If the variation of the present measurement system is not acceptable (over 30%), there is a method that can be used to reduce the variation to an acceptable level until proper measurement system improvements can be made. The unacceptable variation may be reduced by taking multiple statistically independent (non-correlated) measurement readings of the part characteristic being evaluated, determining the average of these measurements and letting the numeric value of the result be substituted for the individual measurement. This method will, of course, be time consuming, but is an alternative (with customer approval), until improvements are made to the measurement system (i.e., redesigning or buying a new system). The procedure for this alternative method is as follows:
1) Determine the number of multiple readings required to meet an acceptable level of variation.
2) Follow the gage study procedure.
Example:
In the XYZ Corporate example, the percentage of tolerance GRR variation is 25.5%, with a 6 sigma spread equal to 0.24. The customer wants to reduce this figure to at least 15%, which would have an equivalent 6 sigma spread of 0.14.
To determine the number of multiple readings required to meet the desired 15% criteria, it must first be understood that the distribution of individual and average measurements has the same mean numeric value. Secondly, the variance of the distribution of averages is equal to the variance of the distribution of individuals divided by the sample size. Understanding this relationship as shown below, the number of multiple readings required can then be determined.
This can be approximated by:
Therefore, 3 multiple readings on the part characteristic will reduce the total measurement system variation to approximately 0.14 and the %GRR to 15%.
This method should be considered as a temporary step until other improvements are made on the measurement system. This should be used only with the concurrence of the customer.
source of Variation : Analysis of measurement systems
