Reference:Managing Quality: Integrating the Supply Chain, 4th Ed. By S. ThomasFoster 1. Interpret the following charts to determine if the processes are stable. 2. A production process for JMF Semicon is monitored using the x-bar and R charts. Ten samples of n=15 observations have been gathered with the following results: Sample Mean Range 1 282 35 2 290 54 3 262 43 4 309 30 5 263 42 6 325 24 7 288 4 8 298 23 9 277 17 10 363 55 a. Develop a control chart and plot the means. b. Is the process in control? Explain. 3. A finishing process packages assemblies into boxes. You have noticed variability in the boxes and desire to improve the process to fix the problem because some products fit too tightly into the boxes and others fit too loosely. Following are width measurements for the boxes. Using x-bar and R charts, plot and interpret the process. Sample 1 2 3 4 5 6 7 8 82.21 82.73 82.39 82.19 82.37 82.01 82.79 82.70 82.15 81.84 82.13 82.73 82.36 82.10 82.73 82.69 82.25 82.25 82.26 82.27 82.34 82.79 82.74 82.76 82.01 82.27 82.52 82.34 81.98 81.62 82.74 82.72 82.15 82.44 82.44 82.43 82.01 81.64 82.73 82.75 82.15 82.44 82.37 82.27 81.89 82.16 82.76 82.74 4. A Rochester, New York firm produces grommets that have to fit into a slot in an assembly. Following are dimensions of grommets (in millimeters): Sample x 1 69 50 81 69 96 2 78 68 81 113 96 3 51 96 54 69 95 4 51 68 71 56 93 5 69 96 113 83 24 a. Using x-bar and R charts, determine if the process is in control. Management 2070Y - Fall 2013 - Assignment #1 Page 2 of 5 1. “Leave Without Treatment” Analysis (10 marks) Periodically, an individual will check-in at a walk-in-clinic, but leave without ever receiving treatment. Employees notice this when they call the individual’s name, but the individual is no longer in the waiting area. It is thought that some of this behaviour can be explained by the individual “feeling better” and deciding to leave, though management fears that individuals are leaving because they have waited too long. These cases are of concern because the individual did not receive treatment which may lead to more extensive health problems, but also because the individual may “bounce around” to various walk-in-clinics creating increased demands on health care staff. In an effort to reduce the frequency of individuals “leaving without treatment”, the local health region has sampled data from the registration system at their walk-in clinics. They selected data from 150 registrations each day for 15 days that they defined as “normal operations” and thus they would like quality control chart(s) to be prepared with control limits based on that data. Furthermore, management would like to see recent sample data (150 registrations per day for the last 15 days) plotted against these control limits. If an out-of-control condition is found, registratio ...

1. Reference:Managing Quality: Integrating the Supply Chain, 4th
Ed. By S. ThomasFoster
1. Interpret the following charts to determine if the processes
are stable.
2. A production process for JMF Semicon is monitored using
the x-bar and R charts. Ten samples of n=15 observations have
been gathered with the following results:
Sample
Mean
Range
1
282
35
2
290
54
3
262
43
4
309
30
5
263
42
6
325
24
7
288
4

2. 8
298
23
9
277
17
10
363
55
a. Develop a control chart and plot the means.
b. Is the process in control? Explain.
3. A finishing process packages assemblies into boxes. You
have noticed variability in the boxes and desire to improve the
process to fix the problem because some products fit too tightly
into the boxes and others fit too loosely. Following are width
measurements for the boxes. Using x-bar and R charts, plot and
interpret the process.
Sample
1
2
3
4
5
6
7
8
82.21
82.73
82.39
82.19
82.37
82.01
82.79
82.70
82.15

3. 81.84
82.13
82.73
82.36
82.10
82.73
82.69
82.25
82.25
82.26
82.27
82.34
82.79
82.74
82.76
82.01
82.27
82.52
82.34
81.98
81.62
82.74
82.72
82.15
82.44
82.44
82.43
82.01
81.64
82.73
82.75
82.15
82.44
82.37
82.27
81.89

4. 82.16
82.76
82.74
4. A Rochester, New York firm produces grommets that have to
fit into a slot in an assembly. Following are dimensions of
grommets (in millimeters):
Sample
x
1
69
50
81
69
96
2
78
68
81
113
96
3
51
96
54
69
95
4
51
68
71
56
93
5
69
96
113

