statistics -quality control
TRANSCRIPT
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Statistics -Quality Control
Prof. Rushen Chahal
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UpComing Events Complete CD-ROM certifications
Review
Final Examination
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Statistical Quality
Control
CD-ROM
SSIGNMENT
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TO DISCUSS THE ROLEOF STATISTICALQUALITY CONTROL
TO DEFINETHETERMS CHANCE CAUSES,
ASSIGNABLE CAUSES,IN CONTROL, & OUT
OF CONTROL.
TO CONSTRUCTAND DISCUSS
VARIABLES CHARTS:MEAN&RANGE.
GOALS
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5GOALS (next class)
TO CONSTRUCTAND DISCUSS
ATTRIBUTES CHARTS: PERCENTAGE
DEFECTIVE&NUMBER OF DEFECTS.
TO DISCUSSACCEPTANCE SAMPLING.
TO CONSTRUCTOPERATING
CHARACTERISTIC CURVESFOR VARIOUS
SAMPLING PLANS.
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Statistical Quality Controlemphasizes in-processcontrol with the objective of controlling the
quality of a manufacturing process or service
operation using sampling techniques.
Statistical sampling techniques are used to aid in
the manufacturing of a product to specifications
rather than attempt to inspect quality into the
product after it is manufactured.
Control Charts are useful for monitoring a
process.
CONTROL CHARTS
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There is
variation in all parts produced by amanufacturing process. There are two sources
of variation:
Chance Variation - random in nature. Cannot be
entirely eliminated.
Assignable Variation -- nonrandom in nature.
Can be reduced or eliminated.
CAUSES OF VARIATION
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Thepurpose of quality-control charts is todetermine and portray graphically just when an
assignable cause enters the production system so
that it can be identified and be corrected. This is
accomplished by periodically selecting a small
random sample from the current production.
PURPOSE OF QUALITY CONTROL
CHARTS
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The mean or thex-barchart is designed tocontrol variables such as weight, length, inside
diameter etc. The upper control limit (UCL)
and the lower control limit (LCL) are obtained
from equation:
TYPES OF QUALITY CONTROL
CHARTS - VARIABLES
andUCL X A R LCL X A R
where X is the mean of the sample meansA is a factor from Appendix B
R is the mean of the sample ranges
! ! 2 2
2
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10FACTORS FOR CONTROL CHARTS
Chart for
averages Chart for ranges
Number of Factors for Factors for Factors for items in control limits central line control limitssample,
n A2 d2 D3 D4
2 1.880 1.128 0 3.267
3 1.023 1.693 0 2.575
4 .729 2.059 0 2.282
5 .577 2.326 0 2.115
6 .483 2.534 0 2.004
7 .419 2.704 .076 1.924
8 .373 2.847 .136 1.864
9 .337 2.970 .184 1.816
10 .308 3.078 .223 1.777
11 .285 3.173 .256 1.744
12 .266 3.258 .284 1.716
13 .249 3.336 .308 1.692
14 .235 3.407 .329 1.671
15 .223 3.472 .348 1.652
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The range chart is designed to show whether theoverall range of measurements is in or out of
control. The upper control limit (UCL) and the
lower control limit (LCL) are obtained from
equations:
TYPES OF QUALITY CONTROL
CHARTS - VARIABLES
UCL D R and LCL D R
where D and D are factors from Appendix B
R is the mean of the sample ranges
! !
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3 4
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12FACTORS FOR CONTROL CHARTS
Chart for
averages Chart for ranges
Number of Factors for Factors for Factors for items in control limits central line control limitssample,
n A2 d2 D3 D4
2 1.880 1.128 0 3.267
3 1.023 1.693 0 2.575
4 .729 2.059 0 2.282
5 .577 2.326 0 2.115
6 .483 2.534 0 2.004
7 .419 2.704 .076 1.924
8 .373 2.847 .136 1.864
9 .337 2.970 .184 1.816
10 .308 3.078 .223 1.777
11 .285 3.173 .256 1.744
12 .266 3.258 .284 1.716
13 .249 3.336 .308 1.692
14 .235 3.407 .329 1.671
15 .223 3.472 .348 1.652
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13EXAMPLEAmanufacturer of ball bearings wishes to
determine whether the manufacturing process isout of control. Every 15 minutes for a five hour
period a bearing was selected and the diameter
measured. The diameters (in mm.) of thebearings are shown in the table below.
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14Compute the sample means and ranges. The
table below shows the means and ranges.
EXAMPLE (continued)
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15Compute the grand mean (X double bar) and the
average range.
Grand mean = (25.25 + 26.75 + ... + 25.25)/5 =
26.35.
The average range = (5 + 6 + ... + 3)/5 = 5.8.
