Description
Case 8- Improving a commercial bank’s operation performance through statistical process control. The paper states that after the elimination of special causes, they observe that “.. the average cycle time and the variances (e.g. the distance between UCL and LCL) tremendously reduced, which were not only reflected in X chart, but in the R chart. ” Please review the control charts and discuss the causes of the performance improvements.Think about your own operations. Can you identify opportunities to use the SPC control map to improve the operation performance? Please discuss. Review and comment on at least one other student submissionControl ChartIf you have used Control Charts or Process Capability Analysis in your business, please share briefly your experience with these tools.Additional Resources are available in the course Content/course resources/statistical ramp-up.SPC 1. Home work is attached
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Journal of the Chinese Institute of Industrial Engineers
Vol. 27, No. 3, May 2010, 226–236
Improving a commercial bank’s operation performance
through statistical process control
Ming-Ching Tsai and Chao Ou-Yang*
Department of Industrial Management, School of Management, National Taiwan University of
Science and Technology, 43 Sec. 4, Keelung Road, Taipei, Taiwan, Republic of China
(Received September 2009; revised November 2009; accepted December 2009)
A cross-border remittance process was selected by a Taiwanese bank to pilot the test application
of statistical process control (SPC). The results support the conclusion that the theoretical model
developed in the last century is also applicable in financial institutions. The main interest of this
research is to follow the success of the pilot case with three more work processes of the bank replicated
SPC to further test its feasibility. The case of branch service counter processing, described in this
article, proves that the adoption of SPC would easily detect special causes and common causes.
Importantly, solutions would be easily generated based on the results of measuring process stability
and capability. The case studies in this research reiterate that SPC is a powerful tool to improve a
bank’s operation performance.
Keywords: statistical process control; process stability; process capability; bank’s operation
1. Introduction
Statistical process control (SPC) is a tool that
applies basic statistics to control processes [3].
Smith [8] proclaimed that statistical process control
must be adopted as an integral part of a long-term
policy for continuous improvement in product
quality and productivity. If SPC is limited to the
use of control charts only, positive results will be
rather limited.
This research aims to understand and prove
whether the SPC tools applied overwhelmingly in
manufacturing sectors are equally practical in
financial institutions. Senior operation officers of
a Taiwanese commercial bank were interviewed
with empirical evidence. To undergo this research,
in the first stage, a pilot case was selected to go
through the whole process of SPC. The second
stage was to select three more work processes of the
bank to test whether the concept and practice of
removing special causes and common causes could
help improve its operation performance in an
efficient manner. This research also tries to provide
a unique opportunity to examine some key success
factors pertinent to SPC implementation in a
financial institution.
2. Literature review
The importance of quality and statistical process
control as strategic tools has been well established in
the manufacturing community, as proven by
*Corresponding author. Email: [email protected]
ISSN 1017–0669 print/ISSN 2151–7606 online
ß 2010 Chinese Institute of Industrial Engineers
DOI: 10.1080/10170661003644152
http://www.informaworld.com
Deming when he introduced the concept of
process stability in his book, ‘‘Some Principles of
the Shewhart Methods of Quality Control,
Mechanical Engineering’’ [2]. The concept has also
been extended to the service sector in the 1990s [11].
There are hundreds of thousands of reports in the
literature focused on quality improvement and the
application of statistical process control in manufacturing sectors. For example, BrännströmStenberg and Deleryd [1] conducted a survey to
find out whether requirements from customers or
other reasons caused organizations within Swedish
industry to implement SPC and process capability
approaches.
Some authors, for instance Wheeler [10], tried
to link the concept of SPC not only to the
production of goods but also to the offering
of services. There have been several investigations
into SPC applications in hospital, logistics, and
hotel industries [4,6,9]. However, very few have
tried to introduce SPC or quality improvement
initiatives in financial institutions. Newman and
Cowling [7] presented an empirical study of major
quality improvement initiatives undertaken by two
British banks. Li et al. [5] conducted a survey of the
entire population of licensed banks in Hong Kong
on their quality management initiatives and analyzed the status of quality management initiatives
in Hong Kong as well as comparing the results with
those from UK financial institutions. Other than
the above-mentioned papers, published literature
Journal of the Chinese Institute of Industrial Engineers
referring to the use of SPC, particularly in financial
institutions, can scarcely be discovered.
