Cost of quality
1. Prevention costs
2. Appraisal costs
3. Internal failure costs
4. External failure costs
5. Opportunity costs
What is quality management all about?
Try to manage all aspects of the organization in order to excel in all dimensions that are
important to “customers”
Two aspects of quality: features: more features that meet customer needs = higher quality freedom from trouble: fewer defects = higher quality
The Quality Gurus – Edward Deming
1900-1993
1986
�Quality is “uniformity and dependability”
�Focus on SPC and statistical tools
�“14 Points” for management
�PDCA method
The Quality Gurus – Joseph Juran
1904 - 2008
1951
�Quality is “fitness for use”
�Pareto Principle
�Cost of Quality
�General management approach as well as statistics
History: how did we get here…
• Deming and Juran outlined the principles of Quality Management.
• Tai-ichi Ohno applies them in Toyota Motors Corp.
• Japan has its National Quality Award (1951).
• U.S. and European firms begin to implement Quality Management programs (1980’s).
• U.S. establishes the Malcolm Baldridge National Quality Award (1987).
• Today, quality is an imperative for any business.
What does Total Quality Management encompass?
TQM is a management philosophy:
• continuous improvement
• leadership development
• partnership development
Cultural Alignment
Technical Tools
(Process Analysis, SPC,
QFD)
Customer
Developing quality specifications
Input Process Output
Design Design quality
Dimensions of quality
Conformance quality
Six Sigma Quality
• A philosophy and set of methods companies use to eliminate defects in their products and processes
• Seeks to reduce variation in the processes that lead to product defects
• The name “six sigma” refers to the variation that exists within plus or minus six standard deviations of the process outputs
σ6±
Six Sigma Roadmap (DMAIC) Next Project Define
Customers, Value, Problem Statement
Scope, Timeline, Team
Primary/Secondary & OpEx Metrics
Current Value Stream Map
Voice Of Customer (QFD) Measure
Assess specification / Demand
Measurement Capability (Gage R&R)
Correct the measurement system
Process map, Spaghetti, Time obs.
Measure OVs & IVs / Queues
Analyze (and fix the obvious) Root Cause (Pareto, C&E, brainstorm)
Find all KPOVs & KPIVs
FMEA, DOE, critical Xs, VA/NVA
Graphical Analysis, ANOVA
Future Value Stream Map
Improve Optimize KPOVs & test the KPIVs
Redesign process, set pacemaker
5S, Cell design, MRS
Visual controls
Value Stream Plan
Control Document process (WIs, Std Work)
Mistake proof, TT sheet, CI List
Analyze change in metrics
Value Stream Review
Prepare final report
Validate
Project $
Validate
Project $
Validate
Project $
Validate
Project $
Celebrate
Project $
Continuous improvement philosophy
1. Kaizen: Japanese term for continuous improvement. A step-by-step improvement of business processes.
2. PDCA: Plan-do-check-act as defined by Deming.
Plan Do
Act Check
3. Benchmarking : what do top performers do?
Tools used for continuous improvement
4. Cause and effect diagram (fishbone)
Environment
Machine Man
Method Material
Tools used for continuous improvement
5. Check sheet
Item A B C D E F G
-------
-------
-------
√ √ √
√ √
√ √
√
√
√ √
√ √ √
√
√
√
√
√ √
Tools used for continuous improvement
7. Pareto Analysis
A B C D E F
Freq
uenc
y
Per
cent
age
50%
100%
0%
75%
25% 10 20
30
40
50
60
Summary of Tools
1. Process flow chart
2. Run diagram
3. Control charts
4. Fishbone
5. Check sheet
6. Histogram
7. Pareto analysis
Case: shortening telephone waiting time…
• A bank is employing a call answering service
• The main goal in terms of quality is “zero waiting time” - customers get a bad impression - company vision to be friendly and easy access • The question is how to analyze the situation and improve quality
The current process
Custome
r B
Operator Custome
r A
Receiving
Party
How can we reduce waiting time?
