Measurement Systems Analysis (MSA): Complete Practitioner Guide

The question has been raised multiple times: when should a measurement study be completed?The rule is very simple:Whenever a measurement is being used to assess the quality or quantity of a product, a measurement system study is required.This means that all measurement systems should be assessed statistically.Of course, some kind of priority has to be set, as it is obviously impossible to complete an assessment of every system in an organization immediately. So, we suggest the following priorities:

New measurement systems/equipment

Assessment of new equipment is a good way to ensure that it meets the organization’s needs. One of the great things about statistically assessing equipment is that the process will indicate whether different people can work effectively with the equipment. It also gives a performance baseline for the equipment, so if you experience deterioration in the equipment, the study will be able to quantify the problem.

Measurement systems/equipment being used for SPC

If the variation from the measurement system is high, then control charts will show changes in the measurement equipment, not changes in the process. So it is essential to assess measurement systems statistically prior to implementing SPC.

Since trends and changes apparent in SPC charts can come from the measurement system itself, it is important when trying to track down issues to understand the effect of measurement variation.

Measurement systems/equipment used at critical decision points

If a measurement is taken to assess whether to pass or fail a batch, it is essential that the measurement system is able to complete the task consistently and reliably.

A common comment from customers is: “We’ve been using this equipment for years and it has never been a problem. We regularly calibrate it and it has certificates. Why should we assess it?” Remember, a statistical assessment is an accurate picture of the everyday variation in measurements. Equipment can pass calibration easily and yet fail the statistical assessment. Often, measurement systems are viewed as being correct, beyond question. Don’t be blinded to this critical area of variation.

You can also use this kind of assessment in other circumstances, including:

Ensuring that you and your customer use similar methods of measurement;
Ensuring that you and your suppliers use similar methods of measurement;
Ensuring that different locations within the organization measure in a similar way;
Assessing a measurement system before and after repair;
Preventing measurement deterioration;
Ensuring that a a new tester is fully trained;
Assessing two different methods of testing;
Assessing the impact of changing environmental conditions.

In garnering these advantages from your measurement system analysis, you will find that GAGEpack provides tools that will assure that measurement studies are completed in a timely and accurate way.

Additional reference material

Additional sections from legacy measurement-systems-analysis:

Measurement Systems Analysis – Improving measurement accuracy with gage R&R

What is it?

Variation is inherent to any system, and the data collection process is no exception. However, excessive variation in the data collection process will appear as variation on the control chart and can have a negative effect on process analysis. In addition to using operational definitions to ensure measurement consistency, you should periodically perform repeatability and reproducibility tests and recalibrate gages.

Gage R&R refers to testing the repeatability and reproducibility of the measurement system. Repeatability is the variation found in a series of measurements that have been taken by one person using one gage to measure one characteristic of an item. Reproducibility is the variation in a series of measurements that have been taken by different people using the same gage to measure one characteristic of an item.

Gage R&R studies let you address two major categories of variation in measuring systems: gage variability and operator variability. Gage variability refers to factors that affect the gage’s accuracy, such as its sensitivity to temperature, magnetic and electrical fields and, if it is mounted, how tight or loose the mount is. Operator variability refers to variation caused by differences among people. It can be caused by different interpretations of a vague operational definition, as well as differences in training, attitude, and fatigue level.

Performing gage R&R studies can be made easier by using software such as GAGEpack.

Measurement Systems Analysis – Improving measurement accuracy with gage R&R

What is it?

Performing gage R&R studies can be made easier by using software such as GAGEpack.

What is it?

Performing gage R&R studies can be made easier by using software such as GAGEpack.

Additional sections from legacy msa-1:

MSA: Measuring your measurement system with a performance curve

By Jackie Graham, Ph.D.

As measurement system variation increases, the probability of getting a correct value from a measurement system reduces. This concept is portrayed best by using a ‘gage performance curve.’ The example ‘gage performance curve’ shown in figure 1, demonstrates an excellent measurement system where the measurement variation is low, with an R&R (reproducibility and repeatability) of less than 10%.

