# Measurement Systems Analysis

Measurement Systems Analysis– If measurements are used to guide decisions, then it follows logically that the more error there is in the measurements, the more error there will be in the decisions based on those measurements. The purpose of Measurement System Analysis is to qualify a measurement system for use by quantifying its accuracy, precision, and stability.

An example from industry serves to illustrate the importance of measurement system quality:

A manufacturer of building products was struggling to improve process yields, which had a significant impact on product cost. Experience indicated that there were several processes and environmental characteristics that influenced the process yield. Data were collected on each of the variables believed to be significant, followed by regression and correlation analysis to quantify the relationships in statistical terms.

The results showed no clear correlation between anything – in spite of years of anecdotal evidence to the contrary! In fact, the underlying strong correlation between variables was confounded by an excessive error in the measurement system. When the measurement systems were analyzed, many were found to exhibit error variation 2-3 times wider than the actual process spread. Measurements that were being used to control processes were often leading to adjustments that actually increased variation! People were doing their best, making things worse.

As you can see from this example, Measurement System Analysis is a critical first step that should precede any data-based decision making, including Statistical Process Control, Correlation and Regression Analysis, and Design of Experiments. The following discussion provides a broad overview of Measurement System Analysis, along with a spreadsheet analytical tool that can be downloaded (Gage R&R Worksheet).

##### Characterization

A measurement system can be characterized, or described, in five ways:

##### Location (Average Measurement Value vs. Actual Value):
• Stability refers to the capacity of a measurement system to produce the same values over time when measuring the same sample. As with statistical process control charts, stability means the absence of “Special Cause Variation”, leaving only “Common Cause Variation” (random variation).
• Bias, also referred to as Accuracy, is a measure of the distance between the average value of the measurements and the “True” or “Actual” value of the sample or part. See the illustration below for further explanation.
• Linearity is a measure of the consistency of Bias over the range of the measurement device. For example, if a bathroom scale is under by 1.0 pound when measuring a 150 pound person, but is off by 5.0 pounds when measuring a 200-pound person, the scale Bias is non-linear in the sense that the degree of Bias changes over the range of use.
##### Variation (Spread of Measurement Values – Precision):
• Repeatability assesses whether the same appraiser can measure the same part/sample multiple times with the same measurement device and get the same value.
• Reproducibility assesses whether different appraisers can measure the same part/sample with the same measurement device and get the same value.

The diagram below illustrates the difference between the terms “Accuracy” and “Precision”:

Efforts to improve measurement system quality are aimed at improving both accuracy and precision.

Figure 1:
##### Requirements

Following are the general requirements of all capable measurement systems:

• Statistical stability over time.
• Variability small compared to the process variability.
• Variability small compared to the specification limits (tolerance).
• The resolution or discrimination of the measurement device must be small relative to the smaller of either the specification tolerance or the process spread (variation). As a rule of thumb, the measurement system should have a resolution of at least 1/10th the smaller of either the specification tolerance or the process spread. If the resolution is not fine enough, process variability will not be recognized by the measurement system, thus blunting its effectiveness.

#### Measurement Systems Analysis Fundamentals

1. Determine the number of appraisers, number of sample parts, and the number of repeat readings. Larger numbers of parts and repeat readings give results with a higher confidence level, but the numbers should be balanced against the time, cost, and disruption involved.
2. Use appraisers who normally perform the measurement and who are familiar with the equipment and procedures.
3. Make sure there is a set, documented measurement procedure that is followed by all appraisers.
4. Select the sample parts to represent the entire process spread. This is a critical point. If the process spread is not fully represented, the degree of measurement error may be overstated.
5. If applicable, mark the exact measurement location on each part to minimize the impact of within-part variation (e.g. out-of-round).
6. Ensure that the measurement device has adequate discrimination/resolution, as discussed in the Requirements section.
7. Parts should be numbered, and the measurements should be taken in random order so that the appraisers do not know the number assigned to each part or any previous measurement value for that part. A third party should record the measurements, the appraiser, the trial number, and the number for each part on a table.

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