Makes
custome
r wait
Absent receiving
party
Working system of
operators
Customer Operator
Fishbone diagram analysis
Absent
Out of office
Not at desk
Lunchtime
Too many phone calls
Absent
Not giving receiving
party’s coordinates
Complaining
Leaving a
message
Lengthy talk
Does not know
organization well
Takes too much time to
explain
Does not
understand
customer
Daily average
Total number
A One operator (partner out of office) 14.3 172
B Receiving party not present 6.1 73
C No one present in the section receiving call 5.1 61
D Section and name of the party not given 1.6 19
E Inquiry about branch office locations 1.3 16
F Other reasons 0.8 10
29.2 351
Reasons why customers have to wait (12-day analysis with check sheet)
Pareto Analysis: reasons why customers have to wait
A B C D E F
Frequency Percentage
0%
49%
71.2%
100
200
300 87.1%
150
250
Ideas for improvement
1. Taking lunches on three different shifts
2. Ask all employees to leave messages when leaving desks
3. Compiling a directory where next to personnel’s name appears her/his title
Results of implementing the recommendations
A B C D E F
Frequency Percentage
100%
0%
49%
71.2%
100
200
300 87.1%
100%
B C A D E F
Frequency Percentage
0%
100
200
300
Before… …After
Improvement
In general, how can we monitor quality…?
1. Assignable variation: we can assess the cause
2. Common variation: variation that may not be possible to correct (random variation, random noise)
By observing variation in
output measures!
Statistical Process Control (SPC)
Every output measure has a target value and a level of “acceptable” variation (upper and lower tolerance limits)
SPC uses samples from output measures to estimate the mean and the variation (standard deviation)
Example
We want beer bottles to be filled with 12 FL OZ ± 0.05 FL OZ
Question:
How do we define the output measures?
In order to measure variation we need…
The average (mean) of the observations:
∑=
=N
i
ixN
X1
1
The standard deviation of the observations:
N
XxN
i
i∑=
−
= 1
2)(σ
Average & Variation example
Number of pepperoni’s per pizza: 25, 25, 26, 25, 23, 24, 25, 27
Average:
Standard Deviation:
Number of pepperoni’s per pizza: 25, 22, 28, 30, 27, 20, 25, 23
Average:
Standard Deviation:
Which pizza would you rather have?
When is a product good enough?
Incremental Cost of Variability
High
Zero
Lower Tolerance
Target Spec
Upper Tolerance
Traditional View
The “Goalpost” Mentality
a.k.a Upper/Lower Design Limits
(UDL, LDL) Upper/Lower Spec Limits
(USL, LSL)
Upper/Lower Tolerance Limits (UTL, LTL)
But are all ‘good’ products equal?
Incremental Cost of Variability
High
Zero
Lower Spec
Target Spec
Upper Spec
Taguchi’s View
“Quality Loss Function”
(QLF)
LESS VARIABILITY implies BETTER PERFORMANCE !
Capability Index (Cpk)
It shows how well the performance measure fits the design specification based on a given
tolerance level
A process is kσ capable if
LTLkXUTLkX ≥−≤+ σσ and
1and1 ≥−−
≤σσ k
LTLX
k
XUTL
Capability Index (Cpk)
Cpk < 1 means process is not capable at the kσ level
Cpk >= 1 means process is capable at the kσ level
−−
=σσ k
XUTL
k
LTLXC pk ,min
Another way of writing this is to calculate the capability index:
Accuracy and Consistency
We say that a process is accurate if its mean is close to the target T. We say that a process is consistent if its standard deviation is low.
X
Example 1: Capability Index (Cpk)
X = 10 and σ = 0.5
LTL = 9 UTL = 11
667.05.03
1011or
5.03910
min =
×
−
×
−=pkC
UTL LTL X
Example
Consider the capability of a process that puts pressurized grease in an aerosol can. The design specs call for an average of 60 pounds per square inch (psi) of pressure in each can with an upper tolerance limit of 65psi and a lower tolerance limit of 55psi. A sample is taken from production and it is found that the cans average 61psi with a standard deviation of 2psi.
1. Is the process capable at the 3σ level? 2. What is the probability of producing a defect?
Solution
LTL = 55 UTL = 65 σ = 2 61=X
6667.0)6667.0,1min()6
6165,
6
5561min(
)3
,3
min(
==−−
=
−−=
pk
pk
C
XUTLLTLXC
σσ
No, the process is not capable at the 3σ level.