Now, to explain what the chart means and how you interpret it. The x-axis shows the range of actual values of the product being measured. The y-axis shows the probability of accepting a product of any of the values using the current measurement system. The straight line in the center of the chart is the center of the specification, while the two straight lines either side of the center line represent the tolerance range. The curve represents the probability of accepting product to the tolerance. From the chart, it can be seen that if the true product value is 30 (the center of the specification) the chance of its being accepted using the measurement system studied is 1.0 or 100%, as it should be. If the product value is 10, well below the lower specification, the chance of its being accepted is 0 or 0%, again as it should be, since it is well below specification. Although a value of 14 is below the lower specification (15), the curve shows it has a small chance of being accepted in error. The curve shows that a product with a value of 16 has a high chance of being accepted, ideally this would be 100%, but due to the variation in the measurement system it has a slight chance of being rejected.

Ideally, the ‘gage performance curve’ should show a reading of 0% up to the lower specification, go straight to 100%, and remain at 100% to the upper specification, then go back to 0%. However, no measurement system is perfect; there will always be some chance of accepting or rejecting product in error, graphically depicted by the gage performance curve.

A measurement system with extremely high variation, say with an R&R of 300% of the tolerance, (generally the maximum acceptable R&R is 30%) would show a very different ‘gage performance curve.’ Figure 2 depicts such a curve.

This chart graphically demonstrates the impact of a highly variable measurement system. In this example, if the product has a value in the center of the specification it only has about a 60% chance of being accepted. This means that when the reading is taken from the measuring equipment, it has a 60% chance of producing a result inside the specification, and a 40% chance of producing a result outside the specification. As the curve shows, product that is way outside the specification still has a chance of being accepted. In this case, the specification is 4.6 to 5.2, yet product could be accepted from less than 4.00 to more than 5.75. This is quite a range when compared to the specification range of 0.6! If you think this kind of measurement system does not exist, unfortunately you are wrong. They occur all too frequently!

When setting up a measurement system it is essential to ensure that it is adequate for its purpose. The only way this can be assured is by completing an R&R study. If this is not completed, expect to accept product that is out-of-specification, and to reject acceptable product in error. The costs of poor measurement systems are enormous.

So, how do your measurement systems measure up? GAGEpack allows easy assessment of measurement systems and subsequent analysis using tools like the gage performance curve. Download a free trial now.

Additional sections from legacy msa-conduct-r-r-study:

How do you conduct an R&R study?

The objective of a simple R&R study, which can be done using software such as GAGEpack, is to determine whether the measurement system in use can adequately distinguish between or among units. There are a number of factors that affect the ability of a measurement system to discriminate among the units it measures. These factors may be categorized as those that typically contribute to any process variation: machine (the gage), operator (appraiser), method (method of measurement followed), material (units being measured), and environment.

In conducting a simple study, an attempt is made to minimize or hold most of these factors constant. (Note: the study should replicate as much as possible the conditions under which the process measurement is occurring. This essentially means that if production operators are making the measurements, the study should use production operators under the same conditions that exist when they are “normally” measuring the output. The study should not be conducted using quality technicians in a lab.) Therefore:

One gage is used. (No inter-gage variation)
One method of measurement is employed by all of the appraisers involved. (No variation due to the appraisers using different methods.)
The same dimension on each part is measured each time. A further assumption is that each part is measured in the same place to eliminate the possibility of within-part variation. (No variation introduced due to different characteristics or because the measurements have been taken at different locations on the part.)
The study is conducted under the same type of conditions that exist when the parts are normally measured. (No variation introduced by the location or environmental concerns of where the measurements are taken.)

The two items that are specifically varied are the number of appraisers and the number of units measured. The selection of these two factors is critical to meeting the objective of an R&R study.

The first one addressed is the number of appraisers. The appraisers should be selected from those individuals who are currently measuring the output. If there is only one appraiser, then only one should be used in the study. If there are two or three, use two or three. If there are more than 4 or 5, use two or three “typical” appraisers.

The second is the number of parts, generally between 5 and 10. The major factor to consider in selecting the parts is that they need to represent the total variation for the characteristic being studied for the process producing them. This means that going down to the line and pulling 5 to 10 consecutive parts or going to a bin and selecting 5 to 10 parts, is a not acceptable. The selection of the parts must be spread out over time so that the parts represent the “typical” variation in the process.

