辅导案例-STAT 3170

COURSE: STAT 3170
DATE & TIME: November 6, 10:30am – November 8, 12:00pm,
UNIVERSITY OF MANITOBA
Term Test 2
DURATION: 49 hours, 30 minutes
PAGE: 1 of 4
INSTRUCTIONS
I. This examination has 4 pages including this cover page.
II. The value of each question is indicated in the lefthand margin beside the statement of
the question.
III. The total value of this exam is 52 points.
IV. You may not collaborate with other students in any regard on this test. If you have any
questions, email me and I will respond to you as soon as I am available.
V. Written answers will be submitted through Crowdmark. R Code will be submitted onto
the ”Term Test 1” folder on UMLearn. You may submit the R code as a .txt file, an .R
file, or as output from RMarkdown (either a .pdf file or a .rmd file). A link has been
emailed to you for you to submit your work through Crowdmark.
VI. Please show all of your work.
VII. Only simplify answers where needed.
VIII. Calculate all probabilities to 6 decimal places, and all other terms to 2 decimal places,
unless otherwise specified.
IX. Submit all of your R code as a single file.
X. Any plagiarism or copying will result on a zero on this test and further penalization as
outlined under the Student Discipline Bylaw for Academic Dishonesty.
XI. Your test will not be evaluated until you have filled out and submitted the Honesty
Declaration Form, which is available on the course UMLearn page.
COURSE: STAT 3170
DATE & TIME: November 6, 10:30am – November 8, 12:00pm,
UNIVERSITY OF MANITOBA
Term Test 2
DURATION: 49 hours, 30 minutes
PAGE: 2 of 4
1.[3] Consider the below control limits for monitoring the sample mean X¯ of a process:
UCL = µX¯ + LσX¯
UCL = µX¯
UCL = µX¯ − LσX¯
What should L be set to so that the ARL of this process is 1000?
2.[2] Download the Phase 1 Datasets dataset on UMLearn. This dataset contains two
columns of data, labelled A and B. Each column gives a sequence of 80 sample means
obtained from an in-control process. Using R, create a line graph for each column. Based
on these graphs, for which process will a Shewhart control chart be more applicable?
Why?
3.[2] Consider the image below. Apply sensitizing rules 1 – 8 to this image and give which of
them would trigger a signal.
4.[1] Suppose that an issue in a process has been pinpointed. Which of the “Magnificent Seven”
tools would you use first to organize a response to this issue? Explain your reasoning
and how this tool would be applied.
5. Consider the use of a control chart to monitor a process.
(a)[1] When using a control chart, what are the Type I and Type II errors?
(b)[1] Widening the control limits will have what effect on the probability of a Type I and
a Type II error?
6.[2] Quality engineers wish to monitor a process to determine if it is in control. They have
the resources to measure 200 outputs a day. Explain the benefits of taking 50 samples
of size 4 each, grouped subjectively, as compared to taking a single sample of size 200.
What is this technique called?
COURSE: STAT 3170
DATE & TIME: November 6, 10:30am – November 8, 12:00pm,
UNIVERSITY OF MANITOBA
Term Test 2
DURATION: 49 hours, 30 minutes
PAGE: 3 of 4
7. The viscosity of a polymer is measured in samples of size 15 every 4 hours. The Viscosity
- Phase I dataset on UMLearn contains 50 samples obtained when the process was in
an in-control state, along with the sample means, the sample ranges, and the sample
standard deviations. The Viscosity - Phase II dataset has the same structure but
consists of 30 samples obtained during the on-line monitoring process.
(a)[1] Choose the most appropriate control charts for monitoring the mean and variation
of this process.
The following questions pertain to the control chart you chose to monitor the process
mean.
(b)[2] Calculate the central line and control limits for this chart.
(c)[1] Create a control chart for this process in R, and attach the image here.
(d)[1] Using the control chart you just created, identify the presence (or lack thereof) of a
shift in the process mean.
The following questions pertain to the control chart you chose to monitor the process
variation.
(e)[2] Calculate the central line and control limits for this chart.
(f)[1] Create a control chart for this process in R, and attach the image here.
