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Gage R&R is the type of Measurement System Analysis (MSA) that is used to quantify how well a variable (continuous) measurement system is working


Resolution (or Discrimination) is the smallest division on the scale of the gauge or the smallest difference in reading that can be shown on the display of a measuring instrument. The higher the resolution, the smaller the measurement it can record


Bias (or Accuracy) is the difference between the average of observed values and the standard (actual value)


Linearity is the consistency of the gauge across its entire range


Stability is consistency in the gauge over a period of time. Stability is observed if observed values are same when the same operator measures the same unit with the same measuring equipment over an extended period of time


Precision is the variation observed between repeated observations of the same unit – either due to operator (Reproducibility) or due to equipment (Repeatability)


An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Nilesh Gham on 3rd January 2020.


Applause for all the respondents - Nilesh Gham, Sudheer Chauhan, Mohamed Asif, Shashikant Adlakha, Shashank Parihar, Saravanan S, Ajay Sharma


Q 223. Resolution, Bias, Stability, Linearity and Precision are the five things that are checked while performing Gage R&R. What is the order in which these 5 things are to be checked?



Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.

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I would prefer in the below order


1.       Resolution

Resolution represents the measurement system’s capability to detect and indicate small changes in the characteristic measured. Resolution is also known as discrimination. E.g. a tape measure with gradations in cm cannot be distinguish between measurements lesser than 1 cm, like 2mm say.

If an instrument is not able to measure the required attribute in the first place, there is no point in proceeding


2.       Bias

Bias can be defined as the difference between the mean or the expected results (say of a standard) and the true/accepted reference value, and can be designated as a systematic error. Bias is checked using calibration.

Once an instrument is able to have the necessary resolution, as above, bias would be the second thing to check.


3.       Linearity

The next question to answer would be if the procedure is able to delivery accurate and precise results (established above), over a range of values (higher or lower)?

Linearity answers this question and performs calibration over a range of the measurement.


4.  Precision

Precision is also an important parameter necessary to demonstrate that a procedure will provide valid result, and helps in quantifying the random error. There may be a myriad of sources of variability in each measurement and many of them can be transient and cannot be easily identified or controlled. Therefore, a variety of approaches are used: Repeatability, Intermediate Precision and Reproducibility.

Once all systematics errors are noted (and removed), through Bias estimation, Precision would be the next thing to check


5.       Stability

Stability, may be interpreted as the change in bias of a measurement over time and usage when such a system is used to measure a master part or standard. One can interpret a stable measurement as one which is in (the variation) is in statistical control.

Once all of the above are established, Stability can be used as an on-going check

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Gage R&R (Gage Repeatability and Reproducibility):-

Measurement System Analysis (MSA) is an important part of Measure Phase in DMAIC.

We must confirm Resolution, Accuracy, Precision and stability of measuring devises before use them in measurement for generating data.


Basically, we can classify the error of measurement system in three main categories

1. Accuracy, 2. Precision and 3. Stability

Resolution - help use in selection the gage as per our process requirements (Part size , specification, standard deviation) 

1. Accuracy: - Accuracy is difference between measured value and actual value of Part that measured. Main component of accuracy measurement is

 a. Bias: It is difference between true value and measured value of part. some time we do not have actual true value of part then we can take the average of several measurements with the most accurate measuring equipment.

b. Linearity: - It is about how part size affects in the bias of measurement system. We should calculate the bias value of all expected range of part size according over process. some time it is proportional or inverse proportional to part size.

2. Precision: - It is about the variation in the measurement. When we measure the same part many times with same devices then the below listed variation occur.

c. Repeatability:  When same operator measures the same part many times with same measuring device then it is called the repeatability. It is a variation due to measuring device.

d. Reproducibility: - It is about the variation between the operators. If same part measures by more then one operator with same measuring device called reproducibility.

3.Stability: - Stability is about how accuracy and precision of the system perform over a time.


Right order of 5 things during performing Gage R&R as below

1. Resolution

2. Bias

3. Linearity

4. Precision

5. Stability  

We can calculate them with the help of minitab

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Value of any measurement is the sum of actual measurement and measurement error.

Measurement system variation/error can occur because of Precision or Accuracy.


Gage R&R tool measures the amount of variation in measurement system. Variation could be from the device or from the people.



"If you cannot measure it, you cannot improve it" - Kelvin


In the below diagram,

Ref 1.1 is a classical example for High Precision and Low Accuracy. Even though Precision is high, values/points are highly biased and inaccurate.

In Ref 1.3, values/points are both Accurate and Precise.