The final parameter is the number of replications, generally 2 or 3. A single replication will not allow for separate estimates for equipment variation and appraiser variation. Too many replications complicate the study without adding much value to the analysis. To be statistically sound, take measurements randomly (see note below). This confounds the factor of time, different in these repeated measurements, from appraisers and parts. As a practical matter, it often comes down to making sure that the appraiser does not know which part is being measured (randomizing the order of measurement) and no appraiser completes two replications before the others finish one replication. For example:

Appraiser 1 measures all five parts once.
Appraiser 2 measures all five parts once.
Appraiser 3 measures all five parts once.
Appraiser 2 measures all five parts a second time.
Appraiser 3 measures all five parts a second time.
Appraiser 1 measures all five parts a second time.

Note: Do not always measure parts in the order of 1-2-3-4-5-6-7-8-9-10

This results in something like Table 1 below once the data are organized.

Appraiser

Part 1

Part 2

Part 3

Part 4

Part 5

John

2.112

2.071

2.101

2.114

John

2.114

2.106

2.073

2.097

2.130

Mary

2.112

2.117

2.084

2.098

2.110

Mary

2.112

2.107

2.082

2.099

2.108

Gerry

2.108

2.116

2.102

2.110

2.108

Gerry

2.110

2.124

2.086

2.104

2.093

If you enter this type of information in GAGEpack as an R&R event, GAGEpack will calculate R&R percentages.

Additional sections from legacy msa-interpret-r-r-study:

How do you interpret an R&R study?

After performing an R&R study, which can be done using software such as GAGEpack, there are a number of ways to interpret the results. Frequently, since R&R is done in response to a customer requirement, the customer will indicate how to interpret the results. The most common here is the AIAG (Automotive Industry Action Group) standards, which are based on the R&R percentage given under study results. These results may be calculated as a percent of study variation, percent of specification, or percent of process variation.

For percent of study, the process variation is based on the spread of the parts (P) determined by . This is considered a range and using the /d2 relationship, a sigma for the process is estimated. This is then used to calculate the percentages.

A second method is to use the spread of the specs (USL – LSL). Now this must be compared to the estimate of the measurement error (R&R). However, one needs to multiply the sigma of the measurement by 5.15 (old method) or by 6.0 (new method) to compare the total measurement spread with the spec spread. (An alternative method is to divide the spec range by the respective numbers given above.)

The third method uses the information from an chart on the process and characteristic being studied. In this case, enter the , the , and the sample size. This is used to estimate the process spread.

Ideally the measurement error (R&R%) is less than 10% of whatever method is used (process spread or spec spread). It is usable in some cases when the R&R percentage is between 10 and 30%. More than 30% suggests that one should not be using it. [page 60 of MSA Manual 2nd edition or page 77 of MSA Manual 3rd edition]

If the number of distinct categories is 5 or more, it can be considered a capable measurement system. Wheeler and Lyday use a concept closely aligned with distinct categories called discrimination ratio, for which greater than four is satisfactory. The differences, in a nutshell, are that the distinct categories is a truncated number (no rounding or fraction used) and the discrimination Ratio assumes that appraiser variation has been reduced to zero and carries the fractional part as well.

Additional sections from legacy msa-faq:

Frequently-asked questions about Measurement Systems Analysis

Can repeatability be less than reproducibility if three appraisers are used?

Repeatability and reproducibility are relatively independent. The desired reproducibility is zero and this would essentially mean that the appraisers are measuring the same average value. That is, one appraiser is not measuring parts on the average as larger than the other two appraisers are.

On an R&R study, if I use the specifications, the study is good. If I use the study parameters, the gage fails.

In AIAG’s Measurement Systems Analysis manual, the standard approach for R&R percentages is to use percent of study variation. This means that the parts selected for the study are used to estimate the product’s variation (more correctly the product’s process variation). This makes the selection of those parts critical to the analysis. You want to know if your measurement system can detect changes in the process and tell if the process goes out of control.

The prior methodology asked a different question: Can I tell whether a product is good or bad. This is an inspection mentality that the automotive manufacturers want to move away from. In this case, the percentages are based on dividing by the specification range.

My general suggestion is to use the percent of study variation. However, given the push to improve Cp and Cpk, we have reduced the variation in our processes considerably. In some cases, we have Cpk’s > 2. In most of these cases, the R&R percentage will be poor because of the reduced variation in the processes. We can improve our measurement system (many times at great cost and sometimes we cannot improve it), but it will not result in a better product. So a suggestion that I frequently make is to specify some Cpk level above which you use R&R percent of tolerance and below which you use R&R percent of study.