5. 83
24
a. Using x-bar and R charts, determine if the process is in
control.
Management 2070Y - Fall 2013 - Assignment #1
Page 2 of 5
1. “Leave Without Treatment” Analysis (10 marks)
Periodically, an individual will check-in at a walk-in-clinic, but
leave without ever
receiving treatment. Employees notice this when they call the
individual’s name, but the
individual is no longer in the waiting area. It is thought that
some of this behaviour can
be explained by the individual “feeling better” and deciding to
leave, though
management fears that individuals are leaving because they
have waited too long. These
cases are of concern because the individual did not receive
treatment which may lead to
more extensive health problems, but also because the individual
may “bounce around”
to various walk-in-clinics creating increased demands on health
care staff.

6. In an effort to reduce the frequency of individuals “leaving
without treatment”, the local
health region has sampled data from the registration system at
their walk-in clinics.
They selected data from 150 registrations each day for 15 days
that they defined as
“normal operations” and thus they would like quality control
chart(s) to be prepared
with control limits based on that data. Furthermore,
management would like to see
recent sample data (150 registrations per day for the last 15
days) plotted against these
control limits. If an out-of-control condition is found,
registration data can be used to
contact the individuals to research the specific cause of why
they left without receiving
treatment.
Calculate the relevant control limits and prepare relevant ±3σ
quality control chart(s).
Provide an analysis of the performance over the past 15 days.
(Do not round standard
deviation values. Control limit values should be rounded to
four decimals.)

7. “Normal”
Day
# leaving
without
treatment
“Recent”
Day
# leaving
without
treatment
1 6 1 6
2 8 2 9
3 5 3 6
4 7 4 11
5 8 5 15
6 6 6 5
7 7 7 8
8 8 8 8
9 7 9 6

8. 10 5 10 5
11 8 11 8
12 5 12 9
13 8 13 8
14 6 14 10
15 7 15 9
Management 2070Y - Fall 2013 - Assignment #1
Page 3 of 5
2. Wait Time Analysis (15 marks)
The primary performance measure for health care services is
waiting time. For walk-in-
clinics, waiting time is the time between when an individual
registers (check-in) and
when the individual is admitted for treatment.
Since “wait time” is critical for health services (customer
satisfaction, government
mandates, etc.), management has tracked historical performance
at their walk-in clinics
and found that the average wait time is 30 minutes and the

9. historical range has been 15
minutes.
The local health region believes that government mandated wait
times are likely to be in
place very soon and thus they want to identify and eliminate
causes of inconsistent wait
times. Specifically, they would like these recent wait time
samples to be analyzed:
Calculate the relevant control limits and prepare relevant ±3σ
quality control chart(s).
Provide an analysis of the “time in system” performance based
on the recent samples,
specifically identifying what, if any, action is recommended.
(Use 4 decimals for
control limit values)

10. Sample
#
Observation
#1 #2 #3 #4 #5
1 32 22 33 28 18
2 42 28 34 24 25
3 27 40 28 24 26
4 24 13 19 21 20
5 29 31 24 36 25
6 26 32 43 17 38
7 31 35 25 39 27
8 31 26 25 32 27
9 29 54 26 38 37
10 38 33 42 34 40
Management 2070Y - Fall 2013 - Assignment #1
Page 4 of 5
3. Process Capability (10 marks)
One of the current government’s campaign promises was to
reduce wait times at health

11. services. Correspondingly, a committee was created and has
been working on
establishing wait time targets for various health services. With
walk-in clinics
impacting the greatest portion of the voters, the government has
been keen to implement
wait time specifications in this area of health services first.
The local health region has received a draft of the government’s
wait time specifications
that they plan to make effective on January 1
st
, 2009. The specification is that 95% of
individuals must have a wait time of less than 60 minutes at a
walk-in-clinic. Only
health regions that meet this specification will be eligible for a
new program where
private donations are matched by the government.
In preparation for adhering to wait time specifications, the local
health region has
researched various improvement alternatives (all with similar
costs), including running
software simulations to obtain statistical data on how each

