IE 361 Homework Set #1 Fall 2001
1. Do problem 2.5 of the text using the range-based formulas. Then redo it using the
ANOVA-based formulas on page 27 of the text. (When making an ANOVA-based
estimate of 5R&R , use the formula given in class rather than using simply computing
É5
s #repeatability € 5
s #reproducibility.)
2. Below is a data set from a real calibration study (taken from a paper by John Mandel
of NBS/NIST). Unfortunately, the units are not given in the paper. For sake of argument,
suppose that they are ppm (parts per million) of some contaminant. B is the "truth"/goldstandard-measurement. C is the local laboratory measurement. All on 8 œ "% different
specimens.
B
C
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a) Fit a simple linear regression model to these data. For a fixed B/specimen, what do
you estimate "5measurement " to be at the local laboratory? What "conversion formula" do
you recommend for translating "local lab measurements" to estimated "gold standard
measurements"?
b) A new specimen is measured as C œ #!!! at the local laboratory. Give an
approximate 95% confidence interval for the "true"/gold standard value for this specimen.
Do this two way. First simply read one interval off a plot of 95% prediction intervals for
an additional C at various fixed values of B. Then use the approximate confidence
interval formula given in class and on the "Class Outline" handout.
1
As suggested in my e-mail to you about statistical software at ISU, you can get help with
using the JMP statistical package by looking at
http://www.public.iastate.edu/~stat/compguide/jmp.html
or by using the statistical software primer written for Vardeman and Jobe's Basic
Engineering Data Collection and Analysis available both at
http://www.duxbury.com/default.htm
(under the "Book Companions") and in a local/development version at
http://www.public.iastate.edu/~vardeman/book_site/index.html
To do the ANOVA part of the first problem, you will need to enter 3 columns of length
60 into the JMP worksheet. The first should give part numbers, the second should give
operator numbers and the third should give the measurements. After entering the data,
click on the "Part" column heading, go to the "Cols" menu and choose "Column Info."
There make sure that the "Modeling Type" is "Nominal." Do the same for the "Operator"
column. Then from the "Analyze" menu choose "Fit Model." You'll get a dialogue box.
The "Measurement" variable gets entered into the "Y" part of the box. The "Part" and
"Operator" variables get entered into the "Construct Model Effects" part of the box. Then
by highlighting the "Part" variable in the "Select Columns" list and the "Operator"
variable already in the "Construct Model Effects" part of the box and clicking the "Cross"
button, you can add the interaction effects to the model. Then clicking "Run Model" will
get you a JMP analysis. The "Effect Tests" part of the report contains the necessary sums
of squares and degrees of freedom to make the necessary estimates.
To do the second problem, you will need to enter 2 columns of length 14 into a new data
table. The first should give B and the second should give C. After entering the data, click
on "Fit Y by X" under the "Analyze" menu. Put the B variable in the "Factor" part of the
dialogue box and the C variable in the "Response" part of the dialogue box and click on
"OK." This will bring up a scatterplot (that can be resized to improve resolution if you
wish). Click the red triangle on the bar above the plot and bring up a menu. Select "Fit
Line." This will produce a SLR analysis for these data (and plot the least squares line). If
you then click on the red triangle by the "Linear Fit" bar below the plot, you can bring up
a menu that includes an entry "Confid Curves Indiv." Checking that option will put 95%
prediction limits for an additional C at the various B's on the plot. You can then select the
cross-hair tool from the JMP toolbar and read off values on these plots of prediction
limits. Other values you'll need (like ÈQWI ) can be read from the JMP report. To get
simple descriptive statistics for the columns (like B and =B ) can be gotten by choosing
"Distribution" from the "Analyze" menu.
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IE 361 Homework Set #2 Fall 2001
Problems 3.18, 3.22, 3.27 and 3.30 of the text.
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IE 361 Homework Set #3 Fall 2001
1. Do problem 4.31.
2. Use JMP and generate 100 standard normal random numbers, placing them in column
1. (Click on the "Rows" menu and add 100 rows. Then after clicking on the Column 1
heading, use the "Cols" menu and select "formula." From the "Random" functions group,
select "Random Normal." This will put the random numbers in column 1.)
(a) Plot column 1 vs row number as an example of "stable process" behavior. (Use the
"Overlay Plot" option in the "Graph" menu to do this.) Then use JMP to find the sample
standard deviation of the normal random values. (Use the "Distribution" option on the
"Analyze" menu.) This should be reasonably close to the "process short term standard
deviation" 5 œ "Þ
(b) Use the "moving range chart" function in JMP to calculate the average moving range
Q V for the data in column 1. (You can find "Control Chart" under the "Graph" menu.
In the dialogue box choose "IR" for the "chart type." The center line on that plot is at the
average moving range.) How does Q V /1.128 serve as an estimate of the "process short
term standard deviation" 5 œ "?
(c) Make up a new column (column 2) by adding the row number to the random numbers
in column 1. (You get a new column using the "Cols" menu. The opportunity to specify
the entries using a formula is activated using the "New Property" pull down menu. The
row number function is in the "Rows" functions group.) Plot this new column vs row
number as an example of a situation where one has samples of size 8 œ " and the process
mean is not constant (in fact .3 œ 3). Use JMP to find the raw standard deviation of the
values now in column 2. How does this value serve as an estimate of the "process short
term standard deviation" 5 œ "?
(d) Repeat part (b) using the new values in column 2. Which estimate of 5 œ " do you
like best? The one in (c) or the one here?
(e) What is the moral told in parts (a)-(d) of this problem?
3. (a) For the data of part c) of Problem 4.2, give the best possible guess at 5 (the
process short term standard deviation) in this 8 œ " situation.
(b) If future monitoring of individual flatness values is contemplated and a mean flatness
of #Þ) is "standard," exactly how do you suggest monitoring these flatness values for an
"all-OK" ARL of 370?
4. Do Problems 5.2; 5.3b,c; 5.17a,b; 5.18; 5.28, 5.31, 5.37.
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