Operations Management - 6 th Edition
Roberta Russell & Bernard W. Taylor, III
Copyright 2009 John Wiley & Sons, Inc.
Beni Asllani
University of Tennessee at Chattanooga

 Basics of Statistical Process Control
 Control Charts
 Control Charts for Attributes
 Control Charts for Variables
 Control Chart Patterns
 Process Capability
Copyright 2009 John Wiley & Sons, Inc.
3-2

Product launch activities:
Revise periodically
Ongoing
Activities
Customer Requirements
Product Specifications
Process Specifications
Statistical Process Control:
Measure & monitor quality
Meets
Specifications?
Yes
Conformance Quality
No
Fix process or inputs

 Statistical Process Control
(SPC)
 monitoring production process to detect, correct, and prevent poor quality
 Sample
 subset of items produced to use for inspection
 Control Chart

Is the process within statistical control limits?
UCL
LCL
Copyright 2009 John Wiley & Sons, Inc.
3-4

Inputs
• Facilities
• Equipment
• Materials
• Energy
• Employees
Transformation
Process
Outputs
Goods &
Services
•Variation in inputs create variation in outputs
•Variations in the transformation process create variation in outputs

Basics of Statistical Process Control
Types of Variation (1)
1. Random variation


Also called common cause variation
This type of variation is inherent in a process.



Caused by usual variations in equipment, tooling, employee actions, facility environment, materials, measurement system, etc.
If random variation is excessive, the goods or services will not meet quality standards.
To reduce random variation, we must reduce variation in the inputs and the process
Copyright 2009 John Wiley & Sons, Inc.
3-6

Basics of Statistical Process Control
Types of Variation (2)
2. Non-random variation

Also called special cause variation or assignable cause variation



Caused by equipment out of adjustment, worn tooling, operator errors, poor training, defective materials, measurement errors, etc.
The process is not behaving as it usually does.
The cause can and should be identified and corrected.
Copyright 2009 John Wiley & Sons, Inc.
3-7

 A process is in control if it has no special cause variation.

The process is consistent or predictable.
 SPC distinguishes between common cause and special cause variation
 Measure characteristics of goods or services that are important to customers
 Make a control chart for each characteristic

The chart is used to determine whether the process is in control

 The target is the ideal value

Example: if the amount of beverage in a bottle should be 16 ounces, the target is 16 ounces
 Specification limits are the acceptable range of values for a variable
 Example: the amount of beverage in a bottle must be at least
15.98 ounces and no more than 16.02 ounces.

Range is 15.98
– 16.02 ounces.

Lower specification limit = 15.98 ounces or LSPEC = 15.98 ounces

Upper specification limit = 16.02 ounces or USPEC = 16.02 ounces

Specifications and Conformance Quality
 A product which meets its specification has conformance quality .
 Capable process: a process which consistently produces products that have conformance quality.

Must be in control and meet specifications

 Discrete measures

Discrete means separate or distinct


Good/bad, yes/no (p charts) - Does the product meet standards?
Count of defects (c charts) – the count is a whole number
 Variables – continuous numerical measures

Length, diameter, weight, height, time, speed, temperature, pressure - does not have to be a whole number

Controlled with x-bar and R charts

 A service defect is a failure to meet customer requirements.

Different customers have different requirements.
 Examples of attribute measures used in services

Customer satisfaction surveys – provides customer

 perceptions
Reports from mystery shoppers, based on standards
Employee or supervisor inspects cleanliness, etc., according to standards
Copyright 2009 John Wiley & Sons, Inc.
3-12

 Examples of variable measures used in services





Waiting time and service time
On-time service delivery
Accuracy
Number of stockouts (retail and distribution)
Percentage of lost luggage (airlines)

Web site availability (online retailing or technical support)
Copyright 2009 John Wiley & Sons, Inc.
3-13

 Hospitals
 timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and checkouts
 Grocery stores
 waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors
 Airlines
 flight delays, lost luggage and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance
Copyright 2009 John Wiley & Sons, Inc.
3-14

 Fast-food restaurants
 waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy
 Catalogue-order companies
 order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time
 Insurance companies
 billing accuracy, timeliness of claims processing, agent availability and response time
Copyright 2009 John Wiley & Sons, Inc.
3-15

Out of control
Upper control limit
Process average
Lower control limit
1 2 3 4 5 6
Sample number
7
Copyright 2009 John Wiley & Sons, Inc.
8 9 10
3-16

 Range chart ( R-Chart )
 uses amount of dispersion in a sample
 Mean chart ( x -Chart )
 uses process average of a sample
Copyright 2009 John Wiley & Sons, Inc.
3-17

 Mean chart: sample means are plotted.
 Range chart: sample ranges are plotted.
 Two cases:

The standard deviation is known

The standard deviation is unknown.
Copyright 2009 John Wiley & Sons, Inc.
3-18


= the population mean

= the standard deviation for the population
99.74% of the area under the normal curve is between

- 3
 and

+ 3


 Samples are taken from a distribution with mean
 and standard deviation

.
k = the number of samples n = the number of units in each sample
 The sample means are normally distributed with mean
 and standard deviation
 x

 n when k is large.

