1. Statistical Process Control (SPC)
Chapter 6

2. Just-in-Time & Lean Systems
MGMT 326
Capacity
and
Facilities
Foundations
of Operations
Products &
Processes
Quality
Assurance
Planning
& Control
Managing
Projects
Managing
Quality
Introduction
Strategy
Product
Design
Statistical
Process
Control
Process
Design
Just-in-Time & Lean Systems

3. Assuring Customer-Based Quality
Customer Requirements
Product Specifications
Process Specifications
Product launch activities: Revise periodically
Ongoing
activity
Statistical Process Control:
Measure & monitor quality

4. Statistical Process Control (SPC)
Basic SPC
Concepts
Types of
Measures
SPC for
Variables
Capable
Processes
 = target
Variation
Attributes
Mean
charts
Range
charts
Objectives
Variables
 and  known
First steps
,  unknown

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

6. Variation in a Transformation Process
Too Much
Variation
Customer
requirements
are not met
Variation
Too Much
Inputs
Facilities
Equipment
Materials
Energy
Transformation Process
Outputs
Goods &
Services
Variation in inputs create variation in outputs
Variations in the transformation process
create variation in outputs

7. Variation
All processes have variation.
Common cause variation is random variation that is always present in a process.
Assignable cause variation results from changes in the inputs or the process. The cause can and should be identified.
Assignable cause variation shows that the process or the inputs have changed, at least temporarily.

8. Objectives of Statistical Process Control (SPC)
Find out how much common cause variation the process has
Find out if there is assignable cause variation.
A process is in control if it has no assignable cause variation
Being in control means that the process is stable and behaving as it usually does.

9. First Steps in Statistical Process Control (SPC)
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

10. Types of Measures (1) Variable Measures
Continuous random variables
Measure does not have to be a whole number.
Examples: time, weight, miles per gallon, length, diameter

11. Types of Measures (2) Attribute Measures
Discrete random variables – finite number of possibilities
Also called categorical variables
The measure may depend on perception or judgment.
Different types of control charts are used for variable and attribute measures

12. Examples of Attribute Measures
Good/bad evaluations
Good or defective
Correct or incorrect
Number of defects per unit
Number of scratches on a table
Opinion surveys of quality
Customer satisfaction surveys
Teacher evaluations

13. SPC for Variables The Normal Distribution
 = the population mean
= the standard deviation
for the population
99.74% of the area under the normal curve is between
 - 3 and  + 3

14. SPC for Variables The Central Limit Theorem
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
when k is large.

15. Control Limits for the Sample Mean when  and  are known
x is a variable, and samples of size n are taken from the population containing x.
Given:  = 10,  = 1, n = 4
Then
A 99.7% confidence interval for is

16. Control Limits for the Sample Mean when  and  are known (2)
The lower control limit for is

17. Control Limits for the Sample Mean when  and  are known (3)
The upper control limit for is

18. Control Limits for the Sample Mean when  and  are unknown
If the process is new or has been changed recently, we do not know  and 
Example 6.1, page 180
Given: 25 samples, 4 units in each sample
 and  are not given
k = 25, n = 4

19. Control Limits for the Sample Mean when  and  are unknown (2)
Compute the mean for each sample. For example,
Compute

20. Control Limits for the Sample Mean when  and  are unknown (3)
For the ith sample, the sample range is
Ri = (largest value in sample i )
- (smallest value in sample i )
Compute Ri for every sample. For example,
R1 = – = 0.19

21. Control Limits for the Sample Mean when  and  are unknown (4)
Compute , the average range
We will approximate by , where
A2 is a number that depends on the sample
size n. We get A2 from Table 6.1, page 182

22. Control Limits for the Sample Mean when  and  are unknown (5)
Factor for x-Chart A2 D3 D4 2
1.88
0.00
3.27 3
1.02
2.57 4
0.73
2.28 5
0.58
2.11 6
0.48
2.00 7
0.42
0.08
1.92 8
0.37
0.14
1.86 9
0.34
0.18
1.82 10
0.31
0.22
1.78 11
0.29
0.26
1.74 12
0.27
0.28
1.72 13
0.25
1.69 14
0.24
0.33
1.67 15
0.35
1.65
Factors for R-Chart
Sample Size
(n)
n = the number of units in each sample
= 4.
From Table 6.1,
A2 = 0.73.
The same A2 is used
for every problem
with n = 4.