The framework proposed in this article aims
to address the limitations of the above-mentioned
research. To supplement the research into SPC
theory built by Shewhart, this article tries to prove
that the SPC framework (or SPC roadmap as
described in later passages) can also be useful in
financial institutions.
for customers. The interviews with pertinent information were conducted in the operation units
located in Taipei.
Because of the implementation of SPC with
positive results of the chosen case of a cross-border
remittance operation, the bank continuously strived
for quality programs in the following years in fields
such as the processing of mortgage loans, vehicle
loan take-down, transactions handled by the bank’s
branch service counter, etc. In addition to the
remittance operation case, three more SPC-related
quality programs implemented from 2005 to 2008
will also be briefly described in this article to illustrate applications of the SPC roadmap.
This article tries to prove a framework that
shows a systematic approach to apply the SPC
technique in improving the bank’s operations
performance. A SPC roadmap is a framework
that the bank adopted for its inception of quality
programs. It is illustrated in Figure 1.
The whole concept of the SPC roadmap is to
review and evaluate the stability and capability of
the existing processes in order to constantly
improve every process for the bank’s products
and services.
The first stage in the quantitative problemsolving case analysis is to identify the top-priority
process to improve. Once the top-priority process
is determined, its current process will then be
documented by cross-functional process mapping.
Afterwards, data collection will be conducted
3. Methodology
A case study methodology was adopted with
analysis of the bank’s documents and
semi-structured interviews in order to track the
processes undertaken by the bank to pursue the
service quality improvement of remittance operations in the back-office. Yin [12] observed, ‘‘The
case study’s unique strength is its ability to deal
with a full variety of evidence – documents,
artifacts, interviews, and observations.’’ A series
of interviews was set up in the bank with the
co-operation and support of the senior managers
responsible for the day-to-day operations. The
purpose of these interviews was twofold: first to
obtain factual information about the use of SPC,
and second to obtain the progress and results of
business process improvement initiatives conducted by the bank’s staff in delivering a higher
quality service level of remittance operations
Choose top-priority process
Document the existing process
Data
collection
Identify &
remove
special cause
variation
Is process
stable?
N
Y
Is process
capable?
Y
Standardize and replicate
Figure 1. Statistical process control roadmap.
227
N
Investigate
common cause
variation &
improve the
capability
228
M.-C. Tsai and C. Ou-Yang
to figure out its performance in terms of either cycle
time or accuracy.
Furthermore, the bank will select an appropriate control chart to evaluate whether the process is
stable. If the process is proved unstable, the bank
will then identify the special causes and come up
with solutions to fix the problems. If the process is
proved stable, the bank shall further analyze the
capability of the process.
In case the process is proved to be incapable,
operation officers of the bank should find out
the common cause to improve its capability. If the
process is later on analyzed to be capable, the
operation officers can then standardize the process,
and replicate it to other processes or systems.
4. The pilot case
Prudential Bank (a pseudonym) is a profitable
commercial bank with headquarters in Taipei,
Taiwan. The bank joined the club of new private
banks in 1991 when the authority deregulated and
encouraged around a dozen new banks to enter the
market to enhance the competitiveness of the
banking industry in Taiwan. The total assets of
Prudential Bank today is more than NTD $1.4
trillion dollars with more than 10% capital adequacy ratio. Prudential Bank has around 10,000
employees and more than 100 branches.
Having restructured the bank’s organization
since 1998, Prudential Bank centralized some of
its processing from branches to operations centers.
The major purpose of operation centralization
is to tackle economies of scale so that the bank’s
operation cost would be significantly reduced.
Meanwhile, along with the independence of credit
and operation, the bank may take the benefit of
more rigid internal control and risk management.
The concept was introduced by several leading USbased banks and was later adopted by Prudential
Bank.
While centralization of operation and credit
becomes a secret recipe for improving the bank’s
operation cost and risk, it generated an unexpected
side effect: an unintended longer cycle time of
processing. Owing to the back-and-forth delivery of
documents and excessive communication between
branches and processing centers, the end-to-end
turnaround time turned out to be longer than
before. As a consequence, the bank’s customer
satisfaction in terms of timeliness and accuracy of
the transaction processing was suffering low scores
after the centralization of operations.
