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A measure of the variation in accuracy or precision of a measurement system over time. When measurements are used as a guide for decisions, it is obvious that there will be more errors in the decisions made based on these measurements. Measurement System Analysis is used to evaluate a measurement system and determine its stability, accuracy, and precision.

A case study from the industry illustrates the importance of measuring system quality.

A manufacturer of building products struggled to increase process yields which had a major impact on product costs. The experience showed that there were many environmental and process factors that could influence the yield of a process. Each variable was examined for significance. The data were then analyzed using regression and correlation to determine the statistical relationships.

Despite years of evidence, the results did not show any clear correlation. The excessive error in the measurement system was the cause of the strong correlation between variables. Many measurement systems showed error variations that were 2-3 times larger than the actual process spread when they were examined. Many measurements that were used to control processes often led to adjustments that increased variability. People did their best and made things worse.

Five ways to describe or characterize a measurement system are available:

#### Location (Average Measurement Value vs. Actual Value):

• Stability refers the ability of a measurement system produce the same values over time while measuring the same sample. Stability, as with statistical process control charts refers to the absence of “Special Cause Variation” and leaves only “Common Cause Variation (random variation).
• Bias is also known as Accuracy. It measures the difference between the average measurement and the “True”, or “Actual,” value of the sample, or part. For more information, see the illustration below.
• Linearity measures the consistency of Bias across the measurement range. If a bathroom scale measures 150 pounds and is below 1.0 pound, but is above 5.0 lbs when it measures 200 pounds, then the Bias scale is non-linear. This is because the degree of Bias changes with time.

#### Variation (Spread Of Measurement Values – Precision):

• Repeatability determines if the same appraiser can measure the exact same part/sample multiple time using the same measurement device and obtain the same value.
• Reproducibility determines if different appraisers are able to measure the same part/sample using the same measurement device, and give the same value.

### Requirements

These are the requirements for all measurement systems capable of measuring:

• Statistics stability over time.
• Variability is very small in comparison to process variability.
• Variability is very small in comparison to the tolerance (specification limits).
• The measurement device’s resolution (or discrimination) must be smaller than the smaller of either process spread (variation) or specification tolerance. The measurement system should have a resolution that is at least one-tenth of the smaller of the process spread or specification tolerance. The measurement system will fail to recognize process variability if the resolution is too low, which can reduce its effectiveness.

### Stability Measurement Assessment

1. Choose a part in the middle of the process spread to determine the reference value relative a traceable standard. If there is no traceable standard, measure the part 10 times in controlled conditions and average the results to calculate the Reference Value. This will be the Master Sample.
2. Measure the master sample three to five times over a minimum of twenty days. You can keep the repeat count fixed. To capture natural environmental variation, take readings throughout the period.
3. You can plot the data on an x & R diagram – refer to the Statistical Process Control section in the Toolbox to calculate control limits.
4. Analyze the control chart to determine statistical control. For further assistance, refer to the section on Statistical Process Control in the Toolbox.