Chapter Topics

• Total Quality Management (TQM)

• Theory of Process Management (Deming’s Fourteen points)

• The Theory of Control ChartsCommon 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

0

20

40

60

1 3 5 7 9 11

X

Time

0

20

40

60

1 3 5 7 9 11

X

Time

• Graph of sample data plotted over time

Assignable Cause Variation

Random Variation

Process Average

Mean

Process Control Chart

UCL

LCL

Control Limits

• UCL = Process Average + 3 Standard Deviations

• LCL = Process Average - 3 Standard Deviations

Process Average

UCL

LCL

X

+ 3

- 3

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 XX

Common Cause Variation: No Points

Outside Control Limit

Special Cause Variation: 2 Points

Outside Control Limit

Downward Pattern: No Points Outside

Control Limit

When to Take Corrective Action

• 1. Eight Consecutive Points Above the Center Line (or Eight Below)

• 2. Eight Consecutive Points that are Increasing (Decreasing)

Corrective Action should be Taken When Observing Points Outside the Control Limits or When a Trend Has Been Detected:

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

n

)p(pp

13

n

)p(pp

13

k

nn

k

ii

1

Average Group Size

k

ii

k

ii

n

X

1

1

Average Proportion of Nonconforming Items

# Defective Items in Sample i

Size of Sample i

# of Samples

LCLp = UCLp =

p_

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

• # NotDay # Rooms Ready Proportion

• 1 200 16 0.0802 200 7 0.0353 200 21 0.1054 200 17 0.0855 200 25 0.1256 200 19 0.0957 200 16 0.080

n

n

kp

X

n

p

ii

k

ii

k

ii

k

1 1

1

1400

7200

121

14000864

3 0864 30864 1 0864

200

0864 0596 .1460

.

.. .

. . or , .0268

p Chart Control Limits Solution

16 + 7 +...+ 16

( )

( )

n

)p(p 1_

p Chart Control Chart Solution

UCL

LCL

0.00

0.05

0.10

0.15

1 2 3 4 5 6 7

P

Day

Mean p_

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 ininspection sample

•e.g., Amount of time required for luggage to be delivered to hotel room

UCL D R

LCL D R

R

R

k

R

R

ii

k

4

3

1

R Chart Control Limits

Sample Range at Time i

# Samples

From Table

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

• Sample SampleDay Average Range

• 1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22

R

R

k

UCL D R

LCL D R

ii

k

R

R

1

4

3

3 85 4 27 4 22

73 894

2114 3 894 8 232

0 3 894 0

. . ..

. . .

.

R Chart Control Limits Solution

From Table E.9 (n = 5)

_

R Chart Control Chart Solution

UCL

02468

1 2 3 4 5 6 7

Minutes

Day

LCL

R_

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

UCL X A R

LCL X A R

XX

kR

R

k

X

X

ii

k

ii

k

2

2

1 1and

Mean Chart

Sample Range at Time i

# Samples

Sample Mean at Time i

Computed From Table

_

__ _

_

_

__

__ _

_

Mean 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

• Sample SampleDay Average Range

• 1 5.32 3.852 6.59 4.273 4.88 3.284 5.70 2.995 4.07 3.616 7.34 5.047 6.79 4.22

X

X

R

X

R

R

X

k

R

k

UCL A

LCL A

ii

k

ii

k

X

X

1

1

2

2

5 32 6 59 6 79

75 813

3 85 4 27 4 22

73 894

5 813 0 577 3 894 8 060

5 813 0 577 3 894 3 566

. . ..

. . ..

. . . .

. . . .

Mean Chart Control Limits Solution

From Table E.9 (n = 5)

__

_

__ _

__ __

_

_

Mean Chart Control Chart Solution

UCL

LCL

02468

1 2 3 4 5 6 7

Minutes

Day

X__

Six sigmaSIGMA 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