12. alternative would perform
regarding wait times (see below).
Process Description Mean Wait Time Wait Time
Standard Deviation
Current Continue as-is
45 15
Alternative #1 Hire additional
doctors / nurses
40 12
Alternative #2 Build additional
assessment rooms
37 15
Alternative #3 Purchase portable
diagnostic equipment
39 9
Prepare a chart that shows how effectively each process would
address the government’s
new specifications (6 marks)

13. Note: Add columns to the above table to calculate z-values,
probability, and to comment
on the capability. Show all calculations to receive full marks.
Z-Value Probability Comment
15-10 = 1.00
5
.8413 Not capable –
not even close
In addition to the calculated values, management is looking for
further insights. They
would first like to know how capable their current process is of
meeting the new
specification. Management would also like to know which of
the alternatives you
recommend, if any, they undertake considering the
government’s new specifications and
why. (4 marks)
Management 2070Y - Fall 2013 - Assignment #1

14. Page 5 of 5
4. Pareto Analysis (10 marks)
Research into causes of excessive wait times has revealed data
on the most common
causes. Prepare a Pareto Analysis graph of the following data
(the Microsoft Excel
graph type of “Line – Column on 2 axes” is recommended) (6
marks)
Cause Details # of occurrences
Doctor calls in sick Fewer doctors available to
service individuals
4
Assessment rooms full Staff available, but no
assessment rooms available
39
Supplies not available Assessment room ran out of
supplies
16
Individual Missing Individuals called for
treatment but not in the

15. immediate vicinity
48
Registration system
issues
Software “crashes” and bugs
delay administration
12
Do you have any suggestions to help address the two most
common causes? (4 marks)
5. Cost of Quality (5 marks)
The local health region has been piloting a “healthphone”
service, where nurses field
calls and provide a preliminary assessment for individuals with
health concerns. This
form of “inspection” has proven to be valuable in reducing wait
times at walk-in-clinics,
while improving customer satisfaction. Many individuals
receive sufficient over the
phone guidance to deal with their health concern and thus do
not go to a walk-in clinic.

16. Thanks to extensive use of information technology (healthphone
nurses can answer calls
in their own homes while connected to the healthphone database
over the internet),
operating costs for the service are considerably less than the
operating costs at a walk-in
clinic.
The healthphone Operations Manager would like to expand their
service by hiring more
nurses, however the health region’s finance department is
adamant that the current
budget is “very tight” and that there is “no new money” for such
expenditures.
Prior to approaching the accounting department for budgetary
approval, healthphone’s
Operations Manager has asked you to prepare a clear and
concise summary explanation
of how the “cost of quality” concept can be applied to this
scenario. It is hoped that
your summary will help to get the expenditure approved even
though “there is no new
money available”. Can include conceptual graph, but apply the

17. concepts to this scenario for written points
Problem 1
Samples of n=4 items each are taken from a manufacturing
process at regular intervals. A quality characteristic is
measured, and x-bar and R values are calculated for each
sample. After 25 samples, we have:
X-bar = 107.5
å
R = 12.5
Assume that the quality characteristic is normally distributed.
a) Compute control limits for the x-bar and R control charts
b) Estimate the process mean and standard deviation
c) Assuming that the process is in control, what are the natural
tolerance limits of the process?
d) If the specifications limits are 4.4
±
0.2. What is the process capability? Is the process capable of

18. meeting the specifications?
e) Assuming that if any item exceeds the upper specification
limit it can be reworked, and if it is below the lower
specification limit, it must be scrapped, what percent scrap and
rework is the process producing?
f) If the unit cost of scrap and rework are $2.4 and $0.75,
respectively, find the total daily cost of scrap and rework.
g) If a process average shifts to 4.5 mm, what is the impact on
the proportion of scrap and rework produced?
Problem 2
Using the following data
Samples
Date/Time
9/8/12 7:30 AM
9/8/12
7:45 AM
9/8/12
8:00 AM
9/8/12
8:15 AM
9/8/12
8:30 AM
9/8/12 8:45 AM
9/8/12 9:00 AM

19. 9/8/12
9:15 AM
9/8/12
9:30 AM
9/8/12
9:45 AM
1
2
3
4
5
6
7
8
9
10
1
18.84
35.41
20.5
34.81
40.97
41.79
36.67
38.75
13.98
20.95
2
23.93
29.52
27.29
32.32

