The Slippery Measurement System Paradox

The Slippery Measurement System Paradox

1. Background

   This article is about the need to clarify how to proceed when Measurement System

Analysis (MSA for short) is necessary, parts from the process have to be measured and chosen

to run the MSA, and no other measurement system is available apart from the one that is

going to be evaluated.

   Some authors and manuals set up criteria on how to select units from the process to

run the MSA. Some of them just say they have to cover most of the actual range, some specify

units have to represent at least 80% of current range of the process, some others establish

100% of either the range or the tolerance width, depending on the purpose of the

Measurement System. All these empirical rules have the same concept behind. Units/parts to

be selected, have to be representative of the process that is going to be measured. MSA

techniques such as Gage R&R compares uncertainty from Measurement System to the

variability of units themselves.

   It has to be said that there is no good or bad measurement system, it is acceptable or

not acceptable to measure the characteristic we need to measure. All Measurement Systems

have uncertainty. The only thing that MSA techniques do is to determine if that uncertainty is

small enough to be dismissed in comparison to parts variation.

   Doubts about if we are proceeding correctly then come up immediately. If we have to

select parts/units from the process in a way that they are going to be representative of it, and

we only have the Measurement System (MS for short) that is going to be evaluated, how do

we know that the parts are selected correctly? Moreover, and the most important question, if

the MS is not acceptable and we do not know it yet, is it possible that the

result of the analysis would tell us MS is acceptable and the reality would be that it is not at all?

   Within the next lines of this text, we are going to explain that the above situation is

indeed a paradox, which means, it cannot happen. We are going to argue and demonstrate

that it is not possible to select parts with an unacceptable MS in a way that the MSA would tell

us to accept that MS.

2. The paradox argument

There are several mathematical expressions to compare MS uncertainty to

parts variation. The most used are:

The acceptance criteria is:

% Study Variation < 10%

% Contribution < 1%

% Tolerance < 10%

Number of distinct categories ≥ 14

   Please note that acceptance criteria can vary among different uses and organizations.

Here we show typical values.

   Let us look at equation (1) and imagine we are using a MS, which is not acceptable in

comparison to parts variation. We know that:

   We can say that in an unacceptable MS, the variation due to the MS itself (Gage) would be big in

comparison to parts variation and thus, it would be a big proportion of the total as well. This

last statement is the key of what could not happen if we use a MS not acceptable. The range

measured, and therefore the variation, during parts selection process, would behave as

equation (5) shows. Therefore, the only thing that may happen is to select parts smaller than

the range of the process and not meeting what the practical rules recommend. That would

imply the variation of the Gage would be even a bigger proportion of the whole variation. The

conclusion driven by equations (1) to (4) and their respective acceptance criteria is that the MS

would be not acceptable as it actually is.

   Based on previous argument, we can also state that MS cannot be accepted when it is

not acceptable as it is not a possible situation, thus a paradox.

3. Discussion and Conclusions

   We have demonstrate in a simple way that a MS cannot be evaluated as good when it

has a big uncertainty when using Gage R&R techniques.

   Main conclusion is that when we need to analyze and evaluate a MS and parts/units

have to selected, we can use the same MS for the selection.

   The risk of evaluating a not acceptable MS as acceptable does not exist based on “the

Slippery Measurement System Paradox”.