IE 355 QUALITY AND APPLIED statistics I
LAB ASSIGNMENT 4
Gage Capability: Repeatability and Reproducibility
Goal
Quality engineers focus their attention on causes of variation as a measurement of product performance. One cause of variation is measurement error. In this exercise students perform a particular type of gage capability analysis: a repeatability and reproducibility (R&R) study. The goal of this study is to evaluate the components of measurement error when using a handheld micrometer to measure the diameter of a cylindrical part.
Introduction
The problem in this assignment is to investigate the use of a micrometer to measure a particular part. To do this, you will develop a method for how the micrometer is to be used. To assess the method, you will perform two R&R studies. The first R&R study will be done using no particular measuring methodology. The second R&R study will be performed using the method you have developed. The focus here is on the measurement system, not on evaluating how well the parts conform to the specifications.
Variability in measurement is due to the measurement device itself and the operator. An R&R study helps us estimate the contribution of both these sources of variability.
· Repeatability is the variation in measurement that is due to the measurement equipment itself. We say a measurement device has poor repeatability when one operator uses a gage to measure a piece several times and obtains different results.
· Reproducibility is the variation in measurements among operators. We say a measurement device has poor reproducibility when several operators use a gage to measure a piece and obtain different results.
Lab Report
Your report should be an engineering report that you would submit in a company given the assignment to design a method for using a micrometer for the measurement of this part. Your report should be written in paragraphs containing complete sentences. Any graph or table you show must be labeled and referred to in the text.
Executive summary
This summary, approximately 1/2 page, briefly describes the goal and the result. “The goal here is to design the method for measuring diameters with the micrometer.” Your result should be stated using some key numbers; i.e., “…without the methodology the precision-to-tolerance ratio was .20 and after redesign of the measurement system the ratio was 0.01, which is excellent improvement.”
Description of the measurement system methodology
Describe your new measurement method. Describe all procedures. Describe or sketch any special equipment you use.
Results
Present your analyses. Show graphical and tabular results that support your analyses. Give estimates of the variance due to operator, measurement device, the product itself, and total. Calculate precision to tolerance ratios. Present the results such that they tell a coherent and clear story.
Recommendation
Give your recommendation; i.e., should the measurement system you devised be used for this part? Do you have other suggestions for improving the measurement system?
Procedure
Week 1
· Students must work in groups of three (or four if the number of students in the lab is not evenly divisible by 3).
· Familiarize yourself with the micrometer and the parts.
· Run an R&R study with no particular measurement methodology for the operators. In fact, try to think of typical ways in which operators might introduce measurement errors given that they have no formal training or procedure to follow.
· Each operator measures the same 10 parts, 2 times.
Week 2
· Based on the experience you obtained in running the R&R study in week 1, design a new measurement system for the part using the micrometer.
· Perform the same R&R study using the measurement method you have developed. Analyze the results in StatGraphics. The report is due the following week.
Concepts of Variance in an R & R Study
Suppose you had many parts, many operators, and many micrometers and then measured the parts. From the measurements you can estimate the mean and the variance of the diameters. We will call this variance the Total variance. There are several components that contribute to the total:
Total variance:
· Variance due to Part differences (caused in manufacturing),
· Variance due to the measurement error - gage variance,
The variance from the gage can be further broken down into two types of measurement error.
Gage variance:
· Variance due to operator differences - reproducibility,
· Variance due to the measurement instrument - repeatability,
Therefore, the Total variance can be written: .
One widely used index is the precision to tolerance (P/T) ratio, a capability ratio that compares the measurement error to the specification interval of the part. The precision to tolerance ratio () is
where and are the specification limits for the part. A rule of thumb is that the gage is acceptable if . The specification for the diameter of our part is .
Steps for Performing an R&R Study
- Collect the data using the micrometer
You are provided with a data sheet (for each week) to record your measurements. Notice that the part numbers are in random order. Randomizing is a standard procedure when collecting data. Perform each measurement in the order given on your data sheet. You must devise a way to label and keep track of the part numbers.
Reading the micrometer
The micrometer we will use is able to measure a distance of 0 to 1 inch. Holding the micrometer as depicted in the bottom diagram of Figure 1, you see vertical and horizontal divisions on the inner sleeve. Every fourth vertical division is labeled with a digit, i.e., 0, 1, 2,…, 9, 0. Each digit represents 0.100 (or 100 thousandths) of an inch. There are four spaces between each digit representing 0.025 (25 thousandths) of an inch therefore, the inner micrometer sleeve divides 1 inch into 0.025 (25 thousandths) inch increments.
