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|Part I: | | |6 |

|Introduction & | | | |

|Overview | | | |

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|Part II: | | |9 |

|Theory of Gage | | | |

|Repeatability & | | | |

|Reproducibility | | | |

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|Part III: | | |12 |

|How to Do a | | | |

|Gage R & R Study | | | |

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|Part IV: | | |21 |

|How to Improve | | | |

|the Gage R & R | | | |

|Result | | | |

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|Part V: | | | |

|Conclusion & | | |24 |

|Wrap-Up | | | |

Preface

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|Description | |

The gage repeatability and reproducibility (gage R & R) study is a cornerstone to the Six Sigma Quality Initiative. Six Sigma promotes the use of data-based decision making. In this type of system the decision is, therefore, only as good as the data on which it is based. Gage R&R studies provide a statistical method to determine the validity of a measurement system.

Using a combination of lecture, group discussion and hands-on exercises, this course will guide the participants through a robust learning experience of continuous data gage repeatability and reproducibility studies. The course will address the foundation of gage R&R studies: why they are performed and what they mean. Once a theoretical understand has been achieved, the course progresses through the mechanics of how to plan, execute, calculate and ultimately improve the total gage R&R result.

This guide is provided as a reference to the instructor to provide a general road map through the course objectives. The instructor should feel free to modify the presentation of the course for the best fit to instructor, participant and available resources/facilities.

|Course | |

|Objectives | |

The objective of this course is to train technical personnel on how to select the right measurement tool and to support that selection with statistical data.

After the successful completion of this training program, participants will understand the need for gage repeatability and reproducibility studies. They will be able to perform the studies and interpret the resulting data to establish a measurement system appropriate to both the measured value and the measurement tool.

Preface (continued)

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This training is ideal for those engineers who will be charged with the implementation and maintenance of Six Sigma Quality Methodologies.

In order to maximize the hands-on experience and instructor-participant interaction, it is recommended that the total group size be 9 to 15 students. The small group activities are designed for triads, although a fourth participant can be added to the groups if required.

|Pre-Course | |

|Communication | |

|to Participants | |

In the letter confirming their attendance, participants should be asked to bring a calculator on the day of the course. If this confirmation occurs well in advance of the scheduled date for the course, the instructor may consider a second reminder a few days prior to the course.

Preface (continued)

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|Supply List | |

The training facility should seat at least 15 participants comfortably for large group discussion with at least five tables for breaking out into small groups. A suggestion for room layout is provided below, but the instructor should feel free to modify this layout as required for the available facilities and for their instructional style.

A check list of suggested supplies is provided for your convenience. These supplies will be necessary for the successful administration and delivery of this training.

Trainer’s Guide (1)

Set of overhead transparencies (1)

Participant’s Guide (20)

Participant Kits (7), each containing the following:

Dowel sticks (10): The samples should be cut so that their lengths cover the full range of the specification with some parts falling outside of the specification.

Specification (1): The drawing should be dimensioned for diameter and length appropriate to the dowel sticks.

Measurement tool (1): Calipers are preferred, but if there are unavailable, a metric ruler can be used. The specification tolerances should be adjusted as appropriate to the measurement tool. If calipers are used, they should be properly calibrated.

Gage R & R Worksheets (2)

Preface (continued)

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|Icebreaker | |

Welcome participants and briefly introduce yourself.

Have each participant introduce themselves: name, position and what type of measurements they take in a given day.

“Tear a Sheet of Paper” exercise (adapted from The Complete Games Trainers Play (Volume 1), page 2.429)

Ask for 3 or 4 volunteers (depending on class size). Do not select participants at random, since each volunteer will ultimately get a prize for participating.

Ask the volunteers to come to the front of the room while you explain the rules of the exercise:

The volunteers must keep their eyes closed, and

The volunteers are not allowed to ask questions.

Give each volunteer a sheet of paper that is about 8” square, and ask them to perform the following tasks:

Fold your piece of paper in half; then tear off the bottom right corner of the paper.

Fold your paper in half again; then tear off the upper right corner.

Fold your paper in half again; then tear off the lower left corner.

Ask the volunteers to open their eyes, unfold their papers and show them to each other and the group. (It is highly unlikely that each paper will look the same.) Award each volunteer with a small prize and thank them for participating in the exercise.

Ask the following questions of the entire group:

What do you think would have happened differently if the volunteers could open their eyes, or ask questions?

What other things could I (the instructor) have done to reduce the variation in the outcome?

