Q 529. There are two types of GRR designs - Crossed and Nested. What is the difference between the two? Provide at least 3 examples from different industries for each type of design.

 

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

• All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/
• Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening 5 PM as per Indian Standard Time. Questions launched on Tuesdays are open till Friday and questions launched on Friday are open till Tuesday. 
• When you respond to this question, your answer will not be visible till it is reviewed. Only non-plagiarised (plagiarism below 5-10%) responses will be approved. If you have doubts about plagiarism, please check your answer with a plagiarism checker tool like https://smallseotools.com/plagiarism-checker/ before submitting. 
• The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term

Crossed GR&R Designs

This design is used when the same parts can be measured multiple times by each operator (Figure 1). This is generally to check how much process variation is due to measurement system variation.

Crossed GR&R design is used for non-destructive scenarios—where parts are not destroyed during measurement and can be used to measure twice.

Examples: -

1.       A company assembles wire connectors. The final wire length is measured in mm manually by operators. Measurement by the same gage is carried out for three parts by three different operators.

2.       An engineer selects 10 parts that represent the expected range of the process variation. All three operators can measure all the 10 parts 3 times per part in random order

3.       The manager of a fitness centre wants to offer body fat percentage measurement to clients. Because skinfold thickness is easily measured and correlates highly with total body fat, the manager decides to purchase a skinfold caliper and teach his fitness trainers to perform these measurements. 10 Clients with varying amounts of body fat participate in the MSA performed by 2 trainers measuring the triceps skinfold thickness 2 times each in random order

In all the above examples, each part is subject to repeated measurements.

 

 

Nested GR&R Designs

This design is used where the same part cannot be used for repeated measurements as the parts get destroyed on testing when only one operator measures each part (Figure 2). This design is called nested because one or more factors are nested under another factor and not crossed with the other factors.

Nested GR&R design is used for destructive testing scenarios.

Examples: -,

1)    Measuring the effect of a drug by dissolving it in a chemical.

2)    Assessing the device used to measure the blood clotting time in a hospital laboratory where a manager selects blood samples the represent the expected range of variation. He assigns 3 technicians to perform the assessment and each sample is unique i.e. no two technicians measure the same sample. They measure 5 samples each for total of 30 m3easurements.

3)    An engineer assigns 3 randomly selected operators to monitor the impact strength of ceramic components. The engineer selects 30 samples randomly and gives 10 random samples to each of the operators.

In all the above examples, the sample is destroyed during testing, making it impossible to test the sample again.

 

Using the Gage R&R technique factors that affect measurement system variation can be studied. In the GR&R system, measurement system variation is characterized by location (stability, bias, linearity) and width or spread (repeatability and reproducibility).

The GR&R technique finds application in most manufacturing-related measurement systems. It may be used for:

Ø  judging new measuring equipment

Ø  comparison among measuring devices

Ø  improving performance of measuring instruments

Ø  comparison of measuring equipment before and after repair

Ø  Calculating the process variations caused due to production factors and the acceptability levels for the production process.

Ø  measuring the need for training in how to use measuring instruments

 

Repeatability

Variability in any measurement system is caused by prime factor -the measurement device. It is the variation that is observed when the same operator measures the same part many times, using the same gage, under similar conditions.

Gage A has less variation, so it is more repeatable than Gage Bin the below figure:

 

Reproducibility

Variability in the measurement system is caused due to differences between the operators. It is the variation that is observed when different operators measure the same part many times, using the same gage, under similar conditions.

Operators 1, 2, and 3 measure the same part 20 times with the same gage.

The three lines are the measurements from Operators. Operator1-blue, Operator 2- red, and Operator 3-green. Therefore, it can be visually seen from the picture that the gage's reproducibility is too low.

 

CROSSED GAGE R&r :

Two factors are crossed when each level of one factor occurs in combination with each level another factor.

 

In a crossed study, each operator measures each part for negating error due to measurement device and ascertaining repeatability. It is called crossed gage r&r because the same parts are measured by each operator multiple times without destroying the batch under observation. Eg:weight of drugs in pharmaceutical industry, mileage testing in automobile industry, software testing.

