Statistical Quality Control (SQC) Final
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Transcript of Statistical Quality Control (SQC) Final
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Statistical Process Control
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Content
Basics of Statistical Process Control
Control Charts
Control Charts for Attributes
Control Charts for Variables
Control Chart Patterns
SPC with Excel
Process Capability
Six Sigma
Design of Six Sigma System
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Basics of Statistical Process
Control Statistical Process Control (SPC)
monitoring production process to detect and prevent poorquality
Sample
subset of items produced to use for inspection Control Charts
process is within statistical control limits
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Variability
Random
common causes
inherent in a process
can be eliminated only
through improvements
in the system
Non-Random
special causes
due to identifiable
factors
can be modified
through operator or
management action
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SPC in TQM
SPC
tool for identifying problems andmake improvements
contributes to the TQM goal of
continuous improvements
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Quality Measures
Attribute
a product characteristic that can be evaluatedwith a discrete response
good bad; yes - no Variable
a product characteristic that is continuous and canbe measured
weight - length
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Where to Use Control Charts
Process has a tendency to go out of control
Process is particularly harmful and costly if it goes
out of control Examples at the beginning of a process because it is a waste of time
and money to begin production process with bad supplies
before a costly or irreversible point, after which product isdifficult to rework or correct
before and after assembly or painting operations thatmight cover defects
before the outgoing final product or service is delivered
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Control Charts
A graph that establishescontrol limits of a process
Control limits upper and lower bands of a
control chart
Types of charts
Attributes
p-chart
c-chart
Variables
range (R-chart) mean (x bar chart)
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Normal Distribution
=0 1 2 3-1-2-3
95%
99.74%
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Control Charts for
Attributes p-charts
uses portion defective in a sample
c-charts uses number of defects in an item
The primary difference between using a p-chart and a c-chart
is as follows.
A p-chart is used when both the total sample size andthe number of defects can be computed.
A c-chart is used when we can compute only the
number of defects but cannot compute the proportion that
is defective.
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p-Chart
UCL = p+ z p
LCL = p- z p
z= number of standard deviations fromprocess average
p= sample proportion defective; an estimateof process average
p = standard deviation of sample proportion
p=p(1 - p)
n
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p-Chart Example
20 samples of 100 pairs of jeans
NUMBER OF PROPORTIONSAMPLE DEFECTIVES DEFECTIVE
1 6 .062 0 .00
3 4 .04
: : :
: : :
20 18 .18
200
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p-Chart Example (cont.)
UCL = p+ z = 0.10 + 3p(1 - p)
n
0.10(1 - 0.10)
100
UCL = 0.190
LCL = 0.010
LCL = p- z = 0.10 - 3p(1 - p)
n0.10(1 - 0.10)
100
= 200 / 20(100) = 0.10total defectives
total sample observationsp =
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p-Chart
Example(cont.)
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Proportiond
efective
Sample number
2 4 6 8 10 12 14 16 18 20
UCL = 0.190
LCL = 0.010
p= 0.10
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c-Chart
UCL = c+ z cLCL = c- z c
where
c= number of defects per sample
c= c
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c-Chart (cont.)Number of defects in 15 sample rooms
1 122 8
3 16
: :
: :15 15
190
SAMPLE
c= = 12.67
190
15
UCL = c+ z c= 12.67 + 3 12.67= 23.35
LCL = c+ z c= 12.67 - 3 12.67= 1.99
NUMBEROF
DEFECTS
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c-Chart
(cont.)
3
6
9
12
15
18
21
24
Numb
erofdefects
Sample number
2 4 6 8 10 12 14 16
UCL = 23.35
LCL = 1.99
c= 12.67
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Control Charts for
Variables
Mean chart ( x -Chart )
uses average of a sample
Range chart ( R-Chart )
uses amount of dispersion in a
sample
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x-bar Chart
deviationstandard
XLCL
XUCL
z
z
z = standard normal variable (2 for 95.44%
confidence, 3 for 99.74% confidence)
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x-bar Chart Example
OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE k 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 0.084 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 0.119 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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x- bar Chart Example
(cont.)
UCL = x+ A2R= 5.01 + (0.58)(0.115) = 5.08
LCL = x- A2R= 5.01 - (0.58)(0.115) = 4.94
=
=
x= = = 5.01 cm= x
k
50.09
10
Retrieve Factor Value A2
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x- bar
Chart
Example
(cont.)
UCL = 5.08
LCL = 4.94
Mean
Sample number
|1
|2
|3
|4
|5
|6
|7
|8
|9
|10
5.10
5.08
5.06
5.04
5.02
5.00
4.98
4.96
4.94
4.92
x= 5.01=
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R- Chart
UCL = D4R LCL = D3R
R=Rk
where
R= range of each samplek= number of samples
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R-Chart Example
OBSERVATIONS (SLIP-RING DIAMETER, CM)
SAMPLE k 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 0.084 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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R-Chart Example (cont.)
RkR= = = 0.1151.1510 UCL = D
4R= 2.11(0.115) = 0.243LCL = D3R= 0(0.115) = 0
Retrieve Factor Values D3 and D4
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R-Chart Example (cont.)
