of 14
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
1/14
Slide
18-1
2/10/2012
Chapter 18
Quality Control: Recognizing and
Managing Variation
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
2/14
Slide
18-2
2/10/2012
Processes Control
Process
Any business activity transforms inputs into outputs
e.g., manufacturing products
e.g., restaurant meals
e.g., information processing
Statistical Process Control
Use of statistical methods to monitor the functioning of
a process Fix when necessary, otherwise leave it alone!
Detect problems and fix them before defects are produced
Variation is due to different causes
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
3/14
Slide
18-3
2/10/2012
Causes of Variation
Assignable Cause of Variation
Due to identifiable causes, e.g.
Dust contamination
Incomplete training of workers
Random Cause of Variation
Due to causes not worth identifying, e.g.
Even a process that is in control and working properly still
shows some variation in its results
Perhaps there is no reason to ensure that each cookie has the
exactsame number of chocolate chips in it, so long as there are
enough!
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
4/14
Slide
18-4
2/10/2012
In Control
A Process is In a StateofStatisticalControl(or,
Simply, In Control)
When all assignable causes of variation have been
identified and eliminated
Only random causes of variation remain
What to do with a Process that is In Control?
Monitor it with control charts Leave it alone, so long as it stays in control
Fix it when it goes outofcontrol
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
5/14
Slide
18-5
2/10/2012
The Pareto Diagram
Pareto Diagram Shows Where to Focus Attention
For a group of defective components
Each defect is classified according to its cause
Pareto Diagram displays the causes in order from mostfrequent to least frequent
Also shows the cumulativepercentage of defects (e.g., due to
the top 3 causes)
Pareto Diagram includes a bar chart, showing the
number of defects due to each cause, most to least
Together with their cumulative sum
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
6/14
Slide
18-6
2/10/2012
Example: Pareto Diagram
Defect Causes and FrequenciesSolder joint: 37 defects, Plastic case: 86 defects,
Power supply: 194 defects, Dirt: 8 defects, Shock: 1 defect
0
100
200
300 97.2%
59.5%
85.9%
100%
Power
supply
Plastic
case
Solder
joint
Dirt ShockNumbero
fdefectiveitems
Percentofdefectiveitems
Fig 18.1.1
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
7/14
Slide
18-7
2/10/2012
Control Chart
Displays successive measurements of a process,
together with
Center line
Control limits (upper and lower)
To Help You Decide if the Process is In Control
A hypothesis test
H0: The process is in control
H1: The process is notin control
Thefalse alarmrate (type I error) How often will you intervene when the system is really OK?
The 5% level is too high
In quality control, 3W limits are often used (as compared to 2W)
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
8/14
Slide
18-8
2/10/2012
AProcess that is In Control
IfProcess is In Control,
Control chart stays within the control limits
Variation within the control limits is to be expected
Variation should be random, without systematic patterns
0 5 10 15 20 25
Group Number
Meas
urement Upper control limit
Lower control limit
Center line
Data
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
9/14
Slide
18-9
2/10/2012
AProcess that is NotIn Control
If Control Chart Extends Beyond a Control Limit
Or if there is a systematic pattern within the limits
Then the Process is NotIn Control
0 5 10 15 20 25
Group Number
Meas
urement
0 5 10 15 20 25
Group Number
Meas
urement
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
10/14
Slide
18-10
2/10/2012
X-Bar Chart
A Control Chart for Averages ofSuccessive
Measurements
Tells you about the stability of thesize of measurement
Often taken in groups of4 or5 at a time Control Chart plots the averages of successive groups
Center line is the grand mean of all measurements
Unless an externalstandard is given
Upper and lower limits are found using multipliers
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
11/14
Slide
18-11
2/10/2012
R Chart
A Control Chart for Ranges ofSuccessive
Measurements
Tells you about stability of the variability of process
Range is largest minus smallest
Often taken in groups of4 or5 at a time
Control Chart plots the ranges of successive groups
Center line is the mean range for all groups
Unless an external standard is given
Upper and lower limits are found using multipliers
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
12/14
Slide
18-12
2/10/2012
Example: Weight of Detergent
25 Groups of
5 measurements
each
Find averageand range
for each group
Plot with
center line andcontrol limits
Its In Control!
15.8
15.9
16.0
16.1
16.2
16.3
16.4
0 10 20 30Group Number
Averages
0.00.10.20.30.4
0.50.60.7
0 10 20 30Group Number
Ranges
Fig 18.3.1
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
13/14
Slide
18-13
2/10/2012
Percentage Chart
A Control Chart for the Percent Defective
Tells you about the stability of the defectrate
Plot the percent defective for successive samples
How to choose n, the sample size?
You should expect at least 5defective items in a sample
Center line is the average defect rate
Unless an externalstandard is given
Upper and lower limits are set at 3binomial standard
deviations above and below the center line
8/3/2019 Statistics- Quality Control Recognizing and Managing Variation
14/14
Slide
18-14
2/10/2012
Example: Purchase Order Errors
25batches ofn = 300purchase orders each
Find percent defective for each batch
Plot with center line and control limits
Its not in control
0%
5%
10%
0 10 20
Group Number
Percentofpurchase
orders
inerror
Fig 18.4.1