4.1 Choose top priority process
In June 2004, Prudential Bank distributed a
customer satisfaction survey to 400 corporate
clients to track customers’ feedback toward the
two major cross-border product processes, namely
outward remittance (OR) and inward remittance
(IR). By comparing the results from the 2003
survey, the bank found that the overall satisfied
ratio in 2004 was higher than 2003, while the
satisfied ratio of IR handling speed was the lowest
among all product items surveyed, as stated in
Table 1. Prudential Bank then decided to focus on
IR processing as a top priority process.
Since cycle time performance has become a
major concern, the bank’s operation head decided
to measure its transaction cycle time in operation
centers and thereafter came up with possible cause
analysis. A possible cause analysis for IR processing
was conducted and is stated in Figure 2.
Examples of these probable causes were: late
approval; waiting for customer’s confirmation; late
processing; insufficient checkers; insufficient
makers; lunch hour; peak load; and data errors.
Two issues were then raised. First of all, those
factors were not specific enough to take specific
actions for cycle time reduction. Secondly, the
possible cause analysis was a semi-annual period
analysis. The period might have been too long for
managers to identify root causes. Hence, the
operation head decided to follow the steps of an
SPC roadmap, as illustrated in Figure 1, and to
understand more about the work processes.
Table 1. Customer survey result.
Overall
Satisfied þ very
satisfied (%)
Dissatisfied þ very
dissatisfied (%)
Service
attitude
Trouble case
handling skill
Outward
remittance
IR
speed
2003
2004
2003
2004
2003
2004
2003
2004
2003
2004
81.39
83.98
82.51
93.35
84.23
92.58
79.76
83.39
70.35
73.25
3.88
5.36
3.26
0.89
4.42
0.88
3.02
2.83
0.78
1.12
229
Journal of the Chinese Institute of Industrial Engineers
90
A
B
C
D
E
F
G
H
I
J
81
80
69
70
60
53
50
41
40
30
Late approval
Wait for customers confirmation
Late processing
Insufficient checkers
Peak load
Lunch time
Wait for documents
Insufficient makers
Data error
Others
24
20
10
0
A
B
C
D
E
11
9
8
7
F
G
H
I
7
Figure 2. Possible causes of long cycle time of inward remittance processing.
1. Swift messages are
routed to Imaging
system automatically
Is transaction
intended to be
credited to
foreign currency
account?
2. Makers call customers and
inquire the source of fund (for
regulatory requirement)
Y
N
5. Checkers verify
and approve
6. Credit to customers’ account
4. Makers manually key in
information into FITAS based
on swift messages
3. Makers inquire customers’
contact telephone numbers
and fee amount (for foreign
exchange)
7. Branch staff inform
customers
Figure 3. Inward remittance process map.
4.2 Document the process
To understand the processing center’s process of
IR, a series of meetings was conducted by key
officers of the processing center so that a process
map describing specific steps of handling IR could
be documented, as shown in Figure 3.
The as-is process of handling IR involved
different systems and stakeholders, including external customers, makers, checkers in the operation
center, and staff in branches. In order to further
understand the nature of the work processes,
data collection to measure cycle time was required.
The total cycle time of IR was defined as being from
‘‘swift message was routed’’ (Step 1 in Figure 3) to
the system to ‘‘customer’s account was credited’’
(Step 6 in Figure 3).
4.3 Data collection
At that time, daily transactions of IR in Prudential
Bank were around 700. The bank’s computer
system was functioning so well that transaction
time was real-time recorded. To manage performance, the bank randomly selected 25 data points
from 30 September 2004 to 5 November 2004 and,
on each day, it also randomly selected six data for
analysis as shown in Table 2.
4.4 Process stability
X and R control charts are constructed based on
the data input and shown in Figure 4. Apparently,
the process was not stable given that two data
points were out of UCL of X chart and one data
point was out of UCL of R chart.
230
M.-C. Tsai and C. Ou-Yang
Table 2. Data collection result: from 9/30 to 11/5.
