# Measurement System Analysis (MSA)

Description:

Measurement system analysis (MSA) uses scientific tools to determine the amount of variation contributed by the measurement system.

It is an objective method to assess the validity of a measurement system and minimize the factors contributing to process variation that is actual stemming from the measurement system. The steps below are generally followed with a goal of obtaining acceptance for each of the five criteria.

Objective:

Confirm that the measurement system used to collect the data is valid. The first goal is to quantify the:

1. Process variation
2. Appraiser variation

and the Total measurement system variation.

Secondly,  minimize the measurement system variation and its impact on the Total Variation so the amount of Process Variation can be understood as precisely as possible.

The following components of measurement error need to be studied and quantified before establishing process capability and making decisions from the data.

• ACCURACY / BIAS
• RESOLUTION / DISCRIMINATION
• LINEARITY
• STABILITY
• REPEATABILITY & REPRODUCIBILITY (Gage R&R)

The MSA is often a very time consuming component of the project and can slow the team’s quick progression through the process.

Continue to focus on low hanging fruit that may be momentum "sustainers" and work vigorously through the MSA process. Most of this work can be done by the GB/BB outside of the team meetings.

### Accuracy / Bias

The difference from the true value and the value from the measurement system. Accuracy represents the closeness to a defined target. Precision is different than accuracy and is covered in Gage R&R under Repeatability.

For best accuracy of the data:

1) Accept all data as it is collected. Assigning special cause and scrutinizing data comes later.

2) Record the data at the time it occurs.

3) Avoid rounding off the data (rounding can create resolution problems).

4) On the data collection plan, record as many details around the data such as the exact source, machine, operator, conditions, collector’s name, material, gage, and time. Record legibly and carefully.

The data should be screened for misplaced decimal points, duplicate data entries by mistake or improper recording procedure, missing date points if frequency is important, and other obvious non-representative data.

5) Verify the gage is accurate. If using a weigh scale, verify it with a known and calibrated weight. Use gage blocks for calipers or micrometers. Use hardness blocks to verify hardness testers.

Accuracy versus Precision

### Resolution / Discrimination

The goal is to have at least 5 distinct values or categories of readings.

Adhere to the 10-bucket rule. If your measurement system requires measurements to the hundredths (x.xx), then divide that by 10. Collect and record the data to the nearest thousandths (x.xxx). The measurement system shall be sensitive to change and capable of detecting change.

The lack of resolution will not allow a measurement system detect change. If you are measuring the downtime and using measurement to the nearest hour and most downtime is less than an hour then most of the reading will either be a 0 (for 0 hours) or a 1 (for 1 hour).

However, using a stop watch and recording data to the nearest minute will provide 60x more resolution and allow better distribution of data points, more variety of data, with fewer repeat measurements. You could have 60 different readings. Actually recording the nearest 6 minutes would satisfy the 10-bucket rule, but it is a guide to help ensure resolution in the measurement system.

This part of the MSA is usually the easiest to fix such as finding a micrometer, caliper, hardness tester that can capably read to the next nearest decimal.

TROUBLESHOOTING:

Try acquiring a larger samples size, with the idea that some of these may create new observations or measurements.

Measure to as much resolution as possible and practical.

### Linearity

When gathering data only collect with the acceptable limits where there is proven linearity. This is a test to examine the performance of the measurement system throughout the range of measurements.

Linearity represents the change in accuracy through the expected operating range of a measurement device.

For example, does the bathroom scale perform the same when weighing a pet of 10 lbs to a man of 250 lbs? The scale has an operating range of 0 lbs to 300 lbs but the scales's accuracy may change at various levels of measurement.

Sources of linearity error may come from age, wear, calibration error, or there may be known linearity error. If there is known error then there may be a calculation to account for it and various ranges of measurement.

### Stability

Stability (also referred to as "drift") of a measurement system can be analyzed using control charts. Ensuring the measurements taken by appraiser(s) for the process indicate stability and consistency over time.

Each appraiser should measure the same way every time over a long period of time and each appraiser should measure the same way as all the others.