R&R percentages don’t tell you how well repeatability is centered. Is it possible to apply Cpk principles to the estimated deviation to determine margin to the spec limits?

When doing an R&R study, you are checking to see if the variation in the measurement is too large to measure a product dimension in reference to either process variation or specification spread. There is no attempt in the R&R study to determine bias. This is done through a linearity or bias study. Without a true “measurement” for each part used in the study, centering cannot be determined and it can vary based on measurement size. Cpk is targeted to how well you are meeting a single value (normally the nominal or target value).

What are Process X-double bar and Process R-bar used for?

There are two ways to do R&R: One is to do the percentages with respect to tolerances (spec spread). The other is to do the percentages with respect to process spread (5.15 sigma). There are two ways to estimate process spread. The first is to do it from the parts used in the study. The second way bases process spread on control chart information from the process. Process and Process are used in the second method. GAGEpack is able to do R&R both of these ways.

What is the difference between tolerance and process variation?

The major difference between the two approaches relates to the purpose for doing the study. In the past, most companies were concerned only with getting good parts. Being able to sort parts (good from bad) was the requirement for the gage. Now most companies require their suppliers to have controlled, capable processes. If you are going to control a process, you need to be able to detect changes in the process (out-of-control conditions). Therefore, the recommended approach uses process variation based on the parts used to do the study. GAGEpack, gage management software, allows you to also estimate the process variation based on a control chart for the process measurement being studied.

The push to improve processes by improving the capability ratios is a complicating factor. This reduces the variability of the process. As a result, many gages do not pass the R&R % required. Often, the alternative comes down to purchasing a “better” measurement system (often a very expensive gage). In some cases, better systems do not currently exist. In any event, there is some question as to the value of improving the measurement system. In cases where Cpk > 2 (or whatever number you like), the customer is not likely to notice any improvement and the cost of producing (measuring in particular) increases. (Side Note: a frequently used major criteria for selecting improvement project is: Will the customer notice the improvement? Will it make a difference to the customer?) In this case, one might want to consider a policy of using tolerances for situations where Cpk is greater than some value, with the stated objective of applying their improvement efforts to situations where the process is not capable and the potential for improvement is greater.

What kind of set-up would you recommend for testing one instrument?

It measures percent acidity. There are six analysts who use the instrument to test acids whose strengths range from 50% to nearly 100%. I could have each analyst run the same of several samples in triplicate. I could fix the sample weights + or – 0.1 gram.

Answer:

It depends on what you are trying to accomplish. To some extent, R&R studies may not be appropriate. One objective would be to see how the gage accuracy varies over the relevant range (50% to 100%). You can do this with a linearity study. The major difference is that the parts used for the study are different products with values that range throughout the gage range, e.g., 55%, 65%, 75%, 85%, & 95%. You need reference values (true values) for each product. These can come from certified samples (like using gage blocks) or from using a “super” gage with better known accuracy. Since you are using different products, the traditional R&R percentages do not mean anything. However, if you wanted to test if the appraisers are measuring things differently, you could use more than one operator and check the operator bias and the operator uncertainty results.

If you want to run a traditional R&R, I would suggest picking a concentration where most of the tests are run. You can use all six operators in the same study. Given the previous results, I would suggest this as well, providings it does not overcomplicate the running of the tests. Here the samples (5-10) need to come from one product, but have values typical of the total range of the product variation. Two or three replications should work fine. This would allow you to check the gages’ ability to discriminate among the values for the product and to evaluate the performance of the operators. Linearity could not be checked for the gage, however.

What are the objectives of an uncertainty study?

The objective of an uncertainty study is to put bounds on a measurement (x plus/minus some interval). Generally a 95% confidence interval and the t-distribution is used since there are not a lot of observations taken. To do the study use one gage, one part, one part characteristic, and one operator. The characteristic is measured on the part a number of times-10, 15, 25, etc. A standard deviation is calculated (that should be all measurement error), and the appropriate t value obtained and multiplied times the standard deviation. This becomes the plus/minus interval estimate about the measured value (uncertainty).