20. 29.12
78.77
34.4
35.93
22.53
40.41
3
19.48
33.55
32.36
36.93
32.74
62.37
31.02
29.83
35.65
37.21
a. Calculate the center lines and the upper and lower control
limits for the average and
standard deviation charts for the three-sigma limits (show
equations and substitution).
b. Create an x-bar and s-chart for the data provided (Use
Minitab or Excel).
c. Using the rule below for out of control conditions, is the
process in control, and which subgroup (s) are out of control?
Rule 1: Points outside the control limits
d. Remove any out of control points, re-calculate the control
limits. What are the revised center lines and control limits?
e. Assuming that the process is in control above (even if it
wasn’t), what is the estimated standard deviation?
Problem 3
Construct charts for individuals using both two-period and
three-period moving ranges for the following observations (in
sequential order). Show the equations used for the control limits

21. and centerline with the substitutions. You can use Minitab or
Excel to build the charts.
Note: those are individual observations.
7.2
8.5
7.4
9.5
16.3
17.1
8.1
7.4
14.7
17.3
15.5
4.3
8.5
16.9
17.2
6.2
15.1
11.5
7.5
12.8
13.5
16.9
Problem 4
The metal body for a spark plug is made by a combination of
cold extrusion and machining. The occurrence of surface
cracking following the extrusion process has been shown by
Pareto diagrams to be responsible for producing virtually all of
the defective parts. To identify opportunities for improvement,
you have been using a control chart to monitor the process. The
probability of a false alarm is 0.0056

22. a. On average, how many samples will you take before getting
an out of control signal?
b. What is the probability that there will be no false alarms in
the next 15 samples taken?
c. What is the probability that there will be at least one false
alarm in the next 50 samples?
d. In a standard control chart the control limits are 3 standard
deviations away from the mean, and the probability of a false
alarm is 0.0027. Given that the probability of a false alarm for
this chart is .0056, how many standard deviations away from the
center line are the control limits?
e. Suppose the process mean shifts such that the probability of
f. What is the probability of failing to detect the shift by the
9th sample collected?
_1459499870.unknown
_1459499871.unknown
_1459499872.unknown
_1459499869.unknown
ENGG381-14A Engineering Statistics Due: Monday 9th June
Assignment 5
1
Produce a report which clearly presents your responses to the fo
llowing tasks. Brevity is appreciated
but explain what needs to be explained! You may discuss suitabl
e approaches with classmates but must
work independently on your own report. You should submit you

23. r report using Moodle by 10.50 pm
Monday 9th June.
TASK A: SPC for Rod Thickness
rodthickness2014.mtw
[23 marks]
A plant manufactured approximately 12,000 connecting rods per
day for use in an engine assembled
in the plant. The rod, illustrated above, connects the piston (at t
he small or pin end of the rod) to the
crankshaft (at the large or crank end of the rod). The plant recei
ved forged blanks and machined the
rods in a large number of process steps.
Management identified the rod line for a variation reduction pro
ject because the overall scrap cost
was greater than budget. The yearly scrap cost was excessive, a
nd the scrap rate had been 3.2% over
the previous four months. Looking at scrap records, the team fo
und that scrap occurred at several
stages in the process and for several reasons. The results showe
d that 65% of the scrap occurred at a
grinding operation. At this operation, the team discovered that a
bout 90% of the scrap was due to
rods with their crank end thickness less than specification. The t
eam focused their attention on
reducing variation in rod thickness. Their first step was to set u
p control charts to see whether the
grinding step produced rods with a stable crank end thickness.
The worksheet contains the output from the first five days of ch
arting. Thicknesses were recorded

24. from subgroups of 5 consecutive rods chosen at 8 times spread t
hrough each day. As in normal
operation, each rod was measured at 4 positions (white circles i
n figure); the worksheet contains their
mean thickness as a deviation from 0.900 inches in thousandths
of an inch (i.e. mil). In that scale the
specification range is [10, 60] mil and in practice if any of the 4
deviation measurements was less than
10 mil the rod would be scrapped. Those with any over 60 mil w
ere reworked.
In this assignment, however, we will assume that the specificati
on interval applies to mean thickness.
To do this, you will need to create a new variable, MnThick, wh
ich is the average thickness across the
four positions for each rod.
based on a Steiner and
MacKay case study
ENGG381-14A Engineering Statistics Due: Monday 9th June
Assignment 5
2
Question 1
a) Display an and X s
chart for MnThick established from the first 3 days but plotting
all data so

