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## Main Question or Discussion Point

Hello Everyone,

Here is my situation: I am using a laser to take distance (height) measurements on a variety of surface types (e.g. mirror, machined surface, plastic, etc.) and I would like to quantify the repeatability of the laser measurements on each surface type. Please note that I care only about the repeatability of the laser and NOT the overall measurement system.

Setup:

The surface samples are mounted to a baseplate which is attached to a linear actuator and the laser is fixed overhanging the baseplate pointing in the negative z-axis direction. I move to a position centered in each surface sample (e.g. surface 1 --> actuator position = 10.50 mm), record the laser distance measurement and the actuator position at time of measurement (may not be exactly 10.50, could be 10.52), and repeat “x” number of times (call this a “batch” of measurements).

Question:

What is the appropriate way to quantify the repeatability of the laser measurements for each surface type?

My Initial Thoughts:

It seems like no matter what I do I will be reporting the repeatability of the entire system, not just the laser.

For example, the standard deviation of each surface in a “batch” would provide some information about the repeatability of the laser on a given surface but it also includes the actuator position variance (and error) at the time of measurement.

Similarly, the standard deviation of several surface-batch-means will provide some information about the reproducibility of the laser on a given surface but it also includes the actuator variance.

Is there any way to extract just the laser repeatability from this data?

Someone else suggested using a Gauge R&R (gauge repeatability and reproducibility) for this purpose but doesn’t that have the same issue (i.e. repeatability and reproducibility of the entire system, not just the laser)? Also, there is only one sample plate (I think there must be at least 10 for a “proper” gauge R&R) and the process is completely automated so there should be no operator variance.

My statistics is a bit rusty so I appreciate any help or feedback.

Thanks!

Here is my situation: I am using a laser to take distance (height) measurements on a variety of surface types (e.g. mirror, machined surface, plastic, etc.) and I would like to quantify the repeatability of the laser measurements on each surface type. Please note that I care only about the repeatability of the laser and NOT the overall measurement system.

Setup:

The surface samples are mounted to a baseplate which is attached to a linear actuator and the laser is fixed overhanging the baseplate pointing in the negative z-axis direction. I move to a position centered in each surface sample (e.g. surface 1 --> actuator position = 10.50 mm), record the laser distance measurement and the actuator position at time of measurement (may not be exactly 10.50, could be 10.52), and repeat “x” number of times (call this a “batch” of measurements).

Question:

What is the appropriate way to quantify the repeatability of the laser measurements for each surface type?

My Initial Thoughts:

It seems like no matter what I do I will be reporting the repeatability of the entire system, not just the laser.

For example, the standard deviation of each surface in a “batch” would provide some information about the repeatability of the laser on a given surface but it also includes the actuator position variance (and error) at the time of measurement.

Similarly, the standard deviation of several surface-batch-means will provide some information about the reproducibility of the laser on a given surface but it also includes the actuator variance.

Is there any way to extract just the laser repeatability from this data?

Someone else suggested using a Gauge R&R (gauge repeatability and reproducibility) for this purpose but doesn’t that have the same issue (i.e. repeatability and reproducibility of the entire system, not just the laser)? Also, there is only one sample plate (I think there must be at least 10 for a “proper” gauge R&R) and the process is completely automated so there should be no operator variance.

My statistics is a bit rusty so I appreciate any help or feedback.

Thanks!