Stability is the total variation (spread and shape of the data distribution) of the measurements using the same parts, measured using the same gauge over a long period of time.

SPC Charts use a variety of tests to determine stability. Many software programs will have these as options when analyzing data and will even indicate the point(s) and test that each failed.

Some of the corrective measures once again include Standard Operating Procedures and re-calibration. Sometimes the gauge will have wear from use over a long period of time and this can not be repaired or re-calibrated. Other times, there may be a build up of dirt, dust, or contamination.

Reminder:

Special cause variation can also occur within the process control limits and these must be given corrective action before proceeding to validate the measurement system.

The I Chart below shows stability in this measurement system example, assuming this is a "longer" period of time that represents actual conditions as close as possible.

## Variable Gage R&R

In a Variable Gage R&R there are generally two to three operators appraisers with 5-10 process outputs measured by each appraiser. Each process output is measured 2-3 times by each operator. Depending on the cost and time involved you can add more appraisers and measurements and replications.

When performing the replicated appraisals it is critical that the measurement are randomized so that no patterns or predictability can be entered in by the appraiser. This bias will mislead the team and create a useless Gage R&R.

For example, an appraiser may remember the 7th part that was measured was borderline and made a decision to give it one measurement. The appraiser may have spent a lot of time on that part in the initial assessment and if the 2nd round of measurements are not randomized, that person will remember the measurement (appraisal) they concluded during the first round.

So...the message is to move the parts around each repetitive set of measurements. However, the parts must be identified so the person entering the data into the statistical software enters the reading under the correct part.

### Four Criteria in Variable Gage R&R

The following four areas will be assessed. A statistical software program will generate these values once the data is entered. The GB/BB will be responsible for finding these values and determining whether each passes and if the entire measurement system is adequate to determine process capability. Process capability can not be determined with reliability if the measurements (the data) are suspect.

1) % Study Variation is based on standard deviation
2) % Tolerance is based on USL and LSL
3) % Contribution is based on variance
4) The number of distinct categories based on process variation

Ideally, all four categories should be in the GREEN zone. Examining the visual aids below shows commonly used judgement criteria for each category.

### 2) % Tolerance

Shown below is an example of a % TOLERANCE calculation. In this case we are using 3 appraisers measuring 6 different parts.

This study shows the measurement error as a percent of tolerance in short period of time. It includes both repeatability and reproducibility, can not be separated.

5.15 Study Variation = 99% (constant)

The TOP TABLE at the top is a part of the d2 distribution. This value is a constant that is found by looking at the column with 3 appraisers and going across with the row with 6 parts. In this example the d2 value is 1.73.

The LOWER TABLE shows that actual measurements that each of the appraisers cam up with using their variable gage. The range of the three measurements for each part is shown on the right. Then the average range is shown (=0.69) and this is carried on to the Gage Error formula.

To convert this gage error of 2.05 to a percentage of tolerance multiply by 100 and divide by the process tolerance for the analysis.

The process tolerance is the difference in the specification limits. For example, if the USL is 27 and the LSL is 2, then the tolerance is 25.

With the tolerance being 25, then:

Referring back to the RED/YELLOW/GREEN criteria display for % TOLERANCE, it shown that 8.2% is a passing value and this part of the Variable Gage R&R is acceptable.

REPRODUCIBILITY:

Ability of one appraiser to get the same result and another appraiser or the ability of all appraisers to get the same results AMONG each other.

To optimize reproducibility in ATTRIBUTE Gage R&R:

1) Create visual aids, templates, definitions, or other specific criteria for each to meet a certain rating, value, or appraisal. Pictures of good, bad, in the middle, and colors, will help each appraiser standardize their response, improving the reproducibility.

Note: If these corrective actions are needed to pass the Gage R&R, it should be instituted as a formal work instruction and everyone involved throughout the company or plant should adhere to same instructions.

To optimize reproducibility in VARIABLE Gage R&R:

1) Create a Standard Operating Procedure with visual aids and definitions. When using humanly subjective "touch" devices such as micrometers and calipers it is important that all appraisers "squeeze" the same amount. Too little or much pressure at higher levels of resolution can be enough to alter the Gage R&R.

