Chapter Topics
• Total Quality Management (TQM)
• Theory of Process Management (Deming’s Fourteen points)
• The Theory of Control Charts
Common Cause Variation Vs Special Cause Variation
• Control Charts for the Proportion of Nonconforming
Items
• Process Variability
• Control charts for the Mean and the Range
Control Charts
•
Monitors Variation in Data
– Exhibits Trend - Make Correction Before
Process is Out of control
•
Show When Changes in Data Are Due to
– Special or Assignable Causes
• Fluctuations Not Inherent to a Process
• Represents Problems to be Corrected
• Data Outside Control Limits or Trend
– Chance or Common Causes
• Inherent Random Variations
Process Control Chart
•
Assignable
Cause time
X
Variation 60
Graph of sample data plotted over
UCL
40
Mean Process
Average
3s
LCL
20
0
Random
Variation
1
3
5
7
Time
9
11
Control Limits
•
•
UCL = Process Average + 3 Standard Deviations
LCL = Process Average - 3 Standard Deviations
X
UCL
+ 3s
Process
Average
- 3s
LCL
TIME
Types of Error
•
First Type: Belief that Observed Value
Represents Special Cause When in Fact it
is Due to Common Cause
•
Second Type: Treating Special Cause
Variation as if it is Common Cause
Variation
Comparing Control Chart
Patterns
X
Common Cause
Variation: No Points
Outside Control Limit
X
X
Special Cause
Downward Pattern:
Variation: 2 Points
No Points Outside
Outside Control Limit
Control Limit
When to Take Corrective
Action
Corrective Action should be Taken When
Observing Points Outside the Control
Limits or When a Trend Has Been Detected:
•
•
1. Eight Consecutive Points Above the
Center Line (or Eight Below)
2. Eight Consecutive Points that are
Increasing (Decreasing)
p Chart
•
•
Control Chart for Proportions
Shows Proportion of Nonconforming Items
–
e.g., Count # defective chairs & divide by
total chairs inspected
•
•
Chair is either defective or not defective
Used With Equal or Unequal Sample Sizes
Over Time
–
Unequal sizes should not differ by more than
± 25% from average sample size
p Chart
Control Limits
p(1 p)
LCLp = p  3
n
Average Group Size
k
n
Average Proportion of
Nonconforming Items
k
 ni
_
p 
i 1
k
p
(
1

p
)
UCLp = p  3
n
# of Samples
 X
i1
k
i
 ni
i 1
# Defective
Items in
Sample i
Size of
Sample i
p Chart
Example
•You’re manager of a
500-room hotel. You
want to achieve the
highest level of service.
For 7 days, you collect
data on the readiness of
200 rooms. Is the
process in control?
p Chart
Hotel Data
•
•
Day
1
2
3
4
5
6
7
# Rooms
200
200
200
200
200
200
200
# Not
Ready Proportion
16
0.080
7
0.035
21
0.105
17
0.085
25
0.125
19
0.095
16
0.080
p Chart
Control Limits Solution
k
n
ni


i 1
k
16 + 7 +...+ 16
k

1400
7
 200
p
 Xi
i 1
k
 ni

121
1400
.0864
i 1
_
p  3  p ( 1  p )  . 0864  3  .0864  (1.0864 )
n
200
 . 0864  .0596 or (
,.1460 )
.0268
p Chart
Control Chart Solution
0.15
P
UCL
_
Mean p
0.10
0.05
LCL
0.00
1
2
3
4
Day
5
6
7
Variable Control Charts: R
Chart
•Monitors Variability in Process
•Characteristic of interest is measured on interval or
ratio scale.
•Shows Sample Range Over Time
•Difference between smallest & largest values in
inspection sample
•e.g., Amount of time required for luggage to be
delivered to hotel room
R Chart
Control Limits
UCLR  D4  R
From
Table
LCLR  D3  R
k
R 
 Ri
i 1
k
Sample
Range
at Time i
# Samples
R Chart
Example
•You’re manager of a
500-room hotel. You
want to analyze the time
it takes to deliver
luggage to the room. For
7 days, you collect data
on 5 deliveries per day.
Is the process in control?
R Chart & Mean Chart Hotel
Data
•
•
Day
1
2
3
4
5
6
7
Sample
Average
5.32
6.59
4.88
5.70
4.07
7.34
6.79
Sample
Range
3.85
4.27
3.28
2.99
3.61
5.04
4.22
R Chart
Control Limits Solution
k
_
R 
 Ri
i 1
k

3.85  4.27 L 4.22
7
 3.894
UCLR  D4  R  2.114  3.894  8.232
LCLR  D3  R  0  3.894  0
From
Table E.9
(n = 5)
R Chart
Control Chart Solution
Minutes
8
6
4
2
0
1
2
UCL
_
R
LCL
3
4
Day
5
6
7
Mean Chart (The X Chart)
•
Shows Sample Means Over Time
–
–
•
Compute mean of inspection sample over time
e.g., Average luggage delivery time in hotel
Monitors Process Average
Mean Chart
_
_
_
_
_
_
Computed
From
Table
UCLX_  X  A2  R
Sample
Mean at
Time i
LCLX_  X  A2  R
_
X i
k
__
X 
i 1
k
k
_
and R 
 Ri
i1
k
Sample
Range
at Time i
# Samples
Mean Chart
Example
•You’re manager of a 500room hotel. You want to
analyze the time it takes to
deliver luggage to the room.
For 7 days, you collect data
on 5 deliveries per day. Is
the process in control?
R Chart & Mean Chart
Hotel Data
•
•
Day
1
2
3
4
5
6
7
Sample
Average
5.32
6.59
4.88
5.70
4.07
7.34
6.79
Sample
Range
3.85
4.27
3.28
2.99
3.61
5.04
4.22
Mean Chart
Control Limits Solution
_
 Xi
k
__
X 
i 1
k

5.32  6.59  L  6.79
7
 5.813
k
_
R
 Ri
i 1

3.85  4.27  L  4.22
 3.894
From
Table E.9
(n = 5)
k _
7
_
_
UCL _  X  A2  R  5.813  0.577  3.894  8.060
X
__
_
LCL _  X  A2  R  5.813  0.577  3.894  3.566
X
Mean Chart
Control Chart Solution
Minutes
8
6
4
2
0
1
2
UCL
LCL
3
4
Day
5
6
7
__
X
Six sigma
SIGMA PPM
(best
case)
PPM
(worst
case)
Misspellings
Examples
1 sigma
317,400 697,700
170 words per page
Non-competitive
2 sigma
45,600
308,733
25 words per page
IRS Tax Advice
(phone-in)
3 sigma
2,700
66,803
1.5 words per page
Doctors prescription
writing (9,000 ppm)
4 sigma
64
6,200
1 word per 30 pages
(1 per chapter)
Industry average
5 sigma
0.6
233
1 word in a set of
encyclopedias
Airline baggage
handling (3,000 ppm)
6 sigma
0.002
3.4
1 in all of the books
in a small library
World class