25. both establishment and monitoring periods may be displayed on
one plot (use Stat > Control
Charts > Variables Charts for Subgroups > Xbar‐S, and enter th
e appropriate details in Xbar‐S
Options under the Estimate tab). You should also include a refe
rence line to distinguish
establishment and monitoring periods. [2 marks]
b)
List what if any actions should have been taken after the establi
shment period and then
during monitoring, given that the objective was to achieve and/o
r demonstrate process
stability. [2 marks]
Question 2
a)
Now repeat the control chart analysis of the process mean using
the EWMA chart (see Stat >
Control Charts > Time‐Weighted Charts > EWMA). You should
as before establish on the first
24 subgroups. [2]
b)
Provide plausible explanations where this chart suggests differe
nt courses of actions
compared to the previous question. [2 marks]
Question 3
Use the Minitab Stat > Quality Tools > Capability Analysis > N
ormal menu to produce a capability
analysis display for the mean thickness data which compares the
data recorded with the specification.

26. [3 marks]
Question 4
Based on the analyses above, write a statement which summaris
es the quality of the rods in relation
to the mean thickness specification, and comment on whether th
e analysis is likely to assist with the
scrap reduction objective. [3 marks]
Question 5
Now construct a new artificial mean thickness variable by subtr
acting 5.54 from each data value after
subgroup 26.
a)
Recreate the charts of questions 1 and 2 for the new variable. [2
marks]
b)
Comment on whether the results are consistent with the informa
tion on average run lengths
displayed in the extracts from Caulcutt’s book in the Topic 9 lec
ture notes. [2 marks]
Question 6
Does treating the specifications as being applicable to the mean
over 4 positions increase or decrease
the percentage of rods classed as out‐of‐specification? Explain
without referring to the data provided.
[2 marks]
Question 7
Investigate whether it is important to consider position when co
nsidering reasons for scrap. [3 marks]

27. ENGG381-14A Engineering Statistics Due: Monday 9th June
Assignment 5
3
TASK B: SPC for Pigment Manufacture Process
dizogoblue2014.mtw
[17 marks]
A company manufactures a range of pigments for use in the text
ile industry. One particular pigment,
dizogo blue, is made by a well‐established plant which has rece
ntly been renovated. For example the
capacity has been increased and the agitation system has been m
ade fully automatic. The data file
contains information collected from the first 50 batches after re
novation. It is feared that the
expected increase in yield has not yet been realised and that the
level of particular impurity has
increased. A data logger has also recorded incidents where the
agitation speed has been
automatically reduced because the agitator was overloaded.
Question 1
a)
Treating the 50 batches as an establishment period, set up indivi
duals control charts to
monitor the average levels of yield and impurity under the new
conditions. [1 mark]

28. b)
Comment on what you conclude from the control charts. [2 mar
ks]
Question 2
a)
Explain why it is more important to check data normality for an
individuals chart than for an
X ‐ s chart. [2 marks]
b)
Use probability plots to check data normality for the two variabl
es being monitored and draw
conclusions, being careful to recognise that non‐normality migh
t sometimes be just an
indicator of the presence of special causes. [3 marks]
Question 3
a)
Repeat the setting up of an individuals chart for impurity but thi
s time choose I Chart Options
> Box‐Cox > Optimal Lambda. [2 marks]
b) Explain what you now conclude. [2 marks]
Question 4
a) Set up a EWMA chart for impurity. [1 mark]
b)
Explain what you conclude, and whether this differs from the pr
evious analysis. [2 marks]
c)
Describe the different purposes of an I chart and a EWMA chart