The thimble (the outer sleeve that rotates around the inner sleeve) has 25 lines numbered from 0 to 24. Each line on the thimble represents 0.001 (1 thousandth) of an inch. For example, the 13th thimble line represents 0.013 (13 thousandths) of an inch. One complete revolution of the thimble is equal to 0.025 (25 thousandths) of an inch, which is also equal to one division on the inner sleeve.
The horizontal lines on the inner sleeve are used to measure increments of 0.0001 (0.1 thousandths) of an inch. To do this, find the horizontal line on the inner sleeve that lines up with a line on the thimble. The digit that labels the horizontal line is the number of 0.1 thousandths of an inch to include in the measurement.
The measured distance of an object will be the total of (0.100 x last digit showing on inner sleeve) + (0.025 x number of vertical divisions on inner sleeve beyond inner sleeve digit) + (0.001 x the number showing on the thimble just below the zero horizontal line) + (0.0001 x the number on the horizontal line on the inner sleeve that lines up with a line on the thimble).
An example of a micrometer reading is shown in Figure 1. We see the edge of the thimble is two vertical divisions beyond 5 on the inner sleeve, so the reading on the sleeve is (0.100 x 5) + (0.025 x 2) = 0.550 inch. The 0 horizontal line on the sleeve is between the numbers 13 and 14 on the thimble, which means the reading on the thimble results in (0.001 x 13) = 0.013. Add this to previous value: 0.550 + 0.013 = 0.563. Now when you look at the horizontal lines on the thimble, you see that the 6 horizontal line is lined up with a line on the thimble. The total measurement is then 0.563 + (0.0001 x 6) = 0.5636.
Figure 1. A micrometer
- Create the R&R setup using StatGraphics.
To set up the data file and variables in StatGraphics: select Special>Quality Control>Gage R&R>Data Setup…. Fill in the fields for the number of operators (should equal number of students in your group), the number of parts, and the number of trials.
An analysis window appears. Click the 4th button from left on the analysis toolbar (red arrow points to a disk). Check all four boxes in the Save section: Operators, Parts, Trials, and Measurements. OK. Now look at the spreadsheet for the data. You will see the four new variables.
- Enter the data into StatGraphics and analyze.
Enter your measurements into the StatGraphics spreadsheet. Note that the measurements you took in the lab were in random order while the worksheet you created above will not be. Be sure to match up the correct part numbers and their measurements. Since the numbers we are working with are out to the 4th decimal place, it is more convenient to work in units of thousandths of an inch, i.e., multiply your measurements by 1000.
You will use two types of R&R analyses in StatGraphics: Average and Range Method and ANOVA Method.
Average and Range Method
To do the R&R study using the Average and Range Method, select Special>Quality Control>Gage R&R>Average and Range Method…. Fill in the dialog fields with the variable names. OK.
You will see the Analysis Summary. Read the StatAdvisor. It explains the results. These estimates are for only. To get estimates of the total and product variances, click the Tabular Options button and select the Gage Report checkbox. Rclick anywhere, select Analysis Options, enter 1 in the Sigma intervals field. OK. The Gage Report gives you a breakdown of all the standard deviations and their Percent Contribution.
Click Graphical Options Button on the Analysis Toolbar. Examine the five graphs. Figure out what each is showing you. Pick at least three graphs to support your analysis. Use the StatReporter to compile a coherent set of outputs for your report.
ANOVA Method
To do the R&R study using the ANOVA Method, select Special>Quality Control>Gage R&R>ANOVA Method…. Fill in the dialog fields with the variable names. OK.
You will see the Analysis Summary. Read the StatAdvisor. It explains the results. These estimates are for only. To get estimates of the total and product variances, click the Tabular Options button and select the Gage Report checkbox. Rclick anywhere, select Analysis Options; enter 1 in the Sigma intervals field. OK. The Gage Report gives you a breakdown of all the standard deviations and their Percent Contribution.
Click Graphical Options Button on the Analysis Toolbar. Examine the five graphs. Figure out what each is showing you. Pick at least two graphs to support your analysis. Use the StatReporter to compile a coherent set of outputs for your report.
Compare the results obtained using the Average and Range Method to the ANOVA Method. Do they give you the same results? What is different if anything?
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