Resolution is pivotal in measurement systems as it discriminates between measurement value. Post looking at resolution, it would make sense to look after the accuracy part, that is to measure the distance between the average value and true value.

Moving from constant bias to Zero bias is the next objective. Linearity is the consistency of the bias existing in the system over the measurement range. Then looking at stability of the system, that is whether the measurement system has the ability to produce the same value over time when same sample is considered and to proceed with Precision - Repeatability and Reproducibility.  


Primary objective is to find out if there is any variation (either process or appraiser) and then look at total measurement system variation.

So best order of checking the variation would start from
1. Resolution / Discrimination against tolerance (smallest unit of measure of the gage)
2. Accuracy / Bias (closeness of the data to target value)
3. Linearity (change in bias value within range)
4. Stability (change in bias over a period)
5. Precision (Repeatability and Reproducibility) (closeness of value with each other)


Other views on the order could be

1. Resolution

2. Accuracy

3. Linearity

4. Precision &

5. Stability


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Gage R&R study is basically used for measuring accuracy in measurement and precision(repeatibilty and reproducibility).

Resolution is predefined, preset at manufacturing level. It is the ability of instrument to detect any deviation in measurement from the reference value. Instrument/process with high resolution is desired.


Accuracy is determined by bias and linearity.

Bias is the difference in measurement from the true value.

Linearity is the difference between extreme values of bias, that affect the measurement system.


Precision is measured in terms of repeatability and reproducibility. Repeatibility is the variation in measurement under same condition by same operator in the same instrument. Reproducibility is the variation in measurement, due to analysis of same parameter  performed by different operator in same instrument.


Long term variation in measurement is due to repeatability, reproducibility and part to part/product variation.


Stability is the indicator of long term performance of the system in terms of accuracy and precision.


Thus the order of measurement in sequential order will be resolution-bias-linearity-repeatibilty-reproducibilty-Stability.


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Measurement System Analysis (MSA) is done to understand the contribution of the variation due to measurement system to the Process variation i.e. variation due to instrument and due to operator.


Our aim is to either minimise the variation due to measurement system or totally eliminate it, so that the Process variation should be only be due to variation in parts only.


M.S.A is mentioned in “ISO/TS 16949:2009 (E) 7.6.1 MSA”


Broadly two types of MSA studies are conducted---

1.    For continuous data- Gage R & R

2.    For attribute data- Attribute Agreement analysis


Measurement system analysis is the study of---

  1. How much error is created by the gage (instrument or measuring device) itself either due to not proper calibration or worn type or both.
  2. How much error is created by the person {operator(s) or appraiser} measuring the part(s) or sample(s) by that gage.


Measurement error- is the difference between true value or reference value of the part(s) and the mean of the observed values or measured values of the part(s) measured by the operator(s) with an instrument i.e.—

Measurement error = gage variation due to repeatability + operators’ variation due to reproducibility

True value or Reference value is provided by an expert.


Variation in data or observed results is due to ----

  1. Variation between parts manufactured due to process variation.
  2. Variation due to measurement.


Process variation = Actual process variation + measurement system variation (we are interested in variation due to MSA)


MSA should be performed as mentioned below---

1.    Determine the gage- if there are more than one gauge used for 

       measurement,  choose the most appropriate one.

2.    Define the procedure of measurement.

3.    Are there any standards available? If yes then use them thoroughly.

4.    Define the design Intent of the gage or demand from the supplier (calibration report of the gage).

5.    Discrimination- (granularity/resolution)- minimum value on the scale that you  can measure.

6.    Accuracy- it is the closeness of the agreement between a measurement         

        result and the true or accepted reference value.it includes---

                i.        Bias- this is the systematic difference between the mean of the     

                          observed result or measurement result and a true value.

                ii.        Linearity-This is the difference in bias value over the expected

                            operating range of the measurement  Gage.

                iii.        Stability-variation in the average of measurements, if the same

                            operator measures the same unit with the same measuring   

                             equipment over a extended period i.e. hours/days/weeks/month.


7.    Precision-Precision- when an identical item is measured several times,

       Variation observed between repeated observations of the same unit using the

       same method either due to operator or due to equipment (how close to each

       other). The components of precision includes----

           i.        Repeatability-When variation in the successive measurements of the

                    same part is observed when the same Appraiser is asked to

                    repeatedly measure the same unit using the same measuring


           ii.        Reproducibility- variation in average of measurements is observed

                     when two or more operators measure the same unit repeatedly with

                     the same method with using same equipment. It is often referred as

                     Appraiser variation. A measurement system is reproducible when

                     different operators produce consistent results.