X1
X2
X3
X4
X5
X6
X1
X2
X3
X4
X5
X6
9/30
10/1
10/4
10/5
10/6
10/7
10/8
10/11
10/12
10/13
10/14
10/15
10/18
1
2
3
4
5
6
7
8
9
10
11
12
13
202.00
120.00
117.00
110.00
117.00
116.00
122.00
176.00
43.00
123.00
113.00
287.00
455.00
453.00
103.00
102.00
135.00
135.00
177.00
36.00 106.00
128.00
34.00 108.00
128.00
56.00 11.00
342.00
56.00
9.00
155.00 138.00
75.00
177.00 296.00
75.00
400.00
174.00
90.00
336.00
279.00
137.00
248.00
250.00
43.00
172.00
42.00
39.00
20.00
20.00
61.00
64.00
25.00
72.00
81.00
44.00
51.00
57.00
100.00
43.00
110.00
111.00
114.00
116.00
116.00
67.00
142.00
162.00
62.00
182.00
66.00
249.00
89.00
89.00
103.00
112.00
114.00
116.00
10/20
10/21
10/22
10/26
10/27
10/28
10/29
11/1
11/2
11/3
11/4
11/5
14
15
16
17
18
19
20
21
22
23
24
25
49.00
137.00
249.00
550.00
168.00
11.00
226.00
111.00
41.00
154.00
153.00
276.00
327.00
203.00
126.00
118.00
22.00
116.00
172.00
163.00
32.00
82.00
425.00
35.00
51.00
67.00
111.00
273.00
56.00
128.00
43.00
9.00
60.00
56.00
130.00
28.00
111.00
67.00
79.00
24.00
15.00
100.00
8.00
13.00
54.00
48.00
141.00
100.00
130.00
90.00 100.00
72.00
21.00
56.00 101.00
87.00
144.00
83.00 97.00 239.00
144.00
9.00 142.00 192.00
155.00 364.00
98.00
19.00
153.00 241.00
8.00 19.00
Figure 4. X bar R control chart plotted by SPC software: from 9/30 to 11/5.
Source: The bank.
4.5 Identify and eliminate special causes
Immediately following the graphing of the control
charts, the task force was asked to identify the
special causes that made the IR process not stable.
Given that these possible causes had been stated by
operations staff in a vague manner before, the
operation head guided the task force to focus on
the special causes which would lead to more specific
causes, as illustrated in Table 3. To remove the
special causes so as to stabilize the process, the task
force generated ideas and proposed the solutions
stated in Table 4.
These solutions were rolled out and, meanwhile,
starting from 5 November to 10 December, the
bank continuously kept using the control limits
that were already established in the previous period
to monitor whether cycle time performance of IR
would be in control or not.
By looking at the control charts of both X and
R charts graphed by the software and indicated
in Figure 5, we realize that its data points were
all laid in the middle of UCL and LCL. As a result,
the daily cycle time samples during the time
between 5 November and 10 December show that
the process turned out to be in control after
implementation of the major solutions.
The performance shown in Table 5 also reveals
that the average cycle time and the variances (e.g.
the distance between UCL and LCL) tremendously
reduced, which were not only reflected in X chart,
but in the R chart.
4.6 Process capability
Although the process in the period of November
and December became stable, the bank tried to
231
Journal of the Chinese Institute of Industrial Engineers
Table 3. Determination of special causes.
Special causes determination
Possible causes
Specific causes
¼)
High volumes of IR Swift messages
Reject
Lunch time
Insufficient manpower of checkers or makers
Got around 300 IR messages during 14:00–15:00
Checker found key-in mistake made by maker
Checkers or makers go to lunch causing no timely handling
Insufficient number of on-duty checkers or makers due to
attending meeting or leaves
Makers or checker do not follow the rule of first-in/first-out
processing
Makers or checkers delay processing
Source: This research.
Table 4. Solutions to remove special causes.
Special causes
Solutions
Received around 300 IR message during 14:00–15:00
Insufficient number of on-duty checker or makers due to
attending meeting or leaver
Makers or checkers do not follow the rule of first-in/
first-out processing
Implement flexible shifts and avoid absence of staff so as
to process daily peak volume
Implement ‘‘idiot proof ’’ by restricting the first-in/
last-out processing in the system
200.00
UCL=151.25
150.00
CL = 86.02
100.00
50.00
LCL=20.80
0.00
1
300.00
250.00
200.00
150.00
100.00
50.00
0.00
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24 25
UCL=239.08
CL = 113.04
LCL= 0
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24 25
Figure 5. X bar R control chart plotted by SPC software: from 11/5 to 12/10.
Source: This research.
figure out whether the process was capable. The
bank determined the upper specification of IR (or
Su) to be 120 min. The bank used those data
collected in the period of 5 November to 10
December to calculate process capability.