If you would like a bias estimate using this same data and have a reference value for the part characteristic used, you may place it in the reference block and the program will take the mean of the measurements and subtract the reference value to give an average bias value.

If you would like the bias expressed as a percent of specification or percent of process variation, you enter the USL, LSL and/or six sigmas for the spread of the process (generally obtained from an X-Bar and Range chart on the process), and the respective percents will be calculated.

I am not aware of any guide lines that have been given for these values. When you do a calibration, there is a plus/minus interval that is acceptable. This might be one source for determining acceptable values for both uncertainty and bias values. When you do an R&R, there are guidelines for the percent R&R. This may provide input into development of acceptable percentages.

Start implementing MSA today. Download a free trial of GAGEpack.

Additional sections from legacy gentlemen-start-your-gages-rr-and-variability:

Gentlemen, start your gages: R&R and variability

A number of factors affect the ability of a measurement system to discriminate among the units it measures. These factors can be categorized generally into those that affect central location and those that affect the variability (spread) of the measurements. Variability factors measured by repeatability and reproducibility are the more familiar, while factors related to the central location of the measurements (stability, bias, and linearity) are relatively new approaches. Both approaches may need clarification. In addition, methods of measurement must be developed along with standards for indicating their acceptability. In a series of articles, these concepts will be addressed.

The first of these will deal with repeatability and reproducibility and combining them into the R&R component. The next article will take this R&R component and calculate R&R percentages based on study variation, process variation, and tolerance. The Measurement Study (classic) typically utilizes one to three appraisers for one measuring instrument that is measuring a single characteristic. Each appraiser measures five to ten units selected from a process two or three times (replications). Before proceeding with the analysis of the study, the ranges for the replications of the measurements made by each appraiser on each part are determined and used to calculate control limits for the range chart. Then each range is checked to determine if it falls inside the limits. Those measurements that result in a range outside the limits should be excluded from further analysis or should be redone. Operative assumptions include:

The measuring instrument stays in calibration (central location does not change);
Appraisers use the same method of measurement;
Parts are measured in the same place. (If the assumption that the parts are measured in the same place is incorrect, the possibility of within-part variation will need to be considered.)

Repeatability refers to the variation in measurements for one characteristic made with one measuring instrument by one appraiser on the same part. An estimate of repeatability is obtained by first determining the average range () of the repeated measurements of the same characteristic, using the same measuring instrument for several parts. Note: if more than one appraiser is used in the study, the average range is the combination for all appraisers, e.g., [If there are three appraisers, a, b, and c, you would determine the average range using ( = a + b + c )/3]. Next, the standard deviation for the repeatability (se) is estimated by dividing by d*2. A 99% (-2.575 < z < +2.575) interval for repeatability is determined by multiplying 5.15 by (se).Reproducibility refers to the difference in the average of the measurements on one characteristic made by different appraisers using the same measuring instrument on the same part(s). Note: if there is only one appraiser using the gage, there will be no reproducibility (appraiser variation). Again, the assumptions are that the instrument stays in calibration, the appraisers use the same method of measurement, and the part is measured in the same place. An estimate of reproducibility is obtained by determining the mean of all the measurements made by each appraiser e.g., [If there are three appraisers, a, b, and c, you would determine the average range using (= a + b + c )]. The range estimate for the operators (Ro) is obtained by subtracting the minimum i from the Maximum i.Next, the standard deviation for reproducibility (so) is estimated by dividing (Ro) by d*2. Again, a 99% (-2.575 < z < +2.575) interval for repeatability is determined by multiplying 5.15 by (so).Since the measuring instrument is used in making the measurements, it is a contributing factor to the calculation of reproducibility. Therefore, the calculation of reproducibility needs to be adjusted by subtracting a portion of repeatability. The adjusted appraiser variation is given by:

Where:
n = number of parts used in the study
r = number of times each part is used

R&R is the combination of repeatability and reproducibility variation and frequently is considered as the total measurement variation excluding within part variation and variation in central location. R&R studies can be done easily and accurately using software products like GAGEpack.

Additional sections from legacy why-use-msa-software:

Why use MSA software?

Measurement Systems Analysis software is designed to identify the components of your measurement system which are contributing to the variation in gage measurements. Variation can come from a number of different sources, including the person using the gage, the parts being measured, the environment where the measurement is taking place, the equipment being used, and so on. MSA studies exist to discover and quantify the amount of variation coming from these different sources, so that corrective action may be taken if necessary.

