1 quality and education business has made progress toward quality over the past several years. but i...
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1
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
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2
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
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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)
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TQMWheel
Customer
satisfaction
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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.
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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”
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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
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Quality Costs
• Prevention costs– Customer requirements/expectations market
research – Product design/development reviews– Quality education programs– Equipment and preventive maintenance– Supplier-rating program administration
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Quality Costs
• Appraisal costs– Testing/inspection equipment – Inspection costs– Audits
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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
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Costs of Detecting Defects
Co
st o
f d
etec
tio
n (
do
llar
s)
Process Final testing Customer
When defect is detected
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Statistical Quality ControlIntroduction
• Control charts and sampling• Simple and R charts• Variation• Common and assignable causes
X
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Control Chart Viewpoint
• Variation due to – Common or chance causes– Assignable causes
• Control chart may be used to discover “assignable causes”
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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
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Some Terms
• Run chart - without any upper/lower limits• Specification/tolerance limits - not statistical• Control limits - statistical
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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)
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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
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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
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Process Control Chart
1 2 3 4 5 6 7 8 9 10
Sample number
Uppercontrollimit
Processaverage
Lowercontrollimit
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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
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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.
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Example: Control Charts for Variable Data
Slip Ring Diameter (cm)
Sample 1 2 3 4 5 X R
1 5.02 5.01 4.94 4.99 4.96 4.98 0.08
2 5.01 5.03 5.07 4.95 4.96 5.00 0.12
3 4.99 5.00 4.93 4.92 4.99 4.97 0.08
4 5.03 4.91 5.01 4.98 4.89 4.96 0.14
5 4.95 4.92 5.03 5.05 5.01 4.99 0.13
6 4.97 5.06 5.06 4.96 5.03 5.01 0.10
7 5.05 5.01 5.10 4.96 4.99 5.02 0.14
8 5.09 5.10 5.00 4.99 5.08 5.05 0.11
9 5.14 5.10 4.99 5.08 5.09 5.08 0.15
10 5.01 4.98 5.08 5.07 4.99 5.03 0.10
50.09 1.15
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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.
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• 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.
Normal Distribution Review
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• Define the 3-sigma limits for sample means as follows:
• What is the probability that the sample means will lie outside 3-sigma limits?
Normal Distribution Review
94345
0503015
3
07755
0503015
3
.).(
. Limit Lower
.).(
. Limit Upper
n
n
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Normal Distribution Review
• Note that the 3-sigma limits for sample means are different from natural tolerances which are at 3
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Constructing a Range Chart
).)((LCL
.).)(.(UCL
R
R
011500
4321150112
3
4
RD
RD
), of values the for App., Table Text or 29 p. see(
range
10samples of number
././R where
43
115010151
DDD
R
k
kR
Note: The control limits are only preliminary with 10 samples.It is desirable to have at least 25 samples.
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Constructing A Mean Chart
94341150580015
07751150580015
2
2
.).(.).(LCL
.).(.).(UCL
X
X
RAX
RAX
) of value the for 3 App., Table Text or 29 p. see(
range
10samples of number
././R
././X where
2
115010151
015100950
AD
R
k
kR
kX
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3-Sigma Control Chart Factors
Sample size X-chart R-chart
n A2 D3 D4
2 1.88 0 3.27
3 1.02 0 2.57
4 0.73 0 2.28
5 0.58 0 2.11
6 0.48 0 2.00
7 0.42 0.08 1.92
8 0.37 0.14 1.86
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Common Causes
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Assignable Causes
(a) MeanGrams
Average
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Assignable Causes
(b) SpreadGrams
Average
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Assignable Causes
(c) ShapeGrams
Average
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The NormalDistribution
-3 -2 -1 +1 +2 +3Mean
68.26%95.44%99.74%
= Standard deviation
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Control Charts
UCL
Nominal
LCL
Assignable causes likely
1 2 3Samples
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Control Chart Examples
Nominal
UCL
LCL
Sample number
Var
iati
on
s
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Control Limits and Errors
LCL
Processaverage
UCL
(a) Three-sigma limits
Type I error:Probability of searching for a cause when none exists
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Control Limits and ErrorsType I error:Probability of searching for a cause when none exists
UCL
LCL
Processaverage
(b) Two-sigma limits
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Type II error:Probability of concludingthat nothing has changed
Control Limits and Errors
UCL
Shift in process average
LCL
Processaverage
(a) Three-sigma limits
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Type II error:Probability of concludingthat nothing has changed
Control Limits and Errors
UCL
Shift in process average
LCL
Processaverage
(b) Two-sigma limits
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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
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Process Capability
Process cannot meet specifications Process can meet specifications
Process capability exceeds specifications
PR
OC
ES
S
PR
OC
ES
S
PR
OC
ES
SNaturalcontrollimits
Naturalcontrollimits
Naturalcontrollimits
Designspecs
Designspecs
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Process Capability
• If the R chart shows control, estimate the standard deviation of items as
• If the R chart does not show control, remove the ones that showed lack of control, calculate a revised and new control limits for R. Repeat the process as long as it is needed. Estimate standard deviation of items as shown above.
• Process capability
d
R
R
33
XUSLLSLXC xxpk ,min
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Process Capability
• By computing 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 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.
pkC
1pkC
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Text Exercise 2.2: Is the following process capable?:
0200
320034041
20
4
.2.050 are limits ionSpecificat
. ,.
samples, of Number
size, Sample
RX
k
n
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Reading and Exercises
• Chapter 1: – pp. 3-24
• Chapter 2: – pp. 37-54– Problems 2.5, 2.6, 2.10