CLX ¼ X ¼ 86:02
Cpk ¼
Su X 120 86:02
¼
¼ 0:21 5 1
3S
3 53:99
Since Cpk 5 1, the cycle time performance of IR
was not capable.
4.7 Identify and eliminate common causes
Any member of staff that plays the role of maker in
the operation center is required to input more than
10 fields, including branch code, into a system
Table 5. Comparison of inward remittance cycle time
(before and after process became stable).
X (before)
UCL
CL
LCL
X (after) R (before)
221.36
151.25
123.91 ¼) 86.02
26.46
20.80
404.33
201.76
0.
R (after)
239.08
¼) 113.04
0
Source: This research.
based on a Swift message sent by remitter’s bank. It
is a tedious and time-consuming manual input.
This was identified as the key common cause of not
making the process capable. To tackle this common
cause, a solution was determined by the task force
where the manual key-in activity might be replaced
by an automatic transfer from the Swift message to
232
M.-C. Tsai and C. Ou-Yang
Figure 6. Data to be input based on Swift message.
Source: The bank.
the bank’s accounting system. The solution would
definitely reduce processing time for data key-in,
makers’ errors, and checkers’ approval time.
Finally, a system automation was launched
in late December, immediately following the discovery of its process incapability. The system screen
would look like Figure 6. The other solution
generated by the task force was to speed up
faxing of information to the customer by automating the fax process. The solution would reduce
processing time to verify the customer-pertinent
information.
One week after the system enhancement was
in place, data collection was made for calculation
of its process capability. Based on the data collection, the process capability of IR for OBU was
determined as follows:
Cpk ¼
Su X 120 86:02
¼
¼ 0:21 5 1:
3S
3 53:99
The average cycle time reduced tremendously
from 239.19 min down to 0.03 min after system
enhancement. Apparently, the process soon became
capable for OBU IR immediately following automation of the data capture process. Likewise,
although only 50% of the DBU remittance could
be automated, the average cycle time for processing
it was reduced to 74.93 min from 123.91 min and its
Cpk value also became larger than 1.
Cpk ¼
Su X 120 74:93
¼
4 1:
3S
3 0:02
5. Replication
In addition to the products of cross-border IR,
from 2005 to 2008, the SPC roadmap was also
applied to the bank’s processing of mortgage loans,
vehicle loans, and branch operations. All of the
three processes were significantly improved
through identification and removal of special
causes and common causes. The case of branch
service counter processing is described next.
5.1 Process stability
To measure performance of branch service counter
transaction processing, 25 data points were collected through randomly selecting five observation
samples each day. The result of the process stability
shows:
CLX ¼ X ¼ 6:43 min
UCL ¼ 10.57 min
LCL ¼ 2.29 min
CLR ¼ R ¼ 7:14 min
UCL ¼ 15.06 min
LCL ¼ 0 min.
Given that there were three data points plotted
beyond the upper control limit of the X control
chart, the process was found not to be well in
control. The data set is shown in Table A1.
5.2 Eliminate special causes
The key special causes were then identified by
experienced operation officers as follows:
(1) Supervisors took annual leave or attended
meetings.
(2) Peak hours in lunchtime.
(3) Delay due to untrained newly recruited
staff.
Journal of the Chinese Institute of Industrial Engineers
The solutions to tackle process issues were
initiated were implemented as follows:
(1) Deputy supervisors are informed in any
event of counter service jam to support
exception cases handling.
(2) Service counter staff members are confined
to takes turns for lunch to alleviate customer queuing.
(3) Update SOPs and put staff certification
program in place.
After solutions were in place, the process finally
became in control. The data is shown below and the
data set is shown in Table A2:
CLX ¼ X ¼ 5:68 min
UCL ¼ 8.33 min
LCL ¼ 3.02 min
CLR ¼ R ¼ 4:58 min
UCL ¼ 9.66 min
LCL ¼ 0 min.
5.3 Process capability
The task force then measured the process capability
of branch service counter transaction handling.
Cpk ¼
4 5:68
¼ 0:31,
3 1:81
where Su ¼ 4 min and S ¼ 1.81. Since Cpk value was
less than 1, the process was not capable.