(g)[1] Using the control chart you just created, identify the presence (or lack thereof) of a
shift in the process variation.
8. Successive heats of single units of a steel alloy are tested for hardness. The Hardness
- Phase I dataset on UMLearn contains 35 observations obtained when the process
was in an in-control state, along with the moving ranges. The Hardness - Phase II
dataset has the same structure but consists of 30 observations obtained during the on-line
monitoring process.
The following questions pertain to the control chart you choose to monitor the individual
observations of the process.
(a)[2] Calculate the central line and control limits for this chart.
(b)[1] Create a control chart for this process in R, and attach the image here.
(c)[1] Using the control chart you just created, identify the presence (or lack thereof) of a
shift in the individual observations of the process.
The following questions pertain to the control chart you choose to monitor the process
variation.
(d)[1] Calculate the central line and control limits for this chart.
(e)[1] Create a control chart for this process in R, and attach the image here.
(f)[1] Using the control chart you just created, identify the presence (or lack thereof) of a
shift in the process variation.
9.[3] For a N (µ, σ) population, compute the relative efficiency of using T1 = R/d2 as an
estimator for σ to using T2 = s/c4 as an estimator for σ, for n = 7, 8, and n = 9.
10. Consider using x¯ and s control charts for monitoring a N (µ, σ) process, and suppose you
know the values µ and σ.
(a)[2] What is the Type I Error Rate (i.e., the False Alarm Rate) for the x¯ chart?
(b)[1] Will the Type I Error Rate for the s chart be the same as for the x¯ chart? Give a
short explanation as to your answer.
COURSE: STAT 3170
DATE & TIME: November 6, 10:30am – November 8, 12:00pm,
UNIVERSITY OF MANITOBA
Term Test 2
DURATION: 49 hours, 30 minutes
PAGE: 4 of 4
11. A produce processing facility takes random samples of 50 tomatoes each, and records
the proportion of tomatoes that are to be rejected. The Tomatoes - Phase I dataset
on UMLearn contains the rejection rates for 40 samples, obtained when the process was
in an in-control state. The Tomatoes - Phase II dataset has the same structure but
consists of 30 observations obtained during the on-line monitoring process.
(a)[1] What is the appropriate chart to monitor this process?
(b)[2] Calculate the central line and control limits for this chart.
(c)[1] Create a control chart for this process in R, and attach the image here.
(d)[1] Using the control chart you just created, identify the presence (or lack thereof) of a
shift in the process.
12. The number of workmanship nonconformities observed in the final inspection of disk-drive
assemblies is recorded every day. The Disk-Drive Assemblies - Phase I dataset on
UMLearn contains the average number of imperfections recorded across all of the daily
inspected assemblies, along with the number of assemblies inspected and the total number
of imperfections observed, obtained over 35 days when the process was in an in-control
state. The Disk-Drive Assemblies - Phase II dataset has the same structure but
consists of 30 observations obtained during the on-line monitoring process.
(a)[1] What is the appropriate chart to monitor this process?
(b)[3] Create a control chart for this process in R, and attach the image here.
(c)[1] Using the control chart you just created, identify the presence (or lack thereof) of a
shift in the process.
13. A factory produces drinking glasses. Periodically, a glass is inspected, and the number
of imperfections in the glass is recorded. The process is known to result in glasses with
an average of 3 imperfections per glass. The Glass - Phase I dataset on UMLearn
contains the number of imperfections observed per glass across 60 glasses, obtained when
the process was in an in-control state. The Glass - Phase II dataset has the same
structure but consists of 30 observations obtained during the on-line monitoring process.
(a)[1] What is the appropriate chart to monitor this process?
(b)[1] Calculate the central line and control limits for this chart.
(c)[1] Create a control chart for this process in R, and attach the image here.
(d)[1] Using the control chart you just created, identify the presence (or lack thereof) of a
shift in the process.
(e)[1] Is there bias in your calculations for the centre line or the control limits?
14.[3] A production facility is known to produce items with a 0.1% nonconformity rate. What
is the minimum sample size required to detect a shift to a 0.2% nonconformity rate with
probability 0.5?

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