# A Study of Gauge Repeatability and Reproducibility For Automated Measuring Systems Using .Net

**Abstract**

Nowadays the automobile industries are interested in automated measuring machines to ensure quality and to compete in the global industry. The Gauge Repeatability and Reproducibility takes a major role to ensure quality by measuring the automobile components. The purpose is to make repeatability and reproducibility of the Measuring Systems like Camshaft, Crankshaft, and so on. A digital sensor is used for measuring the Camshaft and Crankshaft. Then the measured data has been analyzed using Gauge Repeatability and Reproducibility methodology. Gage R&R is a Statistical method for analyzing the measurement data. The result of this system can make the standard system competitive with the global industry.

**Introduction**

I have been worked on several Automation projects. In my project I get a chance to work on Gage R&R. Instead of using third-party tools, I planned to create a simple program using C# for Gage R&R. I finally completed the program and it is running in an automation company. The main purpose of this article is to share what I study for developing a Gage R&R to all other members. When I search in C# Corner for Gage R&R, am unable to find anything related to Gage R&R. So I am happy to write the first article about Gage R&R on this website.

In this article, I have attached a sample Gage R&R Study Excel worksheet for your reference.

It is a fact of nature that all data contains random variation. Part of this variation is due to individual differences, but another part of this variation is due to uncertainty in the measurements caused by variability in the measurement equipment and process. If the measurement uncertainty is too large then the measurement system may be unusable. A gage repeatability and reproducibility (R&R) study looks at this variability [1] .

Gage R&R helps determine the magnitude of the variation in a measurement system as well as the sources of this variation. While the sources of variation can be numerous, three of these sources are fundamental: part-to-part variation, repeatability and reproducibility [1].

Part-to-part variation is the normal range over which measurements are made; the part of your data you actually want to measure. Repeatability is the variation because of the gage itself, while reproducibility is the variation because of various operators using the gage. Repeatability and reproducibility together are called "measurement error," or simply "noise," and are measured as "gage R&R." This noise is a nuisance that adds uncertainty to your data. A good measurement system has very low noise, preferably less than 1% of the total variability in your data, indicated as a gage R&R of less than 10%. A questionable system will have noise between 1% and 9% of the total variability, or a gage R&R between 10% and 30%. A poor system will have noise greater than 9% of the total variation, or a gage R&R greater than 30% [1].

Gage R&R measures the size of the noise relative to the total data variation, that is called % of total variation or %TV, and relative to the specification range, called % of tolerance. It also separates the variability into its sources, namely part-to-part variation, repeatability and reproducibility. This information helps operators determine how to fix a poor measurement system. For instance, a high repeatability relative to reproducibility indicates the need for a better gage. A high reproducibility relative to repeatability indicates the need for better operator training in the use of the gage [1].

**Gage Repeatability**

The variation obtained from one gage and one operator when measuring the same part several times. Understanding measurement System [2].

**Gage Reproducibility**

The difference in the average of the measurements made by various operators using the same gage when measuring the same part. Understanding measurement System [2].

There are various ways by which the R&R of an instrument may be assessed, one of which is outlined below. This method, that is based on the method recommended by the Automotive Industry Action Group (AIAG), first computes for variations due to the measuring equipment and its operators. The over-all GR&R is then computed from these component variations.

There are various ways by which the R&R of an instrument may be assessed, one of which is outlined below. This method, that is based on the method recommended by the Automotive Industry Action Group (AIAG), first computes the variations due to the measuring equipment and its operators. The over-all GR&R is then computed from these component variations.

**Equipment Variation, or EV,**represents the repeatability of the measurement process. It is calculated from measurement data obtained by the same operator from several cycles of measurements, or trials, using the same equipment [4].

**Appraiser Variation or AV,**represents the reproducibility of the measurement process. It is calculated from measurement data obtained by various operators or appraisers using the same equipment under the same conditions. The R&R, is just the combined effect of EV and AV [4].

It must be noted that measurement variations are caused not just by EV and AV, but by Part Variation as well, or PV. PV represents the effect of the variation of parts being measured on the measurement process, and is calculated from measurement data obtained from several parts [4].

Thus, the Total Variation (TV), or the over-all variation exhibited by the measurement system, consists of the effects of both R&R and PV. TV is equal to the square root of the sum of (R&R)2 and (PV)2 squared, in other words:

In a GR&R report, the final results are often expressed as %EV, %AV, %R&R, and %PV,

**%EV = 100(EV/TV)**

**%AV = 100(AV/TV)**

**%R&R = 100(R&R/TV)**

**%PV = 100(PV/TV) [3]**

The gage is good if its %R&R is less than 10%. A %R&R between 10% to 30% may also be acceptable, depending on what it would take to improve the R&R. A %R&R of more than 30%, however, should prompt the process owner to investigate how the R&R of the gage can be further improved [4].

**Application**

An example will be helpful for a gage R&R Study. In our system a maximum of 3 operators, 3 trials and 10 parts can be used here. For example we are using:

2 Operator

2 Trials

4 Parts.

**Using the code**

**Steps need to follow to run the program.**

- Need SQL Server 2005 or 2008
- Create a new Database Name as MLA and restore the attached MLA.bak Db to your new DB.(You can find the "MLA.bak "DB Backup file from attached ZIP file)
- To run the program need DB Connection. From the program setting please provide your DB Server Name and Uid and PWD of your SQL.
- now your Gage R&R program is ready.

**The Gage R&R Result is:**

Where Rp=Max(Part/Avg
data)-Min(Part/Avg data)

In our ex, you can
see its 30.000 as max and min as 25.250

R-Bar=sum( Avg(data) / NoofOperators)

Xdiff=Max(Avg
data)-Min(Avg data)

ACCEPTABILITY CRITERIA Under 10% - Gage system O.K.10% to 30% - May be acceptable Over 30% - Gage needs improvement.

**References**

- Quality Introduction to Gage R&R http://www.qualitymag.com/CDA/Archives/53c9323027f28010VgnVCM100000f932a8c0____
- Understanding measurement System http://www.swtest.org/swtw_library/1998proc/PDF/T1_Hank.PDF
- R & R Repeatability and Reproducibilityhttp://www.sixsigmaspc.com/dictionary/RandR-repeatability-reproducibility.html
- Gage R&R http://www.siliconfareast.com/grr.htm
- http://elsmar.com/Forums/archive/index.php/t-16530.html

**Points of Interest**

The main aim of this article is to create a
simple and Standard Gage R&R Application for the automobile industry. Please
find the attached DB file "MLA.bak" and restore it to your local SQL DB to access
my program.