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Gage R&R


Gage R&R which stands for Gage Repeatability & Reproducibility is a Measurement System Analysis (MSA) process to measure the amount of variation in the measurement system due to the measuring device and the people involved in taking the measurement.


The most important objective of the MSA is to assess the validity of the measurement system and reduce the factors which are causing the process variation that are actually stemming from the measurement system itself.


The following steps are generally followed in the given order to study the errors within a measurement system.

1.  Resolution;

2.  Bias;

3.  Linearity;

4.  Stability;

5.  Precision;


As part of the Resolution step of Gage R&R, the goal is to have a minimum of five distinct readings with respect to the MSA study.  The lack of resolution will not allow the measurement system to detect any defect more accurately or at least close to the accuracy.  This part of the MSA study is usually the easiest to fix such as finding the correct testing device that can capably read the defect to the immediately nearest decimal.  To achieve this, we need to have a large sample size so ensure more resolution in the measuring system.


Technically, Bias and Linearity are part of calibration or accuracy. Bias will tell us the defects in the device as against the industry standards and Linearity will tell us if the bias is consistent across the response of the things to be measured.  Ideally, these two are assessed together as part of the calibration study.

Stability tells us how the accuracy and precision of the system changes over time.


Precision:  Precision is the variation that we see when we measure the same part repeatedly with the same device.  It is common to see that P/T ratio which is the ratio of the precision of a measurement system to the total tolerance of the manufacturing process.  Apparently, if the P/T ratio is low, the impact on product quality of variation due to the measurement system is small and if the P/T ratio is larger, it means the measurement system is huge, and hence intervention is needed.


Precision has two components in it, i.e., Repeatability and Reproducibility, as follows -


Repeatability --> this variation comes as a result of variation in the measuring device.  This comes when the same operator measures the same part with the same device multiple times.


Reproducibility --> this variation comes as a result of different operators measuring the same part with the same device multiple times.


Alternatively, a single large study can be conducted for both repeatability and reproducibility at the same time.


From the above definitions, as we can see, Stability is relatively a larger and a longer study.  Also, since stability step is about the accuracy and precision of the entire system changes over the time, it can be done as a last step in a very big measurement system.  If so, then the order of Gage R&R, changes as follows –

1.  Resolution;

2.  Bias;

3.  Linearity;

4.  Precision (both Precision and Stability can be interchangeable, depending on the size of the system);

5.  Stability; (both Stability and Precision can be interchangeable, depending on the size of the system).


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Gauge R&R-Gauge Repeatability and Reproducibility is done to find out or understand error in Measurement system.

Gauge:-Any device used to do measurement included go/no-go gauges

Measurement system analysis done in following condition:-

  • To accept new measuring equipment

  • Comparing one measuring device with another

  • Before and after repair

  • To know error in measurement system

Type of Measurement system variation

Location variation

  1. Bias

  2. Linearity

  3. Stability

Width Variation

  1. Repeatability (Precision)

  2. Reproducibility

1. Resolution is related with least count or sensitiveness or discrimination of instrument for a small change instrument can detect.

Example:-If we want to check a dimension 20±0.5 mm so as a base rule we have to take instrument with least count of 1/10th of tolerance of measured dimension

2. Bias is the difference of reference or true value with average of observed value

Example:-If reference value=10 mm and average of observed value is 10.01 so Bias=10.01-10=0.01

If Bias is more than permissible limits of instrument it should be reject or repair


3. Stability is the change in the bias with respect to time


Reason of stability error:-

Instrument needs calibration

•Worn Instrument, Lack of air pressure regulator, filter, Poor quality instrument

Environmental drift- temperature, Humidity, vibration, cleanliness


4. Linearity:-Change in the bias throughout the operating range of instruments


Example:-Vernier caliper Bias to be check at 10mm, 25mm, 50mm, 75mm, 100mm, 150mm and graph should be plot and graph should be linear at all

We can detect instrument wear out in any range because wear out of instrument depend of the usage and range of dimension mostly used.


5. Precision variation observed in measurement by same person, same instrument, same dimension on same location in same part .


During R&R we follow below order

1.      Resolution

2.      Bias

3.      Linearity

4.      Precision

5.      Stability


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Excellent Answers. 


Ajay Sharma, Saravanan, Shashank Parihar, Sudheer Sharma, Shashikant Adlakha, and Mohd Asif have explained each term clearly. I liked the response by Nilesh Gham themost as he has explained the reason for the sequence simply and clearly. Today's winner is Nilesh Gham. 

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