29. . [2 marks]
ENGG381-14A Engineering Statistics Due: Monday 9th June
Assignment 5
4
TASK C: Statistical Engineering Algorithmfor
truckpull2014.mtw
Truck Pull [19 marks]
This data set presents another view of the baseline study of Truc
k Pull from Steiner and MacKay
previously described in lectures. The full data set contains data
on the 28,258 trucks manufactured
over 44 days. The data file truckpull2014.mtw has the alignment
information for every tenth truck off
the line and we have restricted the data set to the first 40 produc
tion days, which we will treat as 8
five‐day weeks. (Check the column formulae & descriptions in t
he Minitab worksheets for useful
information.)
Pull = 0.23 × (r‐caster – l‐caster) – 0.13 × (r‐camber –
l‐camber)
crosscaster = (r‐caster –
l‐caster) and crosscamber = (r‐camber – l‐camber)

30. Question 1
a)
Display means and standard deviations for the four alignment an
gles and also pull. [1 mark]
b)
Assume that the alignment angles are approximately independen
t of each other. Show how
you would calculate estimates of the mean and standard deviatio
n of pull from the sample
means and standard deviations for the individual alignment angl
es. [2 marks]
c)
Caculate the percentage error in your calculated estimate of the
standard deviation of pull
compared to the observed sample standard deviation of pull. Sta
te whether you would expect
your calculated values of the mean and standard deviation of pu
ll to match the observed
sample mean and standard deviation. Explain your reasoning.
[3 marks]
Question 2
a)
Note: the following analysis is more easily done in Excel than
Minitab. Assuming the estimate
of the SD of pull you calculated in Question 1 was satisfactory,
for each angle calculate the
reduction in the standard deviation of pull which could be achie

31. ved if you halved the standard
deviation of just that angle (i.e. calculate the reduction for r‐ca
ster, l‐caster, r‐camber, l‐
camber one at a time, separately) . Which alignment angle does
this analysis suggest should
be worked on to reduce variation in pull? [2 marks]
b)
Extend your “theory” from part a) to usefully identify the single
component to be worked on
to most reduce the standard deviation for an “assembly of indep
endent components” of the
general form
21 1 2 3 3 4 4
Y a X a X a X a X . [2 marks]
c)
What practical consideration implies that the strategy suggested
in part b) will not always be
helpful, even if the component angles are independent? [1 mar
k]
Part C, Slide 231
Part A, Slide 59
ENGG381-14A Engineering Statistics Due: Monday 9th June
Assignment 5

32. 5
[OPTIONAL] Question 3
In slide 237 of topic 10, it is suggested that variation in pull mi
ght be reduced if assembly was
“selective” instead of “random”. In other words we might consi
der the theoretical benefit of being
able to match the alignment angles of an assembly to reduce var
iation in pull. In the data file
truckpull2014.mtw I have created two new columns sortxcaster
and sortxcamber by sorting the
crosscaster and crosscamber columns (separately) from lowest t
o highest values.
a)
Plot crosscaster against crosscamber, and sortxcaster against sor
txcamber. Display the linear
correlation coefficients for these two plots.
b)
What can you deduce about the theoretical potential for a reduct
ion in pull variation from
selective assembly? (Be quantitative. Hint: be the manufacturer!
)
Question 4
Staff applying the “statistical engineering algorithm” for improv
ing crosscaster have decided that the
dominant cause of variability lies in the “between trucks” famil
y not the “between weeks” “between

33. days” or “between shifts” families.
a)
Produce a fully nested analysis of variance for the crosscaster v
ariable (see Stat > ANOVA).
Recall that for a nested ANOVA, you need to specify the predict
or variables in order from the
highest level of nesting (i.e. weeks in this case) to the lowest. U
se the output to evaluate the
decision to focus on the variation between trucks. You may assu
me the baseline variation
covers the interval [‐0.1, 2.1]. [2 marks]
b)
Calculate the percentage reduction in the overall standard deviat
ion for crosscaster if we
could completely remove the truck‐to‐truck variation. [2 mark
s]
c)
Based on the estimate of overall standard deviation of crosscast
er from the nested ANOVA,
calculate the Capability Ratio (Cp) for crosscaster when it has s
pecification limits of 0.975 ± 0.9.
What is Cp if we manage to completely eliminate truck‐to‐truck
variation? [2 marks]
d)
What is the implication of the choice of dominant cause on how
the reduction project should
proceed? [2 marks]

34. Part C, Slide 159