Chapter Topics

1
Chapter Topics

• Total Quality Management (TQM)
• Theory of Process Management (Demings 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

2
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

3
Process Control Chart

• Graph of sample data plotted over time

Assignable Cause Variation
UCL
Process Average 3s
Mean
LCL
Random Variation
4
Control Limits

• UCL Process Average 3 Standard Deviations
• LCL Process Average - 3 Standard Deviations

X
UCL
3s
Process Average
- 3s
LCL
TIME
5
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

6
Comparing Control Chart Patterns
X
X
X
Special Cause Variation 2 Points Outside Control
Limit
Common Cause Variation No Points Outside Control
Limit
Downward Pattern No Points Outside Control Limit
7
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)

8
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

9
p Chart Control Limits
LCLp
UCLp
Average Proportion of Nonconforming Items
Average Group Size
Defective Items in Sample i
_
p
of Samples
Size of Sample i
10
p Chart Example

• Youre 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?

11
p Chart Hotel Data

• Not Day Rooms Ready Proportion
• 1 200 16 0.080 2 200 7 0.035 3 200 21 0.105
  4 200 17 0.085 5 200 25 0.125 6 200 19 0.095 7
  200 16 0.080

12
p Chart Control Limits Solution
16 7 ... 16
k
k
å
å
n
X
i
i
1400
121

i
i

1
1





200
0864
.
n
p

k
k
7
1400
å
n
i
i

1
_
(
)

-
0864
1
0864
.
.
p

3


0864
.


3
200
or
)
(


0864
0596
.1460
.
.
,
.0268
13
p Chart Control Chart Solution
P
UCL
0.15
_
0.10
Mean p
0.05
LCL
0.00
1
2
3
4
5
6
7
Day
14
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

15
R Chart Control Limits
From Table
UCL
D
R


R
4
LCL
D


R
R
3
Sample Range at Time i
k
å
R
i
i

1
R

k
Samples
16
R Chart Example

• Youre 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?

17
R Chart Mean Chart Hotel Data

• Sample Sample Day Average Range
• 1 5.32 3.85 2 6.59 4.27 3 4.88 3.28 4 5.70 2.9
  9 5 4.07 3.61 6 7.34 5.04 7 6.79 4.22

18
R Chart Control Limits Solution
k
å
R
_
i



3
85
4
27
4
22
.
.
.
L
i

1
R



3
894
.
k
7

UCL
D




2
114
3
894
8
232
.
.
.
R
R
4
From Table E.9 (n 5)

LCL
D




0
3
894
0
.
R
R
3
19
R Chart Control Chart Solution
Minutes
UCL
8
_
6
4
R
2
LCL
0
1
2
3
4
5
6
7
Day
20
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

21
Mean Chart
Computed From Table
_
_
_
_
X

UCL
A


R
2
X
Sample Mean at Time i
_
_
_
_
LCL
X
A
R

-

2
X
Sample Range at Time i
_
k
k
å
å
R
X
_
i
i
_
_
i
i

1
1


and
X
R

k
k
Samples
22
Mean Chart Example

• Youre 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?

23
R Chart Mean Chart Hotel Data

• Sample Sample Day Average Range
• 1 5.32 3.85 2 6.59 4.27 3 4.88 3.28 4 5.70 2.9
  9 5 4.07 3.61 6 7.34 5.04 7 6.79 4.22

24
Mean Chart Control Limits Solution
_
k
å
X
_
_
i



5
32
6
59
6
79
.
.
.
L
i

1
X



5
813
.
k
7
k
å
R
From Table E.9 (n 5)
_
i



3
85
4
27
4
22
.
.
.
L
i

1
R



3
894
.
k
7
_
_
_
_
X
R
UCL
A






5
813
0
577
3
894
8
060
.
.
.
.

2
_
X
_
_

_
X
R
LCL
A
-


-

5
813
0
577
3
894
3
566
.
.
.
.

2
X
25
Mean Chart Control Chart Solution
Minutes
UCL
8
_
_
6
X
4
LCL
2
0
1
2
3
4
5
6
7
Day
26
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