Introduction & Overview (continued)

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|Why are we here? | |

Ask participants to think of some reasons for why they or their management (depending on who signed them up for training!) think training in gage repeatability and reproducibility is important. Guide discussion toward the reasons listed below. Record student responses on flip chart for future reference.

To make sure measurement data are consistent (over time, operator to operator).

To make sure parts are really in specification when the data says they are in specification.

To make sure that we are using the right type of measurement tool.

To fulfill a customer requirement.

Tell participants that you will revisit this list at the end of the course to verify if gage repeatability & reproducibility will, in fact, address all of their points.

Introduction & Overview (continued)

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|and Timing | |

Review the agenda for the course

Introduction 30 minutes

Theory of gage R & R 50 minutes

How to plan and execute a gage R & R 20 minutes

BREAK

How to calculate the total gage R & R for

a measurement system (includes hands-

on exercise) 75 minutes

BREAK

How to improve a gage R & R

(includes hands-on exercise) 60 minutes

BREAK

Conclusions & Wrap-Up 20 minutes

Breaks should be approximately 15 minutes. The time of each can be altered as required to keep the entire course length to 5 hours.

By the end of the course, participants will understand why gage R & R studies are necessary and the will be able to plan, execute, calculate and improve a gage R & R.

Part II: Theory of Gage Repeatability & Reproducibility

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The emphasis in today’s business environment is on data-based decision making. We often take for granted that data we have collected is correct. How good will our decisions be if the data we have based them on is incorrect?

We expect our data to be both accurate and precise:

Accuracy, also referred to as bias, is how close the data is to the “real” value. Usually accuracy is assured by calibration of the measurement tool.

Precision is how Repeatable and Reproducible is the measurement. This is what is calculated during a gage R & R study.

Adequate results from a gage repeatability and reproducibility study will ensure that a measurement system is capable of producing data that is both accurate and precise.

Repeatability deals with one operator measuring a given part several times. We expect the operator to get the same result each time.

Reproducibility deals with multiple operators measuring a given part. We expect each operator to get the same result.

|Measurement vs. | |

|Measurement | |

|System | |

A measurement is the value or data obtained while measuring.

A measurement system is everything involved in performing the measurement: measurement tool, part, operator, procedure, the environment.

Gage R & R looks at the entire measurement system, not just the measurement.

Theory of Gage Repeatability & Reproducibility (cont.)

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|Resolution | |

The resolution of a gage is the smallest unit of measure that the gage is able to read. For example, on a metric ruler, the gage resolution is typically 1mm.

A gage should have a resolution of less than 10% of the specification tolerance. For example, for a specification of (0.050, the gage should have a resolution of at least 0.010 (and an adequate Gage R & R) to be eligible for use.

|Measurement | |

|Variation | |

The total variation observed in a process is made up of actual part-to-part variation and measurement variation.

Variation in a measurement system can come from anywhere within that system. Remember the 6 M’s: Man (operator), Method, Material (part), Measurement, Machine (tool), Mother Nature (environment).

Small Group Exercise 1: (Total duration: 20 minutes): Measuring the length of a pen using a ruler

Break the class into groups of 3 or 4. Give each group one plastic 6” ruler as a visual aid. Ask the groups to consider the measurement system for measuring one of the participant’s pens with the ruler. As a small group, list some possible sources of measurement variation on the appropriate page of the Student Manual.

Allow 10 minutes, then bring the class back together. Ask each group to give one source of variation for each “M”. Record on flip chart.

There are a near infinite number of possible sources for variation even in this simple example. Imagine how much variation would be in the more complicated systems used day-to-day in your business!

Theory of Gage Repeatability & Reproducibility (cont.)

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Recall that total process variation is a combination of part-to-part and measurement variation. We want to focus just on the measurement variation.

Total Gage R & R has two parts:

Repeatability or Equipment Variation (E.V.)

Reproducibility or Appraiser Variation (A.V.)

Total Gage R & R = (E.V.2 + A.V.2)½

There are generally accepted guidelines for the accepting or rejecting of a gage for use based on the Total Gage R & R. Check with your company or customer to see if their guidelines vary from these, as stated below:

Total Gage R & R < 20%: Acceptable

The gage can be used without reservation for the parameter tested in the Gage R & R study.

Total Gage R & R is between 20% and 30%: Conditional

Be very cautious about using the gage for the tested parameter without any improvements to the measurement system.

Total Gage R & R > 30%: Unacceptable

This gage cannot adequately differentiate between a “good” or “bad” part (as defined by the parameter specifications). It should not be used without improvements to the measurement system.

