OPSM 501: Operations Management
Week 7:
Quality
Koç University Graduate School of BusinessMBA Program
Zeynep [email protected]
The Ottoman Catapult
Lord of the Rings: Mordor Catapult
Lord of the Rings: Gondor Catapult
Angry Birds Catapult
The OPSM Catapult!
Process Capability 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 +/- 6x or 12
x
3 3
process width
min acceptable
max acceptable
Design tolerance width
There are multiple solutions to most parametric design problemsAnalytical Expression for Brownie Mix “Chewiness”
Chewiness = FactorA + FactorB
Where FactorA = 600(1-exp(-7T/600)) + T/10
And FactorB = 10*TimeFactorA
Temperature
FactorB
Time200F 400F 20 min26 min
Option 1
Option 2
HYPOTHETICAL
Options 1 and 2 deliver the same value of “chewiness.” Why might you prefer one option over the other?
Taguchi Methods
1. Any deviation from the target value is “quality lost.”
Minimum acceptable value
Maximum acceptable value
Target value
Quality
Good
Bad
Performance Metric
Target value
QualityLoss
Performance Metric, x
Loss = C(x-T)2
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?
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
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
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
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
Natural and Assignable Variation
1. Process Capability
Design requirements:Diameter: 1.25 inch ±0.005 inch
Specification Limits
Lower specification Limit:LSL=1.25-0.005=1.245Upper Specification Limit:USL=1.25+0.005=1.255
Example:Producing bearings for a rotating shaft
Relating Specs to Process LimitsProcess performance (Diameter of the products produced=D):Average 1.25 inchStd. Dev: 0.002 inch
Frequency
Frequency
DiameterDiameter1.25
Question:What is the probability That a bearing does not meet specifications?(i.e. diameter is outside (1.245,1.255) )
006.0)5.2(1)5.2()002.0
25.1255.1()255.1(
006.0)5.2()5.2()002.0
25.1245.1()245.1(
NORMSDISTzPzPDP
NORMSDISTzPzPDP
P(defect)=0.006+0.006=0.012 or 1.2% This is not good enough!!
Process capability
What can we do to improve capability of our process? What should be to have Six-Sigma quality?
We want to have: (1.245-1.25)/ = 6 =0.00083 inch We need to reduce variability of the process. We cannot change specifications
easily, since they are given by customers or design requirements.
•If P(defect)>0.0027 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
Six Sigma Quality
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
3
X-USLor
3
LSLXmin=Cpk
183.0)002.03
25.1255.1,
002.03
245.125.1min(
xxC pk
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
Process Capability Index Cp
Process Interval = 6
Specification interval = US –LS
Cp= (US-LS) / 6
Process Interval = 60
Specification Interval = US – LS = 60
Cp= (US-LS) / 6 = 60 / 60 = 1
Process IntervalSpecification Interval
99.73%
USLS
100 160
= 10
Process Capability Index Cp
Process Interval = 6 = 30
Specification Interval = US – LS =60
Cp= (US-LS) / 6 =2
Specification Interval6 Process Interval
3 Process Interval
USLS
100 160 = 5
99.73%
99.99998%
Process Mean Shifted
USLS
100 160
= 10
130
Cpk = min{ (US - )/3, ( - LS)/3 }
Cpk = min(2,0)=0
Specification
3 Process
70
2. Statistical Process Control: Control Charts
Can be used to monitor ongoing production process quality
Can be used to monitor ongoing production process quality
970
980
990
1000
1010
1020
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
LCL
UCL
Mean and Range ChartsMean and Range Charts
(a)(a)
These These sampling sampling distributions distributions result in the result in the charts belowcharts below
(Sampling mean is (Sampling mean is shifting upward but shifting upward but range is consistent)range is consistent)
R-chartR-chart(R-chart does not (R-chart does not detect change in detect change in mean)mean)
UCLUCL
LCLLCL
x-chartx-chart(x-chart detects (x-chart detects shift in central shift in central tendency)tendency)
UCLUCL
LCLLCL
Mean and Range ChartsMean and Range Charts
R-chartR-chart(R-chart detects (R-chart detects increase in increase in dispersion)dispersion)
UCLUCL
LCLLCL
(b)(b)
These These sampling sampling distributions distributions result in the result in the charts belowcharts below
(Sampling mean (Sampling mean is constant but is constant but dispersion is dispersion is increasing)increasing)
x-chartx-chart(x-chart does not (x-chart does not detect the increase detect the increase in dispersion)in dispersion)
UCLUCL
LCLLCL
Process Control and Improvement
LCL
UCL
Out of Control In Control Improved
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
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
http://lab.responsive.net/lt/koc/start.html
Code: operations– Screening begins right after all groups are registered: explore interface
and first 50 days’ data– Start simulation Monday Nov 12 @ 17:00– End simulation Monday Nov 20 @ 17:00– Report due-in class week 9
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