Routine and properly-executed MSA studies allow users to find and correct situations where an unacceptably high amount of variance is being introduced into a measurement system. MSA software reduces the time it takes to conduct these studies while increasing the accuracy of the results.

How can GAGEpack help?

GAGEpack performs both variable and attribute gage repeatability and reproducibility (R&R) studies, calculates the uncertainty of your calibrations, and produces accuracy and stability charts.

All the relevant MSA studies that are discussed in the AIAG MSA Manual 4th edition are included in GAGEpack. Users simply enter in the data from the studies and GAGEpack handles all the calculations and generates the charts using the formulas provided by the manual. The results of the studies are stored and available for future reference or easy sharing.

How can GAGEpack help?

GAGEpack performs both variable and attribute gage repeatability and reproducibility (R&R) studies, calculates the uncertainty of your calibrations, and produces accuracy and stability charts.

Additional sections from legacy improving-measurement-accuracy:

Improving measurement accuracy

What is it?

Performing gage R&R studies can be made easier by using software such as GAGEpack.

When is it used?

Gages need to be recalibrated only when repeated test measurements show a lack of statistical control. Calibrating gages that do not need it or failing to calibrate gages that do need it can impair your ability to make accurate judgments about a process. Setting up a regular gage repeatability and reproducibility testing schedule can prevent either problem.

How is it made?

Note: The following are steps for a very basic gage R&R study. For a more in-depth analysis, refer to AIAG’s Measurement Systems Analysis or Evaluating the Measurement Process, by Donald J. Wheeler, Ph.D. and Richard W. Lyday.

Determine the number of operators, the number of parts, and the number of repeat readings. Consider how critical the dimension is. For more critical dimensions, use more parts to increase your degree of confidence in the study results. Also consider the part itself; large parts may be harder to handle and call for fewer samples and more trials.
Select 2 or 3 operators from those who are normally involved with the measurement process you are evaluating.
Collect the parts for the test. Parts should represent the range of variation in the day-to-day operation of the process. Number the parts, but do this in such a way that the operators will not know which part they are measuring.
Let the first operator measure each part in a random order and have another observer record the results. Enter the value in a column that represents that specific part number. Let the second and third operators measure the same parts in the same order without seeing the others’ readings. Record the data in the same manner, keeping data from each operator separated (alternating rows or different pages).
Repeat Step 4 for each trial (repeat reading), with the parts in a different random order each time.
Calculate averages and ranges for each operator for each part.
To analyze the repeatability , create an X-bar and R chart with the data. The range chart will show the consistency of the measurement process. If the range chart is in control, the repeatability of the measurement system is adequate.
The X-bar chart will show the reproducibility (operator variation). Roughly 50% of the sample averages should fall outside the control limits. This indicates that the gage can distinguish among parts. To analyze the consistency among operators, use a Whiskers Plot.

When is it used?

How is it made?

Determine the number of operators, the number of parts, and the number of repeat readings. Consider how critical the dimension is. For more critical dimensions, use more parts to increase your degree of confidence in the study results. Also consider the part itself; large parts may be harder to handle and call for fewer samples and more trials.
Select 2 or 3 operators from those who are normally involved with the measurement process you are evaluating.
Collect the parts for the test. Parts should represent the range of variation in the day-to-day operation of the process. Number the parts, but do this in such a way that the operators will not know which part they are measuring.
Let the first operator measure each part in a random order and have another observer record the results. Enter the value in a column that represents that specific part number. Let the second and third operators measure the same parts in the same order without seeing the others’ readings. Record the data in the same manner, keeping data from each operator separated (alternating rows or different pages).
Repeat Step 4 for each trial (repeat reading), with the parts in a different random order each time.
Calculate averages and ranges for each operator for each part.
To analyze the repeatability , create an X-bar and R chart with the data. The range chart will show the consistency of the measurement process. If the range chart is in control, the repeatability of the measurement system is adequate.
The X-bar chart will show the reproducibility (operator variation). Roughly 50% of the sample averages should fall outside the control limits. This indicates that the gage can distinguish among parts. To analyze the consistency among operators, use a Whiskers Plot.

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