1. OPSM 501: Operations Management
Koç University Graduate School of Business
MBA Program
OPSM 501: Operations Management
Week 7:
Quality
Zeynep Aksin

2. The Ottoman Catapult

3. Lord of the Rings: Mordor Catapult

4. Lord of the Rings: Gondor Catapult

5. Angry Birds Catapult

6. The OPSM Catapult!

8. Process Capability 3 3 process width Design tolerance width
Cp = (design tolerance width)/(process width) = (max-spec – min-spec)/ /6x
Example:
Plane is “on time” if it arrives between T – 15min and T + 15min.
Design tolerance width is therefore 30 minutes
x of arrival time is 12 min
Cp = 30/6*12 = 30/72 = 0.42
A “capable” process can still miss target if there is a shift in the mean.
Motorola “Six Sigma” is defined as Cp = 2.0
I.e., design tolerance width is +/- 6x or 12 x 3 3
process width
Design tolerance width
min acceptable
max acceptable

9. There are multiple solutions to most parametric design problems
Analytical Expression for Brownie Mix “Chewiness”
Chewiness = FactorA + FactorB
Where FactorA = 600(1-exp(-7T/600)) + T/10
And FactorB = 10*Time
HYPOTHETICAL
FactorA
FactorB
200F
400F
Temperature
Time
20 min
26 min
Option 1
Option 2
Options 1 and 2 deliver the same value of “chewiness.” Why might you prefer one option over the other?

10. Taguchi Methods Loss = C(x-T)2 Good Bad Quality Quality Loss
Any deviation from the target value is “quality lost.”
Good
Performance Metric
Performance Metric, x
Bad
Minimum acceptable value
Target value
Maximum acceptable value
Target value

11. Who is the Better Target Shooter?
The mean is important, but the variance is very important as well.
Need to look at the distribution.
What are the sources of variability?
How can obvious sources be eliminated?

12. Take Aways Products and processes are causal systems
Typically have lots of variables
Internal variables are set by the manufacturer/provider
Target settings and associated variance
External variables are set by the environment or the user
Target settings and associated variance (variance often much harder to control than with internal variables)
Impossible to eliminate all variability
GOAL: find target settings for variables such that variability in other values of these variables has minimal effect on output/performance….a “robust design.”
Methodology for achieving robust design
Causal model, even if not explicitly analytical
Early exploratory experimentation
Control of variability and increased robustness through design changes
Focused experimentation to refine settings

13. Statistical Quality Control Objectives
1.Reduce normal variation (process capability)
If normal variation is as small as desired, Process is capable
We use capability index to check for this
2.Detect and eliminate assignable variation (statistical process control)
If there is no assignable variation, Process is in control
We use Process Control charts to maintain this

14. Natural Variations Also called common causes
Affect virtually all production processes
Expected amount of variation, inherent due to:
- the nature of the system
- the way the system is managed
- the way the process is organised and operated
can only be removed by
- making modifications to the process
- changing the process
Output measures follow a probability distribution
For any distribution there is a measure of central tendency and dispersion

15. Assignable Variations
Also called special causes of variation
Exceptions to the system
Generally this is some change in the process
Variations that can be traced to a specific reason
considered abnormalities
often specific to a
certain operator
certain machine
certain batch of material, etc.
The objective is to discover when assignable causes are present
Eliminate the bad causes
Incorporate the good causes

16. Natural and Assignable Variation

17. 1. Process Capability Example:Producing bearings for a rotating shaft
Specification Limits
Design requirements:
Diameter: 1.25 inch ±0.005 inch
Lower specification Limit:LSL= =1.245
Upper Specification Limit:USL= =1.255

18. Relating Specs to Process Limits
Process performance (Diameter of the products produced=D):
Average 1.25 inch
Std. Dev: inch
Question:What is the probability
That a bearing does not meet specifications?
(i.e. diameter is outside (1.245,1.255) )
Frequency
Diameter
1.25
P(defect)= = or 1.2% This is not good enough!!

19. Process capability
If P(defect)> then the process is not capable of producing
according to specifications.
To have this quality level (3 sigma quality), we need to have:
Lower Spec: mean-3
Upper Spec:mean+3
If we want to have P(defect)0, we aim for 6 sigma quality, then, we need:
Lower Spec: mean-6
Upper Spec:mean+6
What can we do to improve capability of our process? What should  be to have Six-Sigma quality?
We want to have: ( )/ = 6  = inch
We need to reduce variability of the process. We cannot change specifications easily, since they are given by customers or design requirements.

20. Six Sigma Quality

21. Process Capability Index Cpk
Shows how well the parts being produced fit into the range specified by the design specifications
Want Cpk larger than one
For our example:
Cpk tells how many standard deviations can fit between the mean and
the specification limits.
Ideally we want to fit more, so that probability of defect is smaller

22. Process Capability Index CpUS LS
100
160
 = 10
m = 130
Process Interval = 6
Specification interval = US –LS
Cp= (US-LS) / 6
99.73%
Process Interval = 60
Specification Interval = US – LS = 60
Cp= (US-LS) / 6 = 60 / 60 = 1
Process Interval
Specification Interval

23. Process Capability Index CpUS LS
100
160
 = 5
m = 130
99.73% %
Process Interval = 6 = 30
Specification Interval = US – LS =60
Cp= (US-LS) / 6 =2
3 Process Interval
Specification Interval
6 Process Interval

24. Process Mean Shifted Cpk = min{ (US - )/3, ( - LS)/3 }
100
160
 = 10
m = 100
Cpk = min{ (US - )/3, ( - LS)/3 }
Cpk = min(2,0)=0
Specification
3 Process 70
130

25. 2. Statistical Process Control: Control Charts
Can be used to monitor ongoing production process quality
970
980
990
1000
1010
1020 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
LCL
UCL

26. Mean and Range Charts (a)
These sampling distributions result in the charts below
(Sampling mean is shifting upward but range is consistent)
x-chart
(x-chart detects shift in central tendency)
UCL
LCL
R-chart
(R-chart does not detect change in mean)
UCL
LCL

27. Mean and Range Charts (b)
These sampling distributions result in the charts below
(Sampling mean is constant but dispersion is increasing)
x-chart
(x-chart does not detect the increase in dispersion)
UCL
LCL
R-chart
(R-chart detects increase in dispersion)
UCL
LCL

28. Process Control and Improvement
Out of Control In Control Improved
UCL 
LCL

29. Process Control and Capability: Review
Every process displays variability: normal or abnormal
Do not tamper with process “in control” with normal variability Correct “out of control” process with abnormal variability
Control charts monitor process to identify abnormal variability
Control charts may cause false alarms (or missed signals) by mistaking normal (abnormal) for abnormal (normal) variability
Local control yields early detection and correction of abnormal
Process “in control” indicates only its internal stability
Process capability is its ability to meet external customer needs
Improving process capability involves changing the mean and reducing normal variability, requiring a long term investment
Robust, simple, standard, and mistake - proof design improves process capability
Joint, early involvement in design improves quality, speed, cost

30. For upcoming weeks
Assignment: Turkish Airlines case-due week 8 (do with your study team)
Discuss all, but answer only Question 2 and 6 for your written assignment
For question 6 submit excel sheet as well as explanation in writing
Littlefield simulation calendar (teams of 3)
Register groups by Friday Nov 9
Code: operations
Screening begins right after all groups are registered: explore interface and first 50 days’ data
Start simulation Monday Nov 17:00
End simulation Monday Nov 17:00
Report due-in class week 9