Part III: How to do a Gage R & R Study

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The typical gage R & R study uses 2 or 3 operators and 10 parts. Measurements are repeated 2 or 3 times. This approach gives you information about both repeatability and reproducibility. It also will give you important information on how to improve the measurement system if the final gage R & R result is unacceptable (> 30%).

DO NOT JUST SELECT 10 PARTS AT RANDOM!!

A gage R & R is used to determine if the gage can distinguish “good” parts from “bad.” Therefore, the study should be conducted on both “good” and “bad” parts.

The samples should cover the full range of the specification and extend beyond the specification as well. For example, if the specification is 1.000 ( 0.025, samples for the gage R & R study should cover the full range from 0.050 to 1.050. (By the way, what is the minimum gage resolution for this case? Answer: 0.005)

|Execution | |

When gathering data for a gage R & R study, it is important to stay as close to actual practice as possible. Use production operators, standard measurement procedures, etc.

For instance, in the case of an inspection station on an assembly line, do not give the operators special instructions on how to measure the parts. They should measure them as they normally would during the inspection process.

If possible, have an extra person act as the scribe. This saves time and prevents data corruption (“Well, last time I measured this part I got 1.050, this time I got 1.020. It was probably closer to 1.035 – I’ll record that…”).

How to do a Gage R & R Study (continued)

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|Understanding | |

|the Worksheet | |

Reminder: Several statistical constants are used during the calculation for total gage R & R. This course was designed to instruct the participants on how and why to conduct a gage R & R study. It does not go into the derivation of these constants. If further information on the statistical theory behind gage R & R is required, please refer to a statistical resource.

Each Student’s Manual contains a paper copy and an electronic copy (3.5” diskette, MS Excel for Windows format) of the “Gage Repeatability & Reproducibility Worksheet”. The worksheet will do all of the calculations automatically, but it is important to be able perform the calculations by hand – a computer is not always readily available.

The shaded cells of the worksheet contain calculations. Do not enter data into these cells or the equations will be lost. Data should be entered in un-shaded cells only. It is recommended that a master copy of the worksheet be retained in a “read only” format as a backup.

How to do a Gage R & R Study (continued)

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|Understanding | |

|the Formulas | |

|(Page 1) | |

NOTE: For the two sections on Understanding the Formulas, refer directly to the MS Excel spreadsheet and the associated formulas. Overheads of the worksheet are provided in the event of computer malfunction.

Range – the difference between the maximum and minimum value for each operator-sample combination.

Avg (R-bar) – the average range for each operator.

Avg (X-bar) – the average measurement for each trial.

How to do a Gage R & R Study (continued)

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|Understanding | |

|the Formulas | |

|(Page 2) | |

R-bar, X-bar diff., and Rp are carried over from the calculations performed on Page 1 of the worksheet.

How to do a Gage R & R Study (continued)

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|Gage R & R | |

|Studies | |

The format of the gage R & R study presented here is for the most common type of measurement system: continuous data. Gage R & R studies are conducted differently for destructive measurements, such as torque, tensile strength or hardness, and for cases of discrete data.

Continuous or variable data is that which can be meaningfully divided into smaller and smaller increments. Examples: dimension, weight, temperature, time

Discrete or attribute data cannot be divided into smaller increments. Examples: pass/fail data, count or frequency data, categorical data (color, location, shift, etc.)

The procedure for a destructive measurement gage R & R is identical to that for continuous data, except the parts cannot be re-measured for the multiple trials and operators. In this case, all of the “Part #1” subgroup of samples are taken from the process as close together as possible to minimize the variation. As with continuous data gage R & R, the subgroup samples should cover the full range of the process, both in and out of specification.

A discrete data gage R & R study checks for percent agreement among all operators. The data should agree for all trials and all operators (100% agreement), however there are cases where less than 100% agreement may be acceptable.

How to Do a Gage R & R Study (continued)

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|Exercise 2 | |

Break the group into small groups of 3-4 participants per team. Each group will be asked to conduct a Gage R & R study with two operators, two trials per operator and ten samples.

Give each team one Participant Kit, but instruct them not to open the Kit until instructed to do so.

Assign the team tasks by alphabetizing the team members’ first names:

Albert – Operator 1

David – Scribe

Marie – Observer

Xavier – Operator 2

Teams of three participants will not have an Observer.

Have all of the Operator 2’s leave the room.

The Scribe may open the Kit once Operator 2 has left. The Operators are split up so they do not observe each other’s measurement procedures. The idea in this exercise is to create a situation that will maximize the measurement variation.

Throughout this exercise, the Observer takes notes on how each Operator measures the samples. This information will be used later, but should not be shared with the rest of the members of the team until after all data has been collected and calculated.