5.4 Eliminate common causes
The following major common causes were discovered by the bank’s branch officers:
(1) It is quite time consuming for service counter
clerks to manually record the events book,
the events log, and complete filing.
(2) The system was, on the other hand, already
upgraded to be able to record and generate
reports for the audit trail.
The solutions stated below were quickly implemented through the information department’s
assistance:
(1) Substitute hand-writing of the events book
and records with a printed report generated
from the system.
(2) Eliminate the hand-writing tasks of event
logs and filing.
After the system solutions and process simplification were implemented, the process capability
was calculated and the data set is shown in
Table A3. The result was
Cpk ¼
4 3:94
¼ 0:01,
3 1:33
233
where Su ¼ 4 min and S ¼ 1.33. Although Cpk value
was less than 1, the process capability was
improved significantly now that the average processing time became less than specification
required.
6. Conclusion
(1) The model, namely the SPC roadmap, was
developed and tested using empirical evidence from various operation units of a
Taiwanese commercial bank. Two cases
were tested and the results show that the
theoretical model is effective and workable.
(2) The two case studies indicate that all of the
average and the standard deviation (SD) of
the cycle time (or processing time) of those
processes were tremendously reduced
through the use of the SPC roadmap.
(3) These case studies also reveal that the more
the bank invested in system enhancement
to improve processes, the more the Cpk value
might be raised. The solutions implemented
to remove common causes in the case of the
remittance operation explain themselves.
(4) The whole concept of using an SPC roadmap
is proved to easily undergo a continuous
improvement approach through identifying
special causes and common causes and then
remove them. After removal of common
causes, even though the Cpk value may not
always become equal to or larger than 1, the
processes in question were all significantly
improved.
(5) The key success factors of adopting SPC,
as described in the cases and expressed by
the operation heads and key staff of the
bank, are as follows:
. To remove special causes, system
enhancement may not be so critical.
Instead, the effort to streamline
process of the bank’s operations
(e.g. reschedule an employee’s onduty shift, follow the rule of first-in/
first-out) is vital for success.
. To remove common causes and
fundamentally improve the bank’s
process capability, system enhancement (e.g. automatic file transfer,
auto-faxing, consolidate functions
among different systems) should be
a key success factor.
. The special causes and common
causes must be identified in a
manner that underlying solutions
can be generated and implemented
to make the bank’s operation
234
M.-C. Tsai and C. Ou-Yang
processes stable as well as capable.
The SPC roadmap does allow the
bank’s operation officers to specify
root causes rather than just brainstorm possible but vague causes.
Notes on contributors
Ming-Ching Tsai (also known as Mark Tsai) is a
doctorate degree student of the Executive Doctor of
Business Administration (EDBA) program of NTUST.
Chao Ou-Yang is a professor in the Department of
Industrial Management, National Taiwan University of
Science and Technology. He received his PhD from
the Department of Industrial and Systems Engineering,
The Ohio State University. His main research interests
include business process management, concurrent engineering, and collaborative engineering. He is also
Associate Dean of School of Management of NTUST.
References
[1] Brännström-Stenberg, A. and M. Deleryd,
‘‘Implementation of statistical process control and
process capability studies: requirements or free will?,’’
Total Quality Management, 10, 439–446 (1999).
[2] Grant, E.L. and R.S. Leavenworth, Statistical
Quality Control, John Wiley & Sons, New York
(1988).
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Appendix
Table A1. Data set of branch counter service processing
before special causes were removed (from 5 March 2007
to 11 April 2007).
Table A2. Data set of branch counter service processing
after special causes were removed (from 15 May 2007 to
15 June 2007).
Data set
Data set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
.
