Quality and Education
Business has made progress toward quality over the
past several years. But I don’t believe we can truly make
quality a way of life … until we make quality a part of
every student’s education
Edwin Artzt, Chairman and CEO, Proctor & Gamble
Co., Quality Progress, October 1992, p. 25
1
Quality and Competitive Advantage
• Better price
– The better customers judge the quality of a
product, the more they will pay for it
• Lower production cost
– It is cheaper to do a job right the first time than do
it over
• Faster response
– A company with quality processes for handling
orders, producing products, and delivering them
can provide fast response to customer requests
2
Quality and Competitive Advantage
• Reduced Inventory
– When the production line runs smoothly with
predictable results, inventory levels can be
reduced
• Improved competitive position in the marketplace
– A customer who is satisfied with quality will tell 8
people about it; a dissatisfied customer will tell 22
(A.V. Feigenbaum, Quality Progress, February
1986, p. 27)
3
TQM
Wheel
Customer
satisfaction
4
Customer-Driven Definitions of Quality
• Conformance to specifications
– Conformance to advertised level of performance
• Value
– How well the purpose is served at a particular
price.
– For example, if a $2.00 plastic ballpoint pen lasts
for six months, one may feel that the purchase
was worth the price.
5
Customer-Driven Definitions of Quality
• Fitness for use
– Mechanical feature of a product, convenience of a
service, appearance, style, durability, reliability,
craftsmanship, serviceability
• Support
– Financial statements, warranty claims, advertising
• Psychological Impressions
– Atmosphere, image, aesthetics
– “Thanks for shopping at Wal-Mart”
6
Defectives and Defect
• In the popular sense, a defect is some characteristic
that makes a product unsatisfactory for its intended
purpose
• Technically, a defect is a failure to conform to some
specification e.g., 0.140  0.003 in.
• To avoid ambiguity, following words are suggested
– Nonconformity or Nonconformance: defect
– Nonconforming: defective
7
Quality Costs
• Prevention costs
– Customer requirements/expectations market
research
– Product design/development reviews
– Quality education programs
– Equipment and preventive maintenance
– Supplier-rating program administration
8
Quality Costs
• Appraisal costs
– Testing/inspection equipment
– Inspection costs
– Audits
9
Quality Costs
• Internal failure costs
– Rework, scrap, repair
• External failure costs
– Returned goods, warranty costs, liability costs,
penalties
• Intangible costs
– Customer dissatisfaction, company image, lost
sales, loss of customer goodwill
10
Cost of detection (dollars)
Costs of Detecting Defects
Process
Final testing
Customer
When defect is detected
11
Statistical Quality Control
Introduction
•
•
•
•
Control charts and sampling
Simple X and R charts
Variation
Common and assignable causes
12
Control Chart Viewpoint
• Variation due to
– Common or chance causes
– Assignable causes
• Control chart may be used to discover “assignable
causes”
13
Scientific Sampling
• Inspection
– Incoming materials, in-process products, finished
goods
• JIT inventory control makes formal sampling
impractical except for quality audit purposes
– The supplier performs sampling inspection and
provides statistical evidence of conformance to
specifications
• 100% inspection may be impractical or uneconomical
14
Some Terms
• Run chart - without any upper/lower limits
• Specification/tolerance limits - not statistical
• Control limits - statistical
15
Weakness of Plotting Individual Measurements
against Specification/Tolerance Limits
• If individual measurements are plotted against
specification/tolerance limits, following problems may
occur
– If specification/tolerance limits are too wide, the
systems may fail to detect some variations that are
less likely to be caused by chance and more likely
to be caused by some problems in the production
system (see Example 1.1)
– If specification/tolerance limits are too narrow,
unavoidable random variations may be considered
as defects and too many items may be rejected
(see Example 1.2)
16
Control Charts
• Take periodic samples from a process
• Plot the sample points on a control chart
• Determine if the process is within limits
• Correct the process before defects occur
17
Types of Data
• Variable data
• Product characteristic that can be measured
• Length, size, weight, height, time, velocity
• Attribute data
• Product characteristic evaluated with a discrete
choice
• Good/bad, yes/no
18
Process Control Chart
Upper
control
limit
Process
average
Lower
control
limit
1
2
3
4
5
6
Sample number
7
8
10
9
19
Constructing a Control Chart
•
•
•
•
•
•
Decide what to measure or count
Collect the sample data
Plot the samples on a control chart
Calculate and plot the control limits on the control chart
Determine if the data is in-control
If non-random variation is present, discard the data (fix the
problem) and recalculate the control limits
20
Control Charts For Variables
• Mean chart (X-Bar Chart)