Often, a crossed gage R&R study is used to determine how much of process variation is due to measurement system variation. R&R value will be higher in case of crossed study method, because in nested method Reproducibility component of R&R is Nil.

CROSSED GAGE R&R DESIGN FOR NON-DESTRUCTIVE MEASUREMENT SYSTEMS

 

Nested Gage R&R:

Two factors are nested when the levels of one factor are similar but not identical, and each occurs in combination with different levels of another factor, with no two combinations being the exact same.

 

In a Nested Gage R&R, each part is unique to the operator since no two operators measure the same part but similar parts are used. This study is called nested because one or more factor is nested under the other factor and, therefore not crossed with the other factors.

Nested R&R is used in case of destructive testing (component cannot be measured many times and gets destroyed / changed during the measurement process).Eg: composition of drugs in pharmaceutical industries, crash test of vehicles in automobile industry, composition of individual elements in chemical industry.

NESTED GAGE R&R DESIGN FOR DESTRUCTIVE MEASUREMENT SYSTEMS

 

Expanded gage r&r :

An Expanded Gage R&R study is used when below mentioned conditions exist:

Ø  more than two factors -operator, gage & part.

Ø  declare some factors as fixed factors.

Ø  both crossed and nested factors.

Ø  unbalanced design.

This study is called expanded because it can be used in several types of situations.

 

Differences between a standard and expanded Gage R&R

Ø  The expanded GR&R study allows multiple factors to be evaluated simultaneously.

Ø  Interactions between the additional factors and the operator and part also can be measured.

Ø  The expanded GR&R study allows analysis of the data even in case of missing data points.

Ø  The data collection is adjusted for the expanded GR&R. Since repetition for each additional factor is costly, so the number of parts is often reduced. In a standard GR&R study, more parts can be selected, but this is an unacceptably large sample size for expanded GR&R and may cost much.

Ø  When enough data for a standard GR&R study does not exist, an expanded GR&R is an ideal tool to characterize the measurement system.

For non-destructive measurement systems, the crossed Gage R&R design is used because each operator can test each part multiple times.  With the destructive measurement systems, the batches must be similar with similar conditions. Crossed Gage R&R analysis is used only if each operator can test multiple parts from each batch without destroying it.  However, if there are not enough parts in each batch to accomplish this, the nested Gage R&R design is brought into use. Examples of when to use nested design and crossed design have been explained with relevant examples in this article.

 

GRR i.e., Gage repeatability & reproducibility is a Measurement System Analysis (MSA) method to evaluate a gauging instrument’s accuracy (and consistency) by validating its measurements repeatability & reproducibility.

Repeatability is the measure of variation obtained when same measuring instrument is used several times by same operator to measure identical characteristics of same part.

Reproducibility is the measure of variation obtained when different operators use the same measuring instrument several times to measure identical characteristics of same part.

A series of measurements are taken using same instrument by same as well different operators (also called appraisers). However, parts which are subject to measurements can be same or different based on the design depending upon the nature of testing, non-destructive or destructive.

There are primarily two types of designs in GRR –

Crossed designs: In this design each part can be measured repeatedly i.e., each operator inspects the same part.

Nested designs: This design is used when same part cannot be tested for repeated measurements as the part gets destroyed in testing. Thus, the operators are given different parts from the same batch.

 

Here are some examples:

Crossed designs (parts are not destroyed in testing, hence same part can be tested by different operators) –

·        Measuring weight of drug in Pharma industry

·        Measuring the dimensions of parts of a vehicle or fuel efficiency of the vehicle in Automobile industry

·        Measuring dimensions, shape, and/or size etc. of parts like sheet metals in Engineering industry

Nested designs (parts are destroyed in testing, hence same part cannot be tested by different operators) –

·        Measuring the effect/ chemical properties of a drug by dissolving it in a chemical in Pharma industry

·        Crash test for vehicles in Automobile industry

·        Measuring the ductility, malleability and/or chemical properties of parts like sheet metals in Engineering industry

 

 

Congratulations to Anuj Bhatnagar for the best answer.

 

Suresh's answer is also correct but lost out due to mention of some Figures (Figure 1 and Figure 2) which are not available in the response. Gulshan Kumar has provided a detailed answer but one of the examples on Crossed Gage R&R (usage in software testing) is unclear.