3
4.5
6.4
5
4.5
6.5
5.5
4
5
3
3
3
4
6
5
6
5
4
5
6
7
6
5
4
6.5
7
8.4
7.6
3
6.5
3.4
6.5
25
4
4
5
6.5
6
21
12
4
5
13
4
3
24
15
4
6
5
7
4
6
2.5
7.5
5.3
7
7.5
3.5
7
5
5
6
4
5
7
6.5
4.5
5
6
3
6
4
5
3.5
8
3.2
9.5
7
8.5
5.5
6.5
9.5
7.5
7.5
6.5
7.5
20
22
3.5
5
4.5
5.5
5
6.5
17
2
4
3
7.5
6.5
5
8.5
5
3.2
7.6
4.3
8.6
6
6.5
7.5
4.5
3.5
4.5
5.5
5.5
4.5
4.5
7.5
6
5.5
7
6.5
8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
4.5
5.5
5
6.5
5
6.5
6.4
9
8.3
4
5
5.7
4
3
6
7.1
5
5.3
4.8
3
5.2
6.4
3.7
8.5
5.6
5
6
5
4
5
6
7
5
3.4
6
3
6.5
10
4
9.5
3
4
7
4.4
5
5.5
9.2
8.4
5
6.2
5
5
7
4
6
2.5
7.5
5
7.5
3.5
4
6
6.5
8
4.2
4
5
5
3
4.5
3
4.7
3
4.5
5.3
7
7.5
3.5
7
5
5
6
4.7
5
7.8
5
4.6
5
6.4
3
6
4
4.3
9
5.3
8.2
6.2
4.6
4
3.8
7.5
8
12
3.5
8
3.2
9.1
7
5.2
5.5
8
8.2
8
7.5
6.5
5
8.4
4.4
4
9.2
5
6
4.5
5.2
7.5
Journal of the Chinese Institute of Industrial Engineers
Table A3. Data set of branch counter service processing
after common causes were removed (from 23 July 2007 to
24 August 2007).
Data set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
4.1
2
3
5.5
4
4
5.2
4.5
3
4.5
2
2.4
2
2.3
4.7
3
2.9
3.3
3.4
3.8
5
4.4
2.9
3
4.3
4.2
6
4
4.5
3.3
3.6
4.4
5.8
8.3
3
3.6
5
7.4
6.8
7.8
6.6
2.8
3.8
4
2
3.7
7
6
3.5
3
4.7
5
3.8
4
4.7
2
3
3
3
3.8
4
3.9
2.7
3.3
2.7
2
3.8
5
3.8
3.4
3
1.9
4
3.7
2.7
3.8
3
4.2
4.2
4
2.4
2
2
2.7
3.7
3.6
5
5
7.8
2.8
3.8
4
3
4
5
4.5
5
4.3
3
1.9
2.2
2
3
4.8
5
4
4
3
3
4
3.8
3.7
4.9
5.8
6
4.6
4.5
3.9
3.8
2.8
2.8
3.7
5.8
6.3
4.8
235
236
M.-C. Tsai and C. Ou-Yang
*
4
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Session 8 Homework Problems
1- The following data are the production units from a manufacturing line for the past 8
weeks. The manager wants to know if the process is stable and in control. Produce Xbar and R charts and comment on the process
Week
1
2
3
4
5
6
7
8
Monday
12
6
15
8
20
13
10
10
Tuesday
15
9
11
7
12
10
14
15
Wednesday Thursday
8
7
11
13
9
6
6
11
10
5
9
8
11
8
17
11
Friday
10
7
12
14
14
12
5
9
2- A project manager at Q Corporation has a commitment to deliver 200 cylinders to a
customer. The internal diameter of these cylinders must be 60 centimeters. The
tolerance is +1 and -0.5 centimeter. If the mean value of the production process is 60.4
and the standard deviation is 0.5,
a- Calculate the process capability index (CP and CPk) and indicate if the process is
capable.
b- How many cylinders the PM should plan to produce in order for 200 of them to meet
specification.
c- What should be the standard deviation in order for the process to become capable?
Note the process is not centered.
3- A product has specification limits of 18 to 20. If the process mean is 19.2 and the
standard deviation is 0.6, calculate
a. The process capability for this production line.
b. Is the process Cable?
c. What % of the products are out of specs if any?
d. What should be the process standard deviation in order for the process to
become capable?
1
© UMGC/MHFallah
4- An IT organization has a service level agreement (SLA) with a major customer requiring
that tier 1 calls/problems be resolved within 12 hours. There is a penalty of $150 for
each call that takes more than 12 hours to resolve.
The IT manager has developed the following data:
Average Daily volume of tier one calls is 30 with a standard deviation of 8 calls
Mean processing time in the center is 10 hours with a standard deviation of 1.1 hour
a- Calculate the % daily tier 1 problems that misses the SLA.
b- Estimate the annual penalty cost to the center.
c- If you were the manger, would you add another technician to help desk to avoid the
penalty cost. Why or why not. Use your own estimate and rationale.
2
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