2) Visual aids also help. When using an optical comparator to get a higher resolute data point there is subjectivity where to place the template or the starting and end point(s) on the shadow. Pictures of acceptable and non-acceptable will help reduce this variation. Templates of complex figures or shapes also help reduce subjectivity and improve R&R.

REPEATABILITY

This describes the ability for an appraiser to repeat his/her measurements each time when analyzing the same part, unit, etc. In destructive testing (such as tensile testing) these reading will not be possible and some statistical software programs have options to select for destructive testing.

The goal is to have an appraiser repeat unit readings at least three times. The person administering the test should randomize the sequence each time to prevent and patterns and bias (the appraiser may remember or try to remember what a measurement was and tend to alter real measurements to get the Gage R&R to pass). It is important for the administrator to record carefully to ensure readings correlate the correct part/unit each time.

Avoid writing down measurements and then typing them into a statistical program. The fewer times measurements are recorded and copied the lower the risk for human error to add even more variation and possibly fail (or pass) the Gage R&R when it shouldn't have.

Precision is the ability to have the same repetitive result (or appraisal in this case). Visually, it means that all your shots of an arrow are very close to one another. It does not mean that they are near the bulls eye. In other words, it does not mean that your shots are accurate.

If your shots are accurate and precise, then they are tight circle centered around the target.

It is also possible to be accurate without being precise. For example, there may be several shots all around the bulls eye (target) but they may be scattered all around it in a large diameter cluster (area).

If you take a look at the group the center (mean) may be on the bulls eye but the shots are not in control or precise. In others words, there is a lot of unpredictability or variation. This would represent a set of data with an acceptable mean (on target) but too much variance (high standard deviation).

This is the essence of Six Sigma. The methodology focuses on VARIATION REDUCTION as primary goal and then with the inputs under control, the mean can be shifted if it is necessary. It is not possible to shift the mean with sustainability without having process control (control over sources of variation).

## Attribute Gage R&R Example

Using the example of data gathered from two appraisers assessing 20 samples as Good (G) or No-Good (NG) draw your conclusions on the outcome.

## Variable Gage R&R Example

Examining the output of a measurement system analysis below what conclusions can be drawn?

As mentioned before, cleaning up a measurement system can elevate hidden causes of scrap, rework, customer concerns and a lot of cost itself....and it can turn into a project itself.

Expect to update or create new Standard Operating Procedures (or work instructions) at a minimum to mistake-proof the appraisal process and robust measurement methods so that as much variation as possible is PART to PART.

 This module provides additional insight in measurement systems analysis. This is critical component of the MEASURE process that is often overlooked or skipped and could lead to incorrect conclusions and rework in the later stages of the DMAIC journey.Click here to purchase the MSA module  and view other topics available to download.

## ANOVA

Analysis of Variance is another technique to analyze sources of variation of measurement error (and for any sources of variation - hence the name).

With statistical software, the method has the advantage over the "average and range" technique since it provides more information, such as interactions between the parts being measured and appraisers.

The variation can be distinguished between four categories:

1) Appraisers (those that are measuring)

2) Parts or item being measured

3) Interaction of Appraisers and Parts

4) Replication error from the gauge

Subscribe for complete site access

Proceed to Subjective Root Cause Analysis Tools

Test your knowledge with sample certification problems

#### Six Sigma & LeanCourses (online, onsite, classroom)

Six Sigma

Templates & Calculators

#### Six Sigma & LeanCourses (online, onsite, classroom)

Six Sigma

Templates & Calculators

Six Sigma Modules

Green Belt Program (1,000+ Slides)

Basic Statistics

SPC

Process Mapping

Capability Studies

MSA

Cause & Effect Matrix

FMEA

Multivariate Analysis

Central Limit Theorem

Confidence Intervals

Hypothesis Testing

T Tests

1-Way Anova Test

Chi-Square Test

Correlation and Regression

SMED

Control Plan

Kaizen

Error Proofing