Solution
P(defect) = P(X<55) + P(X>65) =P(X<55) + 1 – P(X<65) =P(Z<(55-61)/2) + 1 – P(Z<(65-61)/2) =P(Z<-3) + 1 – P(Z<2) =G(-3)+1-G(2) =0.00135 + 1 – 0.97725 (from standard normal table)
= 0.0241
2.4% of the cans are defective.
Example (contd)
Suppose another process has a sample mean of 60.5 and a standard deviation of 3. Which process is more accurate? This one. Which process is more consistent? The other one.
Control Charts
Control charts tell you when a process measure is exhibiting abnormal behavior.
Upper Control Limit
Central Line
Lower Control Limit
Two Types of Control Charts
• X/R Chart
This is a plot of averages and ranges over time (used for performance measures that are variables)
• p Chart
This is a plot of proportions over time (used for performance measures that are yes/no attributes)
When should we use p charts?
1. When decisions are simple “yes” or “no” by inspection
2. When the sample sizes are large enough (>50)
Sample (day) Items Defective Percentage
1 200 10 0.050
2 200 8 0.040
3 200 9 0.045
4 200 13 0.065
5 200 15 0.075
6 200 25 0.125
7 200 16 0.080
Statistical Process Control with p Charts
Statistical Process Control with p Charts
Let’s assume that we take t samples of size n …
size) (samplesamples) ofnumber (defects"" ofnumber total×
=p
n
pps p
)1( −=
p
p
zspLCL
zspUCL
−=
+=
066.0151
200680
==×
=p
017.0200
)066.01(066.0=
−=ps
015.0 017.03 066.0
117.0 017.03 066.0
=×−=
=×+=
LCL
UCL
Statistical Process Control with p Charts
When should we use X/R charts?
1. It is not possible to label “good” or “bad”
2. If we have relatively smaller sample sizes (<20)
Statistical Process Control with X/R Charts
Take t samples of size n (sample size should be 5 or more)
∑=
=n
i
ixn
X1
1
}{min }{max ii xxR −=
R is the range between the highest and the lowest for each sample
Statistical Process Control with X/R Charts
X is the mean for each sample
∑=
=t
j
jXt
X1
1
∑=
=t
j
jRt
R1
1
Statistical Process Control with X/R Charts
X is the average of the averages.
R is the average of the ranges
RAXLCL
RAXUCL
X
X
2
2
−=
+=
define the upper and lower control limits…
RDLCL
RDUCL
R
R
3
4
=
=
Statistical Process Control with X/R Charts
Read A2, D3, D4 from Table TN 8.7
Example: SPC for bottle filling…
Sample Observation (xi) Average Range (R)
1 11.90 11.92 12.09 11.91 12.01
2 12.03 12.03 11.92 11.97 12.07
3 11.92 12.02 11.93 12.01 12.07
4 11.96 12.06 12.00 11.91 11.98
5 11.95 12.10 12.03 12.07 12.00
6 11.99 11.98 11.94 12.06 12.06
7 12.00 12.04 11.92 12.00 12.07
8 12.02 12.06 11.94 12.07 12.00
9 12.01 12.06 11.94 11.91 11.94
10 11.92 12.05 11.92 12.09 12.07
Example: SPC for bottle filling…
Sample Observation (xi) Average Range (R)
1 11.90 11.92 12.09 11.91 12.01 11.97 0.19
2 12.03 12.03 11.92 11.97 12.07 12.00 0.15
3 11.92 12.02 11.93 12.01 12.07 11.99 0.15
4 11.96 12.06 12.00 11.91 11.98 11.98 0.15
5 11.95 12.10 12.03 12.07 12.00 12.03 0.15
6 11.99 11.98 11.94 12.06 12.06 12.01 0.12
7 12.00 12.04 11.92 12.00 12.07 12.01 0.15
8 12.02 12.06 11.94 12.07 12.00 12.02 0.13
9 12.01 12.06 11.94 11.91 11.94 11.97 0.15
10 11.92 12.05 11.92 12.09 12.07 12.01 0.17
Calculate the average and the range for each sample…
Finally…
91.1115.058.000.12
09.1215.058.000.12
=×−=
=×+=
X
X
LCL
UCL
Calculate the upper and lower control limits
015.00
22.115.011.2
=×=
=×=
R
R
LCL
UCL