Crossed Measurement System Study

Why it matters

Measuring the same part with different results is not production variability. On the other hand, different parts giving different results is not measurement error by itself either. A crossed study sets up a data layout that can separate these two cases: all the selected parts are measured repeatedly by all the observers. In this way the repeats on the same part and the difference between parts can be seen in the same table, but as different sources. The purpose of the layout is not to rank workers by speed or skill. The aim is to test whether the defined measurement method can serve as the basis for the same decision with different operators. The bias and resolution examined in the previous lesson still apply; the crossed design does not remove their shortcomings by itself.

In this design, reproducibility covers the variability between observers and the part-by-observer interaction included in the model. Repeatability describes the scatter when the same observer measures the same part again under the same defined conditions. A systematic difference between observers is a separate component. In addition, an observer may read high on some parts and low on others; this is called part-by-observer interaction. For example, difficulty in choosing the contact surface may appear only on certain geometries. This is not the same as an observer difference seen in one direction on all parts. The size of the interaction also affects the choice of improvement. General training in use may not be enough; how the part is positioned or how the contact point is determined must be described again. For this reason, comparing only the observer means is not sufficient.

Variance is the square of the standard deviation; for length its unit is mm². Components that are independent and properly separated add on the variance scale. Adding standard deviations directly does not give the same result. In this lesson the components are given as the inputs of a solved decomposition; the detailed calculations of decomposing from raw data are not done. This limit must be clear. If it is not known with which design and model the components were produced, just adding the numbers does not make a reliable analysis. Missing cells, a changing measurement order and uncontrolled conditions can distort the meaning of the components. Correct arithmetic does not fix a wrong experimental layout afterwards. Checking the data structure comes before calculating the result.

Diagram: [Same part ID] → [all observers] → [repeats with re-placement] → [separation of repeat / observer / interaction]. The same part goes to all observer arms; dividing different groups of parts among the arms mixes observer with part. A crossed design is for cases where the same object can be measured again. If the measurement changes or consumes the part, a second observer cannot measure the same item. In that case another design and additional assumptions are needed; the layout taught here is not applied automatically. In addition, the parts selected for the study must represent the range of use. A ratio calculated only with parts that are very similar to each other cannot be carried to production as a whole. Conversely, a very wide part range can make the measurement contribution look small. The decision record must carry both the absolute measurement variability and the coverage of the selected part group. This prevents the mistake of putting different product families or different decision needs under the same acceptance by looking at a single percentage. All numerical scenarios in this lesson's short quiz are also covered by the following notice: This dataset was generated synthetically for training; it does not represent a real business, employee or customer study.

Formula