Determine the UCL and LCL for the averageaverage
diameter.
UCL = 26.35 + 0.729(5.8) = 30.58. LCL = 26.35 - 0.729(5.8) = 22.12.
EXAMPLE (continued)
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16FACTORS FOR CONTROL CHARTS
Chart for
averages Chart for ranges
Number of Factors for Factors for Factors for items in control limits central line control limitssample,
n A2 d2 D3 D4
2 1.880 1.128 0 3.267
3 1.023 1.693 0 2.575
4 .729 2.059 0 2.282
5 .577 2.326 0 2.115
6 .483 2.534 0 2.004
7 .419 2.704 .076 1.924
8 .373 2.847 .136 1.864
9 .337 2.970 .184 1.816
10 .308 3.078 .223 1.777
11 .285 3.173 .256 1.744
12 .266 3.258 .284 1.716
13 .249 3.336 .308 1.692
14 .235 3.407 .329 1.671
15 .223 3.472 .348 1.652
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17Determine the UCL and LCL for the range
diameter.
UCL = 2.282(5.8) = 30.58.
LCL = 0(5.8) = 0.
Is the process out of control?
Observe from the next slide that the process is in
control. No points are outside the control limits.
EXAMPLE (continued)
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18FACTORS FOR CONTROL CHARTS
Chart for
averages Chart for ranges
Number of Factors for Factors for Factors for items in control limits central line control limitssample,
n A2 d2 D3 D4
2 1.880 1.128 0 3.267
3 1.023 1.693 0 2.575
4 .729 2.059 0 2.282
5 .577 2.326 0 2.115
6 .483 2.534 0 2.004
7 .419 2.704 .076 1.924
8 .373 2.847 .136 1.864
9 .337 2.970 .184 1.816
10 .308 3.078 .223 1.777
11 .285 3.173 .256 1.744
12 .266 3.258 .284 1.716
13 .249 3.336 .308 1.692
14 .235 3.407 .329 1.671
15 .223 3.472 .348 1.652
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19EXAMPLE (continued)X-bar and R Chart for the Diameters
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Control ChartsW. Edwards Deming
Short Video Clip
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Thepercent defective chart is also called ap-chart or thep-barchart. It graphically shows
the proportion of the production that is not
acceptable.
TYPES OF QUALITY CONTROL
CHARTS - ATTRIBUTES
The proportion of defectives is found by
pSum of the percent defectives
Number of samples
:
!
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The equation below gives the UCL and LCL forthep-chart.
TYPES OF QUALITY CONTROL
CHARTS - ATTRIBUTES
The UCL and LCL are computed
as the mean percent defective plus or times thestandard error of the percents
UCL and LCL p p pn
minus 3
3 1
:
( ) .! s
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23A manufacturer of jogging shoes wants to
establish control limits for the percent defective.
Ten samples of 400 shoes revealed the mean
percent defective was 8.0%. Where should the
manufacturer set the control limits?
EXAMPLE
008 3008 1 008
400008 0041
.. ( . )
. .
s
! s
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The cc--chart of the cc--barbarchart is designed tocontrol the number of defects per unit. The
UCL and LCL are found by:
UCL and LCL c c! s 3
TYPES OF QUALITY CONTROL
CHARTS - ATTRIBUTES
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25A manufacturer of computer circuit boards
tested 10 after they were manufactured. The
number of defects obtained per circuit board
were: 5, 3, 4, 0, 2, 2, 1, 4, 3, and 2. Construct the
appropriate control limits.
EXAMPLE
c Thus
UCL and LCLor
! !
! s
s
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102 6
2 6 3 2 62 6 484
. .
. .. . .
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26Acceptance samplingis a method of determining
whether an incoming lot of a product meets
specified standards.
It is based on random sampling techniques.
A random sample ofn units is obtained from theentire lot.
c is the maximum number of defective units that
may be found in the sample for the lot to still beconsidered acceptable.
ACCEPTANCE SAMPLING
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An OCcurve,
or operating characteristic curve,
isdeveloped using the binomial probability
distribution, in order to determine the
probabilities of accepting lots of various quality
levels.
OPERATING CHARACTERISTIC
CURVE
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28EXAMPLE
Suppose a manufacturer and a supplier agree on
a sampling plan with n = 10 and acceptancenumber of 1. What is the probability of
accepting a lot with 5% defective? A lot with
10% defective? P(ren = 10,p = 0.05) = 0.599 + 0.315 = 0.914.
P(ren = 10,p = 0.1) = 0.349 + 0.387 = 0.736
etc.
P rn
r n rp
rq
n r( )!
!( )!!
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29Statistical Quality Control HomeworkComplete CD-ROM exercises