–Measures central tendency of a sample
• Range chart (R-Chart)
–Measures amount of dispersion in a sample
• Each chart measures the process differently. Both the
process average and process variability must be in control
for the process to be in control.
21
Example: Control Charts for Variable Data
Sample
1
2
3
4
5
6
7
8
9
10
Slip Ring Diameter (cm)
1
2
3
4
5.02 5.01 4.94 4.99
5.01 5.03 5.07 4.95
4.99 5.00 4.93 4.92
5.03 4.91 5.01 4.98
4.95 4.92 5.03 5.05
4.97 5.06 5.06 4.96
5.05 5.01 5.10 4.96
5.09 5.10 5.00 4.99
5.14 5.10 4.99 5.08
5.01 4.98 5.08 5.07
5
4.96
4.96
4.99
4.89
5.01
5.03
4.99
5.08
5.09
4.99
X
R
4.98 0.08
5.00 0.12
4.97 0.08
4.96 0.14
4.99 0.13
5.01 0.10
5.02 0.14
5.05 0.11
5.08 0.15
5.03 0.10
50.09 1.15
Normal Distribution Review
• If the diameters are normally distributed with a mean of
5.01 cm and a standard deviation of 0.05 cm, find the
probability that the sample means are smaller than
4.98 cm or bigger than 5.02 cm.
23
Normal Distribution Review
• If the diameters are normally distributed with a mean of
5.01 cm and a standard deviation of 0.05 cm, find a
lower value and an upper value of the sample means
such that 97% sample means are between the lower
and upper values.
24
Normal Distribution Review
• Define the 3-sigma limits for sample means as follows:
3
3(0.05)
Upper Limit   
 5.01 
 5.077
n
5
3
3(0.05)
Lower Limit   
 5.01 
 4.943
n
5
• What is the probability that the sample means will lie
outside 3-sigma limits?
25
Normal Distribution Review
• Note that the 3-sigma limits for sample means are
different from natural tolerances which are at   3
26
Constructing a Range Chart
UCL R  D4 R  ( 2.11)( 0.115)  2.43
LCLR  D3 R  (0)( 0.115)  0
where R   R / k 1.15 / 10  0.115
k  number of samples  10
R  range
(see p. 29 or Text Table D, App. for the values of D3 , D4 )
Note: The control limits are only preliminary with 10 samples.
It is desirable to have at least 25 samples.
27
Constructing A Mean Chart
UCL X  X  A2 R  (5.01)  0.58(0.115)  5.077
LCL X  X  A2 R  (5.01)  0.58(0.115)  4.943
where X   X / k  50.09 / 10  5.01
R   R / k 1.15 / 10  0.115
k  number of samples  10
R  range
(see p. 29 or Text Table D, App. 3 for the value of A2 )
28
3-Sigma Control Chart Factors
Sample size
n
2
3
4
5
6
7
8
X-chart
A2
1.88
1.02
0.73
0.58
0.48
0.42
0.37
R-chart
D3
0
0
0
0
0
0.08
0.14
D4
3.27
2.57
2.28
2.11
2.00
1.92
1.86
29
Common Causes
30
Assignable Causes
Average
(a) Mean
Grams
31
Assignable Causes
Average
(b) Spread
Grams
32
Assignable Causes
Average
(c) Shape
Grams
33
The Normal
Distribution
 = Standard deviation
Mean
-3 -2 -1
+1 +2 +3
68.26%
95.44%
99.74%
34
Control Charts
Assignable
causes
likely
UCL
Nominal
LCL
1
2
Samples
3
35
Control Chart Examples
Variations
UCL
Nominal
LCL
Sample number
36
Control Limits and Errors
Type I error:
Probability of searching for
a cause when none exists
UCL
Process
average
LCL
(a) Three-sigma limits
37
Control Limits and Errors
Type I error:
Probability of searching for
a cause when none exists
UCL
Process
average
LCL
(b) Two-sigma limits
38
Control Limits and Errors
Type II error:
Probability of concluding
that nothing has changed
UCL
Shift in process
average
Process
average
LCL
(a) Three-sigma limits
39
Control Limits and Errors
Type II error:
Probability of concluding
that nothing has changed
UCL
Shift in process
average
Process
average
LCL
(b) Two-sigma limits
40
Process Capability
• Range of natural variability in process
– Measured with control charts
• Process cannot meet specifications if natural variability
exceeds tolerances
• 3-sigma quality
– specifications equal the process control limits.
• 6-sigma quality
–specifications twice as large as control limits
41
Natura
l
control
limits
Design
specs
PROCESS
Process cannot meet specifications
PROCESS
PROCESS
Process Capability
Natural
control
limits
Process can meet specifications
Natural
control
limits
Design
specs
Process capability exceeds specifications
42
Process Capability
• If the R chart shows control, estimate the standard
deviation of items as
R

d
• If the R chart does not show control, remove the ones that
showed lack of control, calculate a revised R and new
control limits for R. Repeat the process as long as it is
needed. Estimate standard deviation of items as shown
above.
 X  LSL USL  X 
x
x
,

• Process capability C pk  min 

3
3

43
Process Capability
• By computing C pk we can conclude whether the mean has
shifted towards upper/lower specification limit and if it has
shifted at all. If both the numbers are equal, the mean is at
the center. If the first number is smaller, the mean has
shifted towards LSLx. If the second number is smaller, the
mean has shifted towards USLx.
• If C pk  1 then the process is capable of producing
99.74% items within the specification limits. Else, either
the process needs improvement or the specification limits
must be widened.
44
Text Exercise 2.2: Is the following process capable?:
Sample size, n  4
Number of samples, k  20
 X  41.340,  R  0.320
Specification limits are 2.050  0.020
45
Reading and Exercises
• Chapter 1:
– pp. 3-24
• Chapter 2:
– pp. 37-54
– Problems 2.5, 2.6, 2.10
46