Repeatability & Reproducibility - R&R Study

The problem

In the world of industry, there are often situations where there is a dispute between the customer and the supplier whether a particular product or batch of product is or is not within the specified tolerances.

Also sometimes there are different evaluations, made by the same operator to the same product, or by different operators to the same product.

These situations happen when the control process is not robust, that is, we cannot have the same result, regardless of the operator, or the way the operator controlled it.

Solution

In order to solve this problem, the R&R study was created.

The R&R study, and a statistical approach to determine whether a gauge or control system is suitable for the process under measurement.

R&R study helps to investigate:

• If the variability of your measurement system is small compared to the variability of the process.
• How much of the variability in the measurement system is caused by differences between operators.
• The extent to which your measurement system is able to discriminate between different parts.

The R & R study identifies whether inspectors are consistent in their measurements of the same part (repeatability) as well as whether the variation between inspectors is consistent (reproducibility).

This study, in addition to evaluating a control process, also aims to quantify the factors that may contribute most to a negative result in that same evaluation.

A practical case

For example, if several operators measure an egg with a caliper to ensure it meets specifications.

For the same egg, we can obtain numerous different values, in addition to measurements A, B and C, represented in the figure.

If we also add the dimensional variations that exist in a batch of eggs, as well as the different ways of measuring each of the inspectors, we will have an infinity of possible values.

Let's think about the Ishikawa diagram (see Ishikawa - Cause-and-effect diagrams )

to identify potential causes of error, let's focus on 6M:

• Manpower / mind power (personnel)
• Machine (equipment, technology)
• Material (includes raw material, consumables, and information)
• Method (process)
• Measurements / medium (inspection)
• Mother nature (environment)

A measurement system is not just about measuring equipment, but also:

• Labor – training given to inspectors (training), both in the use of the measuring instrument and in the method of measuring the piece;
• Method – operative measurement instructions;
• Machine – adequacy of measurement equipment (precision, error, scale);
• Measurements – values of the tolerance interval required by the customer;

Types of Measurement System Variation

Trend

Trend is the difference between the average observed in the measurement and the reference value.

It is the systematic error of a measuring instrument.

The reference value is determined by averaging several measurements using standard measuring equipment.

Repeatability

Repeatability is the variation in measurements obtained with a measuring instrument when used multiple times by an appraiser when used in measuring identical features on the same part.

It is commonly known as equipment variation.

Reproducibility

Reproducibility is the variation in the average of measurements made by different appraisers using the same instrument when measuring identical features on the same part.

It is commonly known as appraiser's variance.

Stability

Stability is the total variation in measurements obtained with a measurement system on the same standard or parts when measuring a single characteristic over an extended period of time.

Stability is sometimes referred to as drift.

Linearity

Linearity is the difference between trend values over the range of system utilization.

Parts variation

Part Variation is essentially a measure of process variation.

If a large number of parts manufactured by a process are measured, 99% (5.15σ) of the parts would be within the variation limits.

The parts variance is always less than or equal to the total variance. In most industrial processes the variation of the parts is large compared to the variation of the measurement system and so the hypothesis that the observed standard deviation is approximately equal to the standard deviation of the total population, therefore the measurement system is valid.

Example of an R&R study

• 10 pieces are measured
• 3 inspectors are used, duly trained, as we want to assess whether the defined measurement method is capable of increasing reproducibility.
• Each inspector measures the 10 pieces, 3 times (3 tests).

Final evaluation of the measurement system

The outcome to monitor is the Total Gage R&R (GRR).

If the GRR is less than 10%, the measurement system is acceptable.

If it is between 10% and 30%, the measurement system is acceptable, depending on:

• the application;
• the cost of the measurement device;
• the cost of repair;
• or other factors.

If it is greater than 30%, the measurement system is not acceptable and must be improved.

In this example, the GRR value is between 10% and 30% for which the measurement system is acceptable, depending on the application, the cost of the measurement device, the cost of repair, or other factors.

We can also see that the %PV is very large, so the dimensional variation of the measured parts is quite significant.

The %EV value is greater than the %AV value, this means that the variation in measurements, in measurements made by the same inspector, has a greater impact on the final result than the variation in measurements between inspectors.

Translated and re-edited article from the article I published on my blog in April 2015.

#quality ; #qualitymanagement ; #qualitymanagementsystems ?