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Statistical Process Control
Chapters 20
1
A
B
C
D
E
F
G
H
2
3
4
5
6
7
8
Some Common Problems in Planning
We plan in terms of actions (tasks) rather
than objectives
Responsibilities are not clear
We plan in silos, out of context
We underestimate the time and effort
required to implement
We don’t make reviews part of the plan.
Six-Step Problem-Solving Process
Step 1: Identify and Select the problem
Step 2: Analyze the problem
Step 3: Generate Potential Solutions
Step 4: Select and Plan the Solution
Step 5: Implement the Solution
Step 6: Evaluate the Solution
Types of
Statistical Quality Control
Statistical
Quality Control
Process
Control
Variables
Charts
Attributes
Charts
Acceptance
Sampling
Variables
Attributes
Statistical Quality Control (SPC)
key tool for 6 Sigma
Measures performance of a process
Uses mathematics (i.e., statistics)
Involves collecting, organizing, &
interpreting data
Objective: Regulate quality
Used to
 Control
the process as products are
produced or service is performed
Control Chart Types
Continuous
Numerical Data
Control
Charts
Categorical or
Discrete Numerical
Data
Variables
Charts
R
Chart
Attributes
Charts
`X
Chart
P
Chart
C
Chart
Quality Characteristics
Variables
¨ Characteristics that you
measure, e.g., weight,
length
¨ May be in whole or in
fractional numbers
¨ Continuous random
variables
Attributes
 Characteristics for
which you focus on
defects
 Classify products as
either ‘good’ or ‘bad’, or
count # defects

e.g., radio works or not
 Categorical or discrete
random variables
Statistical Process Control
 Variations
Common cause: due
to process itself
Special cause
 2 ways of
investigating
variation
Plot data using
histogram, looking for
a normal distribution.
Standard Deviation
 1 σ away from mean in either direction accounts for
approx. 68% of readings in the group (red area)
 2 σ away from mean in either direction accounts for
approx. 95% of readings in the group (red and green
area)
 3 σ away from mean in either direction accounts for
approx. 99% of readings in the group (red, green, and
blue areas)
Process Control Charts
Sample Value
Plot of Sample Data Over Time
70
60
50
40
30
20
10
0
Sample
Value
UCL
Average
LCL
1
5
9
13
Time
17
21
Control Chart Purposes
Show changes in data pattern
 e.g.,
trends
 Make
corrections before process is out of control
Show causes of changes in data
 Assignable
 Data
causes
outside control limits or trend in data
 Natural
causes
 Random
variations around average
`X Chart
Type of variables control chart
 Interval
or ratio scaled numerical data
Shows sample means over time
Monitors process average
Example: Weigh samples of coffee &
compute means of samples; Plot
R Chart
Type of variables control chart
 Interval
or ratio scaled numerical data
Shows sample ranges over time
 Difference
between smallest & largest values
in inspection sample
Monitors variability in process
Example: Weigh samples of coffee &
compute ranges of samples; Plot
Formulas
p Chart
Type of attributes control chart
 Nominally
scaled categorical data
 e.g., good-bad
Shows % of nonconforming items
Example: Count # defective chairs &
divide by total chairs inspected; Plot
 Chair
is either defective or not defective
p Chart
Control Limits
UCL
LCL
p
= p + z
p (1 - p )
n
p
= p -z
p (1 - p )
n
k
n =
i =1
k
 xi
# Defective
Items in
Sample i
 ni
Size of
sample i
k
 ni
and
p =
z = 2 for 95.5%
limits; z = 3 for
99.7% limits
i =1
k
i =1
Statistical Process Control Chart
Using SPC to Address On-Time Medication Delivery
c Chart
Type of attributes control chart
 Discrete
quantitative data
Shows number of nonconformities
(defects) in a unit
 Unit
may be chair, steel sheet, car etc.
 Size of unit must be constant
Example: Count # defects (scratches,
chips etc.) in each chair of a sample of
100 chairs; Plot
c Chart
Control Limits
UCL
LCL
c
c
= c + 
c
= c - 
c
k
c =
 ci
i=1
k
Use 3 for 99.7%
limits
# Defects in
Unit i
# Units
Sampled
Process Capability Cpk
Upper Specification Limit - x x - Lower Specification Limit 
C pk = minimum of 
,





where x = process mean
= standard deviation of the process population
Assumes that the process is:
•under control
•normally distributed
What Is
Acceptance Sampling?
Form of quality testing used for
incoming materials or finished goods
 e.g.,
purchased material & components
Procedure
 Take
one or more samples at random from a
lot (shipment) of items
 Inspect each of the items in the sample
 Decide whether to reject the whole lot based
on the inspection results
What Is an
Acceptance Plan?
Set of procedures for inspecting incoming
materials or finished goods
Identifies
 Type
of sample
 Sample size (n)
 Criteria (c) used to reject or accept a lot
Producer (supplier) & consumer (buyer)
must negotiate
Producer’s & Consumer’s Risk
Producer's risk (a)
 Probability
of rejecting a good lot
 Type 1 error – results in over adjustment
Consumer's risk (ß)
 Probability
of accepting a bad lot
 Type II error – results in under adjustment
ANY QUESTIONS?