Using the specification in the Kit, the Scribe and Observer complete the background information on the Gage R & R Worksheet provided.

NOTE: The specification has two dimensions. The instructor should assign the dimension to be measured as follows: if the Kits contain calipers, assign diameter or length (same for all teams, or alternate for each group); otherwise, assign length.

How to Do a Gage R & R Study (continued)

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|Exercise 2 | |

Ask the Scribe from each group to report their group’s results. Record on the flip chart the percent repeatability, percent reproducibility, and percent total gage R & R for both the Tolerance and Study analyses. There will be a total of six numbers for each group. Also record the Scribe’s name or initials so that these values can be compared to those obtained during the next exercise.

Explain the design of the exercise. Operators were separated to prevent them from consciously or unconsciously agreeing on a measurement procedure. Unconscious agreement could occur if both Operators were present during all of the measurement. Operator 2 could end up duplicating Operator 1’s measurement method simply because it was observed prior to Operator 2’s performance of the measurements.

How to Do a Gage R & R Study (continued)

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|Theory | |

Repeatability is associated with equipment variation. Can one operator measure one part several times and get the same result?

Reproducibility is associated with appraiser variation. Can several operators measure one part and get the same result?

Tolerance analysis judges the validity of using the measurement system to make decisions about product acceptance.

Study analysis judges the validity of using the measurement system to make decisions about process control.

|Review of | |

|Results from | |

|Exercise 2 | |

Review the flip chart of results from Exercise 2. Ask the class as a whole to draw conclusions from each set of results.

Is each measurement system acceptable, unacceptable or under caution for use in making decisions about product acceptance (go/no go, pass/fail)? Process control?

For each measurement system, is the measurement variation more attributable to equipment variation or appraiser variation?

How to Improve the Gage R & R Result (continued)

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|to Direct Further | |

|Improvement | |

If a measurement system has a high percent repeatability element, the improvement should focus on ways to enhance an operator’s ability to achieve the same result on repeated measurements of a given sample.

Does the gage require operator judgment to obtain a value?

Is the sample awkward to measure? Would a fixture make the sample easier to manipulate?

Is the gage properly calibrated? Was the gage dropped or damaged between measurements?

Is there a specification associated with using this gage? Is it being followed?

If a measurement system has a high percent reproducibility element, the improvement should focus on how to eliminate variation between the results obtained by one operator versus another.

Is there a specification associated with measuring this part? Is it being followed? Is it open to interpretation?

Is the sample always in the same state or position when it is being measured?

Are the operators trained to perform this measurement?

|Small Group | |

|Exercise 3 | |

Break the group into the same teams as used in Exercise 2.

This time, the group should remain together and discuss ways to improve their measurement system based on what they learned from the result of the first study (Exercise 2).

How to Improve the Gage R & R Result (continued)

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|Exercise 3 | |

Record on the flip chart (preferably, directly below the Exercise 2 results for each group) the same data for each group as was recorded for Exercise 2. Calculate the percent improvement for the Total Gage R & R result for both the Tolerance and Study analysis methods.

% Improvement = [(Exercise 2 Result) – (Exercise 3 Result)]

(Exercise 2 Result)

Ask each group what they did to improve their overall Gage R & R result.

Award a small prize to each member of the team with the highest Gage R & R improvement.

NOTE: Each team should be able to achieve at least a 10% improvement over the Exercise 2 result. If not, ask to meet with these teams during the break. Carefully review and discuss with the participants their results from both exercises. Guide the team members to discover other possible ways to improve the Gage R & R. Ask them to repeat the study again (using the MS Excel worksheet to save on calculation time).

Part V: Conclusion & Wrap-Up

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|Objectives | |

Briefly review the topics taught during the course.

How to plan, execute and improve a Gage R & R Study.

Repeatability versus Reproducibility

Tolerance Analysis versus Study Analysis

Review the flip chart of student comments complied at the beginning of the course (Objectives: Why are we here?).

Review each point and obtain agreement from the class on whether or not each point was covered. If a point was not addressed, explain why.

|Questions & | |

|Answers | |

Ask participants if there are any questions regarding gage R & R studies.

Remind students that an electronic copy of the Gage R & R Worksheet is on a 3.5” floppy in their Student Manuals.

|Concluding | |

|Thoughts | |

There is an exam associated with this class. A passing score is 80%. Give students the date of the exam.

Distribute the course evaluation forms. Ask that each participant complete a form and hand it in (face down on the front table) before leaving. Thank the students for their participation, as appropriate, and share any other concluding remarks that you may have.

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