Hello Saeid,

If profile similarity were conceptualized as distance in (x-dimensional) space, you could use any number of measures (e.g., Mahalanobis distance, city-block, Minkowski, MAD, etc.) as the quantification of similarity. Smaller values would be better, of course, for presuming dependability.

If similarity is conceptualized as pattern matching, then correlational/association measures would be a useful choice. Higher values would be better for inferring dependability.

Apologies if I've misunderstood your query.

Good luck with your work.

Thank you very much David,

This is a pattern matching problem. Maybe more details would be more clarifying.

We have built a high precision dimensional measurement system to measure the inline dimensional deviations between the artifacts.

We know that there various systematic errors in the measurement system, but we cannot measure them, and also it is not required because the illustration of the deviations between the measurements is important. However, the determination of the deviations should be accurate enough.

This is why I call it a pattern matching problem in which we assume a systematic error in each point of the measurement and then we try to conduct a repeatability test for some specimens to evaluate the random error.

I would appreciate it if you could tell me more details about correlational measures.

SUGGESTION-QUANTITATIVE ASSESSMENT FOR THE REPEATABILITY OF THE MEASUREMENT SYSTEM FOR A TARGET PROFILE.

Repeatability is defined as the measurement of one point.

SETTING UP THE FRAMEWORK OF THE REPEATABILITY OF THE MEASUREMENT SYSTEM FOR THE TARGET PROFILE.

1.The Repeatability of the Measurement system with a static target profile.

2The Repeatability of the Measurement system with a moving target profile.

3.The Totality of the Space from which the Measurement System approaches the target profile.

Given that the radius 2 is a good representation of infinity,the totality of the area from which the M. System approaches to measure the target profile =4pii r(squ)=8pii.

4.Given that the Systematic Error(SE)% deviates from the target profile and the Randomn Error(RE)% deviates from the target profile with a single attempt.

Repeatedly with a single attempt ranges from

100%-(SE%×RE%) to 100%-(SE%+RE%) = Ra( Re).

From the Total Area of 8pii,Repeatedly with

1.A static target profile is given as 8pii ×Ra(Re)

2.A Moving target profile is given as 8pii×6pii×Ra(Re)

The Repeatability of the Measurement Systems taking Situations 1& 2 into consideration thus give a range of 8pii×Ra(Re)+24pii(squ)×Ra(Re) to 8pii×Ra(Re)×24pii(squ)×Ra(Re)

Grateful for a feedback,please.

SUGGESTION(2)

Alternatively,if the totality of the space from which the Measurement System approached the target profile is computed in reference to volume rather than an area,then the 8pii is replaced by 32pii÷3.

POINT OF CORRECTION.

For the

2.Moving Target Profile,the repeatabilty of the Measurement System,given that the area of approach is 8pii = 8pii ×4÷3piir(cube)×Ra(Re)

=8pii×4÷3pii8×Ra(Re).

Given that the moving Target Profile occurs within a sphere with a radius of 2.

The Resultant of the range of the repeatability of the measuring system for situation 1.Ra(Re)

2.Ra(Re)2 for the static target profile and

3.Ra(Re)3 for the moving target profile

Is the Intergral of the product Ra(Re)×Ra(Re)2×Ra(Re)3=Ra(Re)+Ra(Re)2+Ra(Re)3, all ÷3× square root of 3.=Resultant RaRe.

The Repeatability of the Measuring System in respect of the target Profile= The lower limit of Ra(Re) +Resultant RaRe.

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Hi, Richard. It very much depends on the application. Gauge R&R as part of the Measurement System Analysis (MSA) performs well in the Semiconductor industry.