## Introduction

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

I have been working on several automation projects. In one of my projects I got 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 studied for developing a Gage R&R with other members. When I searched on CodeProject for Gage R&R , I was unable to find anything related to Gage R&R. So I am happy to write the first article about Gage R&R in 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 variations. 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].

Simply said, Gage Repeatability is checking the final result of parts with one operator multiple times.

#### Gage Reproducibility

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

Simply said, Gage Reproducibility is checking the final result of parts with multiple operators multiple times. 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 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. For example, we are using:

- 2 Operators
- 2 Trials
- 4 Parts

## Using the code

Steps needed to run the program.

- Need SQL Server 2005 or 2008
- Create new database named MLA and restore the attached
*MLA.bak* DB to your new DB. (You can find the "*MLA.bak*" DB backup file in the attached ZIP file.)
- To run the program you need a DB connection. From program settings, please provide your DB server name and the UID and PWD of your SQL Server.
- Now your Gage R&R program is ready.

The Gage R&R Result is: In my sample program the maximum number of parts that can be used is 10, number of operators is 3 and number of trials is 3.

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)

## 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 Reproducibility http://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 Server DB to access my program.

## History

- Initial release on 2013/07/16.