**The Gage R & R is used to measure the reliability of a measuring system.**

## Introduction

The Gage R & R, also known as MSA for *measurement Systems analysis* or MSE for *measurement System Evaluation*, is used to measure the repeatability and reproducibility of a system of measurement: ruler, sliding feet, stopwatch… we For validating the method by which data is collected.

## The reproducibility

The reproducibility, **AV** for *appraiser Variation*, is the capacity of a means to be measured under variable conditions: operators, switchgear, time… The greater the variabilité́ of the experimental conditions, the greater the number of causes of errors taken into account in the dispersion of the results.

At the most the reproducibility is great, the more our measuring system is subject to the variations of the operators.

## Repeatability

The repeatability, **EV** for *equipment Variation*, represents the quality of the agreement between measurements of the same sample carried out under very low variable experimental conditions. It is obtained by repeating a measurement protocol on the same sample, the apparatus and the operator being identical and the measurements being carried out in a small interval of time.

At the most the repeatability is large, the more our measuring system is subject to the variations of the measuring system.

## Measure the Gage R & R

The measurement principle of Gage R & R is based on the fact of several measurements on several parts with different operators. This measure follows the following protocol.

### 1. The parts to be measured

You select a number (n) of random pieces that you identify to measure them several times.

### 2. Staff

We identify a number (p) of people who will perform the measurements.

### 3. Construction of the Information collection table

Build the measurement chart:

Part n° | Operator 1 | Operator 2 |
||
---|---|---|---|---|

1 | Measure 1 | Measure 2 | Measure 1 | Measure 2 |

2 | Measure 1 | Measure 2 | Measure 1 | Measure 2 |

3 | Measure 1 | Measure 2 | Measure 1 | Measure 2 |

4 | Measure 1 | Measure 2 | Measure 1 | Measure 2 |

5 | Measure 1 | Measure 2 | Measure 1 | Measure 2 |

6 | Measure 1 | Measure 2 | Measure 1 | Measure 2 |

According to the AIAG and standard QS 9000, automotive Industry Action Group, 2 standards for Gage R & R studies are recognized:

**Short formula:**5 pieces measured 2 times by 2 different operators.**Long formula:**10 pieces measured 3 times each by 3 different operators.

### 4. Proceed with the measures

Make sure that the measurements are made under the same conditions for the 2 operators, same machine, same Part… and in a reduced time interval. Also make sure that the operators do not communicate or that the parts have not fallen in the meantime.

Attention, **it is necessary to make sure that our data follow a normal law**. Without this condition, we will not be able to reliably calculate our pledge.

### 5. Choose the method of calculation

Standard QS 9000 offers 3 calculation methods. The choice will be based on the level of precision we want. We find the following 3 methods:

**Source of calculated variability**

Range | Averages and ranges | Anova |
---|---|---|

Total variation | Equipment operators Equipment and operators Parts Total variation | Equipment operators Equipment and operators Interaction operators / parts Variation totale |

The extents method is the least precise since it distinguishes only the total variation in the measure. On the other hand, the method by analysis of Variance is the most precise since it allows to distinguish between the set of parameters that fit into account in the measure.

It is noted that by the level of accuracy of the ANOVA, the results are more “*Conservative*“: There will be more tendency to define as not capable a means via an anova than through the other methods. Therefore, use it when the measurement is particularly critical.

### 6. Perform the calculations

Depending on the method, the calculation of the different indicators will not be the same. The details in the dedicated articles:

### 7. Analysis of the level of accuracy of the equipment

The first analysis is whether the equipment is by itself accurate or not. The following indicators are calculated for this:

## Interpretation

**P/T < 10%:** the measurement system is good

**10% < w/T < 30%:** the measurement system is acceptable

**P/T >30%:** The measurement system is not acceptable

- If
**reproducibility is bad**: look for training, standards and definition. - If the
**repeatability is bad**: Look on the side of the measuring tool itself.

Generally, the variability due to parts (% PV) is the most important.

## 8. Analysis of the capability of the measuring system

This analysis answers the question: *does our means allow us to measure what our client asks us?*

This analysis will be done via 2 parameters:

**The tolerance interval:**This is the interval desired by the customer for the accuracy of his parts.- The range
**of K distribution:**the “*breadth*” that we want to take into account. This plays an important role, since at the most we will take an important value, at the most our means are accurate. More generally, you take a value of 6. Nevertheless, the AIAG indicates that 5.15 is sufficient.

Using these data, the following indicators are calculated and interpreted:

**Capability of the equipment of control (CMC)**

**IT/(K * Gage R & R)**

CMC >4: The method is quite capable with respect to the customer.

2 < CMC < 4: Put under control the equipment and implement improvements.

CMC < 2: Change the equipment or method.

**Capability index of the control equipment (CI)**

**(K * Gage R & R)/IT **

+ 30%: unacceptable,

10 to 30%: Acceptable but recommended improvements

-10%: quite capable.

### Your measurement system is not capable, but you can not do better!

It may happen that we are faced with the inability to reduce the vagueness of our system of measurement, for reasons of cost, feasibility…

The only possibility is to “control” this vagueness by carrying out an analysis by **confidence interval** on average.

By comparing your target and your tolerance to the average and theConfidence interval obtained, you will be able to demonstrate that your measurement system meets the demand.

## Source

A. J. Duncan (1986)-Quality Control and industrial statistics

D. Durat, M. Pillai (2005) – Quality in production: from ISO 9000 to Six Sigma

K. Horell (1991)-Introduction to Measurement Capability analysis

Boeing (1998) – Advanced Quality System Tools

D. S. Ermer (2006) – Improved Gage R & R Measurement studies

A. de Frenne (2008) – Analysis of the measurement system