23. Control Limits for the Sample Mean when  and  are unknown (6)
The formula for the lower control limit is
The formula for the upper control limit is

24. Control Chart for The variation between LCL = 15.74 and UCL = 16.16
is the common cause variation.

25. Common Cause and Special Cause Variation
The range between the LCL and UCL, inclusive, is the common cause variation for the process. When
is in this range, the process is in control.
When a process is in control, it is predictable. Output from the process may or may not meet customer requirements.
When is outside control limits, the process is out of control and has special cause variation. The cause of the variation should be identified and eliminated.

26. Control Limits for R From the table, get D3 and D4 for n = 4. D3 = 0
Factor for x-Chart A2 D3 D4 2
1.88
0.00
3.27 3
1.02
2.57 4
0.73
2.28 5
0.58
2.11 6
0.48
2.00 7
0.42
0.08
1.92 8
0.37
0.14
1.86 9
0.34
0.18
1.82 10
0.31
0.22
1.78 11
0.29
0.26
1.74 12
0.27
0.28
1.72 13
0.25
1.69 14
0.24
0.33
1.67 15
0.35
1.65
Factors for R-Chart
Sample Size
(n)
From the table,
get D3 and D4
for n = 4.
D3 = 0
D4 = 2.28

27. Control Limits for R (2) The formula for the lower control limit is
The formula for the upper control limit is

28. fig_ex06_03
fig_ex06_03

29. Statistical Process Control (SPC)
Basic SPC
Concepts
Types of
Measures
SPC for
Variables
Capable
Processes
 = target
Variation
Attributes
Mean
charts
Range
charts
Objectives
Variables
 and  known
First steps
,  unknown

30. Capable Transformation Process
Inputs
Facilities
Equipment
Materials
Energy
Outputs
Goods &
Services
that meet
specifications
Capable Transformation Process
a specification that meets customer requirements
+ a capable process (meets specifications)
= Satisfied customers and repeat business

31. Review of Specification Limits
The target for a process 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 15.8 ounces and no more than 16.2 ounces.
The allowable range is 15.8 – 16.2 ounces.
Lower specification limit = 15.8 ounces or LSL = 15.8 ounces
Upper specification limit = 16.2 ounces or USL = 16.2 ounces

32. Control Limits vs. Specification Limits
Control limits show the actual range of variation within a process
What the process is doing
Specification limits show the acceptable common cause variation that will meet customer requirements.
Specification limits show what the process should do to meet customer requirements

33. Process is Capable: Control Limits are within or on Specification Limits
Upper specification limit
UCL X
LCL
Lower specification limit 9

34. Process is Not Capable: One or Both Control Limits are Outside Specification Limits
UCL
Upper specification limit X
LCL
Lower specification limit 9

35. Capability and Conformance Quality
A process is capable if
It is in control and
It consistently produces outputs that meet specifications.
This means that both control limits for the mean must be within the specification limits
A capable process produces outputs that have conformance quality (outputs that meet specifications).

36. Process Capability Ratio
Use to determine whether the process is capable when  = target.
If , the process is capable,
If , the process is not capable.

37. Example
Given: Boffo Beverages produces 16-ounce bottles of soft drinks. The mean ounces of beverage in Boffo's bottle is 16. The allowable range is 15.8 – The standard deviation is Find and determine whether the process is capable.

38. Example (2) Given:  = 16,  = 0.06, target = 16
LSL = 15.8, USL = 16.2
The process is capable.

39. Process Capability Index Cpk
If Cpk > 1, the process is capable.
If Cpk < 1, the process is not capable.
We must use Cpk when  does not equal the target.

40. Cpk Example
Given: Boffo Beverages produces 16-ounce bottles of soft drinks. The mean ounces of beverage in Boffo's bottle is The allowable range is 15.8 – The standard deviation is Find and determine whether the process is capable.

41. Cpk Example (2) Given:  = 15.9,  = 0.06, target = 16
LSL = 15.8, USL = 16.2
Cpk < 1. Process is not capable.

42. Statistical Process Control (SPC)
Basic SPC
Concepts
Types of
Measures
SPC for
Variables
Capable
Processes
 = target
Variation
Attributes
Mean
charts
Range
charts
Objectives
Variables
 and  known
First steps
,  unknown