Measurement Systems Analysis - A Case Study

Background

When we examine processes for stability and capability, we must use some type of measurement system to capture the process and product information. We are all familiar with the basic measurement tools used, including micrometers, calipers, drop gages, scales, and various go/no-go gages. However, before making decisions regarding the acceptability of the data we must first understand how variation in the measurement system contributes to the overall observed process variation at the highest level.

We can express the observed variation in a system using the following equation:

The total observed variance of the system (the numbers you observe and write down on the paper) is equal to the sum of the variance of the product plus the variance of the measurement system. (Remember that variance is the square of standard deviation.) To get a clear picture of the process variation, you would like to quantify, separate, and minimize the variance in the measurement system. The way to do this is through measurement systems analysis (MSA), also known as gage reproducibility and repeatability (GR&R).

Definitions

Repeatability: The variation between successive measurements of the same part, same characteristic, by the same person using the same instrument

Reproducibility: The difference in the average of the measurements made by different persons using the same or different instruments when measuring the same characteristic.

What is exactly is Gage R&R / MSA?

There are actually two ways to express the GR&R result. The one we are most familiar with is expressing the gage error as a percentage of the tolerance (P/T ratio). This addresses what percent of the tolerance is taken up by measurement error. It includes both repeatability and reproducibility. The worst case acceptable P/T ratio for accepting or rejecting product is 30%. In other words, the measurement error should consume no more than one third of the tolerance band. This ratio is a good estimate for classifying production samples (i.e. accepting or rejecting product) but is not generally used for process improvement studies.

The second way to express GR&R is a percentage of the total observed variation (the process sigma). This term estimates how well the measurement system is performing as a part of the system (remember the equation above). This method is the best estimate of R&R when performing process improvement studies, because the variation in the measurement system must be reduced before we can progress to improving the process.

Another reason to care about gage R&R: your R&R number directly affects your ability to estimate the process capability. If your true process variation is being inflated due to a poor gaging system, then you may be underestimating your true process capability. In other words, if my observed sigma is some number x, while the true product sigma is less than x, my process capability is underestimated (dividing by a bigger number gives a smaller result, right?).

Some things to take into account when selecting your measurement system

• Choose a system with adequate resolution, usually 4 to 10 times more precision than the characteristic you are measuring. For example, you may use pin gages with .001" resolution to measure a through hole with a tolerance of +/-.010", but not to measure a hole with a tolerance of +/- .001", because the pin gage resolution consumes 50% of the allowable tolerance.
• One indicator that you probably do not have enough resolution is if all R&R measurements come out identical with no variation. You effectively have a go/no-go gage which requires a different technique for GR&R. If the gage system does not have enough resolution to pick up process variation, then you cannot effectively perform a statistical study on the data. No variation in the data means standard deviation = 0, which means your Cpk number blows up when you divide by zero.
• GR&R setup: In general, the gage R&R range method, or "short form" (two operators, 5 samples, two measurements per sample) is adequate for performing your P/T assessment for production. However if you do not meet the P/T guideline of 30% or you wish to perform a more rigorous investigation of a measurement system then you should use at least ten samples and take multiple readings per sample. More information on which gage R&R method to use can be found at various web sites or within your statistical package help files.

Case Study

A processing defect was identified on an injection molded cassette. It was observed that a sink on a rib feature exceeded the specification of .008". A deviation was written to increase inspection for this characteristic. A measurement systems analysis was performed to validate the ability to accurately measure this characteristic.

Setup: One characteristics was being measured. A GR&R was set up using 10 samples, three operators, and two trials. This setup was designed using Minitab ANOVA method.

Data Collection: The data were gathered using a drop gage witha digital indicator. The operators included a QA technician, a QA floor inspector, and a production operator. All operators were trained in the use of the measurement equipment and the product feature being measured.

Analysis

The data were analyzed using Minitab using the ANOVA method. The GR&R is expressed both as a P/T ratio and as a percentage of observed variation.

A two-way ANOVA was performed to look for variability due to the part, the operator, and any interactions between the parts and operators.

The Minitab GR&R analysis shows that all observed variation was due to lack of repeatability (variation when measuring the same part over and over again.) There was no evidence of variation due to reproducibility (variation among operators).

The P/T ratio was calculated by multiplying the sigma times 5.15, then dividing by the tolerance (max sink allowed was .008"). The P/T ratio was 101%, which exceeds the 30% allowable. The observed variation in measurement consumes more than the entire allowable tolerance!

Also note the number of distinct categories = 1. In other words, the measurement system is unable to distinguish one part from another. This is clearly an inadequate system for measuring this characteristic.

Conclusions

After reviewing the measurement setup, it was determined that the variation occurred because the part was not being reliably positioned beneath the gage, and the maximum sink point was not being determined. The corrective action including development of a fixture to allow the part to be fixtured, the drop gage zeroed on the datum plane, then moving the part with the drop gage in constant contact in the part to measure the maximum displacement (similar to using a dial indicator to measure runout on a shaft).

The fixture had three benefits. First, the gaging accuracy was improved. After implementing the actions, the GR&R was repeated with a P/T ratio of less than 30%. The second benefit was that gaging speed was improved, because the inspector did not have to "fuss" with the part to achieve a good measurement. Finally, based on the measurement improvements, the parts were found to be within specifications which decreased scrap costs.