UCL = x + z
 x x = x
1
+ x
2 n
+ ... x n
LCL = x z
 x where x = average of sample means
Copyright 2009 John Wiley & Sons, Inc.
3-21

Given: The standard deviation is 0.08
Copyright 2009 John Wiley & Sons, Inc.
3-22

Copyright 2009 John Wiley & Sons, Inc.
3-23

UCL = x
=
+ A
2
R LCL = x A
2
R
A
2 is a factor that depends on n, the number of units in each sample
Copyright 2009 John Wiley & Sons, Inc.
3-24

In this problem, n = 5
Copyright 2009 John Wiley & Sons, Inc.
3-25

OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE k
1
6
7
4
5
8
2
3
9
10
1 2 3 4 5 x R
5.02
5.01
4.94
4.99
4.96
4.98
0.08
5.01
5.03
5.07
4.95
4.96
5.00
0.12
4.99
5.00
4.93
4.92
4.99
4.97
0.08
5.03
4.91
5.01
4.98
4.89
4.96
0.14
4.95
4.92
5.03
5.05
5.01
4.99
0.13
4.97
5.06
5.06
4.96
5.03
5.01
0.10
5.05
5.01
5.10
4.96
4.99
5.02
0.14
5.09
5.10
5.00
4.99
5.08
5.05
0.11
5.14
5.10
4.99
5.08
5.09
5.08
0.15
5.01
4.98
5.08
5.07
4.99
5.03
0.10
50.09
1.15
Example 15.4
Copyright 2009 John Wiley & Sons, Inc.
3-26

R =
∑ R k
=
1.15
10
= 0.115
 x
x = = = 5.01 cm k
50.09
10
=
2
R = 5.01 + (0.58)(0.115) = 5.08
=
2
R = 5.01 - (0.58)(0.115) = 4.94
Retrieve Factor Value A
2
Copyright 2009 John Wiley & Sons, Inc.
3-27

x- bar
Chart
Example
(cont.)
5.10 –
5.08
–
5.06
–
5.04
–
5.02 –
5.00 –
4.98 –
4.96
–
4.94
–
4.92
–
UCL = 5.08
LCL = 4.94
|
1
|
2
|
3
| | |
4 5 6
Sample number
|
7
|
8
|
9
|
10
Copyright 2009 John Wiley & Sons, Inc.
3-28

1. There are no sample points outside limits &
2. Most points are near the process average &
3. The number of points above and below the center line is about equal &
4. The points appear to be randomly distributed
This is only a rough guide. Quality analysts use more precise rules.
Copyright 2009 John Wiley & Sons, Inc.
3-29

UCL = D
4
R LCL = D
3
R
R =

R k where
R = range of each sample
k = number of samples
Copyright 2009 John Wiley & Sons, Inc.
3-30

SAMPLE k
1
5
6
7
2
3
4
8
9
10
OBSERVATIONS (SLIP-RING DIAMETER, CM)
1 2 3 4 5 x R
5.02
5.01
4.94
4.99
4.96
4.98
0.08
5.01
5.03
5.07
4.95
4.96
5.00
0.12
4.99
5.00
4.93
4.92
4.99
4.97
0.08
5.03
4.91
5.01
4.98
4.89
4.96
0.14
4.95
4.92
5.03
5.05
5.01
4.99
0.13
4.97
5.06
5.06
4.96
5.03
5.01
0.10
5.05
5.01
5.10
4.96
4.99
5.02
0.14
5.09
5.10
5.00
4.99
5.08
5.05
0.11
5.14
5.10
4.99
5.08
5.09
5.08
0.15
5.01
4.98
5.08
5.07
4.99
5.03
0.10
50.09
1.15
Example 15.3
Copyright 2009 John Wiley & Sons, Inc.
3-31

UCL = D
4
R = 2.11(0.115) = 0.243
LCL = D
3
R = 0(0.115) = 0
Retrieve Factor Values D
3 and D
4
Example 15.3
Copyright 2009 John Wiley & Sons, Inc.
3-32

0.28 –
0.24 –
0.20 –
0.16 –
0.12 –
0.08 –
0.04 –
0 –
UCL = 0.243
R = 0.115
|
LCL = 0
|
1 2
|
3
|
4
|
5
|
6
Sample number
|
7
|
8
|
9
|
10
Copyright 2009 John Wiley & Sons, Inc.
3-33

 Process average and process variability must be in control
 It is possible for samples to have very narrow ranges, but their averages might be beyond control limits
 It is possible for sample averages to be in control, but ranges might be very large
 It is possible for an R-chart to exhibit a distinct downward trend, suggesting some nonrandom cause is reducing variation
Copyright 2009 John Wiley & Sons, Inc.
3-34

Non-random Patterns in Control Charts
Change in Mean
UCL
UCL
LCL
Sample observations consistently below the center line
LCL
Copyright 2009 John Wiley & Sons, Inc.
Sample observations consistently above the center line
3-35

Non-random Patterns in Control Charts
Trend
UCL
UCL
LCL
Sample observations consistently increasing
LCL
Copyright 2009 John Wiley & Sons, Inc.
Sample observations consistently decreasing
3-36

 Tolerances
 design specifications reflecting product requirements
 Process capability
 range of natural variability in a process — what we measure with control charts
 A capable process consistently produces products that conform to specifications
Copyright 2009 John Wiley & Sons, Inc.
3-37

Copyright 2009 John Wiley & Sons, Inc.
All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley &
Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.
Copyright 2009 John Wiley & Sons, Inc.
3-38