Does the definition of the P/T ratio (precision to tolerance) assume that the measurement process is centered at some nominal dimension analogous to the definition of process capability ratio (PCR)?

Is there a separate index for an off-center measurement process scenario similar to the PCRk?

Formulas:

P/T = (6*sigma)/(USL-LSL)
PCR = (USL-LSL)/(6*sigma)
PCRk = min [(USL-mean)/(3*sigma),(mean-LSL)/(3*sigma)]

(the gage/instrument sigma is used in the P/T ratio calculation while the process sigma is used for PCR)

Thanks in advance.

Welcome to the Cove :bigwave:

I'm not sure I understand what you are asking. Does "off center" mean there is a "correcting factor" (if a micrometer reads .010" but the true measurement is .015" - you add .005" to whatever the reading is)?

Traffic here is kind of slow during the weekends. Tomorrow, most of the more knowledgeable Covers will be back from the weekend and you should get much better feed back than I am able to give for Gage R&R questions.

Yes, by "off-center measurement process" I meant that the measurement process would be biased (lack of trueness). Samples with accepted reference values would be needed in the gage R&R study to detect this bias. I guess that bias/trueness estimation is out of the scope of these studies as normally in practice they are carried out with random samples from the production process for which the true values are unknown.

Anyway, after giving it some thought, I just realized that an analogous PCRk (Cpk) index might be unnecessary for measurement processes. If I knew a measurement process was biased, I would adjust the results with a correcting factor and be done with it. For a production process the story would be different, if the process deviated from the nominal value (off-center scenario) I wouldn't be able to "correct" the results, some units would come out defective and would be discarded.

Does the definition of the P/T ratio (precision to tolerance) assume that the measurement process is centered at some nominal dimension analogous to the definition of process capability ratio (PCR)?

Is there a separate index for an off-center measurement process scenario similar to the PCRk?

Formulas:

P/T = (6*sigma)/(USL-LSL)
PCR = (USL-LSL)/(6*sigma)
PCRk = min [(USL-mean)/(3*sigma),(mean-LSL)/(3*sigma)]

(the gage/instrument sigma is used in the P/T ratio calculation while the process sigma is used for PCR)

Thanks in advance.

No. The P/T Ratio has no equivalent to Cpk/Ppk. The purpose of the P/T Ratio is to define what percentage of the tolerance is consumed by Repeatability and Reproducibility, which is independent of the distance from nominal.

A Linearity study will define the bias of the gage over its working range, which is somewhat analogous to Cpk/Ppk. I have seen several different Linearity indices, but have seen serious drawbacks to those that I have seen.