, there is interaction between operator # 1 and the parts.
I will illustrate the interaction between them through two simple examples. In most cases, the reason is the shape error of the product I mentioned earlier or some other accidental factors, so I define "the interaction between parts and operators" as "the error caused by measuring different parts of the product between operators."
Case 1: For example, suppose the thickness of a product is measured, but the parallelism of the two planes used to measure the thickness is not good. Three operators used three different technical measurement methods: 1) random measurement at any position on the plane; 2) Always on the edge; 3) Always keep a certain distance from the edge x.
1 method will include parallelism deviation; The second method will randomly include abnormal changes of edges, such as burrs; The third method does not include the deviation of parallelism, nor does it include the abnormality of edges. In cases 1 and 2, the interaction between the operator and the part will be displayed.
Case 2: For example, when measuring the diameter of a shaft, the shape of the shaft is different (poor roundness), and the degree of burr at the end is also different. Two operators adopt different measuring methods: Operator A: Measure at the center of the shaft, take the maximum and minimum diameters, take their average values and record the average values. Measuring in the center can eliminate the influence of any burr, and calculating the average value can reduce the influence of roundness. Operator B: Random measurement is at the shaft end, which means that some measurements may be affected by burrs, while random measurement will be affected by roundness. This may appear as an "operator * part" interaction, because different operators measure different parts in different ways.
From the above analysis, we can see that the interaction between factors in analyzing repeatability and reproducibility is slightly different from that in experimental design (DOE), but this phenomenon is the same when analyzing the variance of data.
So how to eliminate the interaction between them? As can be seen from the above cases, the method of avoiding interaction is actually very simple. Just find the best measurement method and standardize the operation.
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