UCL = 0.243
LCL = 0
Range
Sample number
R= 0.115
|1
|2
|3
|4
|5
|6
|7
|8
|9
|10
0.28
0.24
0.20
0.16
0.12
0.08
0.04
0
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Using x- bar and R-Charts Together
Process average and
process variability must
be in control. It is possible for samples
to have very narrow
ranges, but their
averages is beyond
control limits. It is possible for sample
averages to be in control,
but ranges might be very
large.
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A Process Is in
Control If
1. no sample points outside limits
2. most points near process average
3. about equal number of points above
and below centerline
4. points appear randomly distributed
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Control Chart Patterns
UCL
LCL
Sample observationsconsistently above thecenter line
LCL
UCL
Sample observations
consistently below thecenter line
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Control Chart Patterns (cont.)
LCL
UCL
Sample observations
consistently increasing
UCL
LCL
Sample observationsconsistently decreasing
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Revise the charts
Interpret the original charts Isolate the causes
Take corrective action
Revise the chart
Only remove points for which you can determine an assignablecause
DOE (d i f i t ) A l th
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DOE - (design of experiments) Analyse the
Process
The Process
X1 X2 X3
Controllable Inputs
N1 N2 N3
Inputs:
Raw
Materials,
components
, etc.
Uncontrollable Inputs
Y1, Y2, etc.
Quality
Characteristics:
OutputsLSL USL
Key Outputs: Variable How Measured When Measured
1
2
3
Noise Variables: Variable How Measured When Measured
1
2
3
4
5
Con trol la ble I np ut s V ar ia ble How M ea su re d Wh en M ea su re d
1
2
3
4
5
Overall Sampling Plan:
Run Temperature Pressure
1 Hi Hi2 Hi Hi
3 Lo Hi
4 Lo Hi
5 Hi Lo
6 Hi Lo
7 Lo Lo
8 Lo Lo
3.52.51.5
Capability Histogram
4321
3.0
2.5
2.0
1.5
Xbar and R Chart
S u b g r
Means
M U=2 . 3 7 6UCL =2 . 5 6 8
L CL =2 . 1 8 3
0.9
0.6
0.3
0.0
Ranges
R=0 . 5 1 6 2
UCL =0 . 9 6 2 1
L CL =0 . 0 7 0 2 7
4321
Last 4 Subgroups
3.0
2.5
2.0
1.5
Su b g ro u p Nu mb e r
Values
41
2 . 9 1 9 5 81.83175
Cp :2 .7 6CPU:2 .9 9
CPL :2 .5 3Cp k :2 .5 3
Capability PlotPro c e s s To le ra n c e
Sp e c i f i c a t i o n s
StDev :0.181306
III
III
3.52.51.5
Normal Prob Plot
Capab i l i t y us ing Poo led S tandard Dev ia t ion
DOE (d i f i t ) I th
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DOE - (design of experiments) Improve the
Process
Uncontrollable Inputs
The Process
X1 X2 X3Controllable Inputs
N1 N2 N3
Inputs:
Raw
Materials,
components
, etc.
Y1, Y2, etc.
Quality
Characteristics:
OutputsX
X
XLSL USL
LSL USL
ScrewRPM
PrimWdth
Nip FPM
Three Factor Design
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Examine the process
A process is considered to be stable and in
a state of control, or under control, when
the performance of the process fallswithin the statistically calculated control
limits and exhibits only chance, or
common causes.
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Process Capability
Tolerances
design specifications reflecting product
requirements
Process capability
range of natural variability in a process what we
measure with control charts
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Process Capability
(b) Design specificationsand natural variation thesame; process is capableof meeting specificationsmost of the time.
DesignSpecifications
Process
(a) Natural variationexceeds designspecifications; processis not capable of
meeting specificationsall the time.
DesignSpecifications
Process
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Process Capability (cont.)
(c) Design specificationsgreater than naturalvariation; process iscapable of always
conforming tospecifications.
DesignSpecifications
Process
(d) Specifications greaterthan natural variation,but process off center;capable but some outputwill not meet upperspecification.
DesignSpecifications
Process
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Process Capability Measures
Process Capability Ratio
Cp =
=
tolerance range
process range
upper specification limit -lower specification limit
6
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Computing Cp
Net weight specification = 9.0 oz 0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz
Cp =
= = 1.39
upper specification limit -lower specification limit
6
9.5 - 8.5
6(0.12)
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What is a Sigma process
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Precision
Lesser the standard deviation of the process, more precise or
consistent is the process
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Meaning of a Sigma process
From a sigma process we come to know that at what
distance, in terms of the standard deviation, the
specification limits are placed from the target value.
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3 Sigma Vs 6 Sigma
The goal of Six Sigma program is to reduce the variation in every
process to such an extent that the spread of 12 sigmas i.e. 6Sigmas on either side of the mean fits within the process
specifications. The figure on next slide shows what this looks
like.
3 Si V 6 Si
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2 3 4 5 6 7 8 9 1210 16151413111
LSL USL
6 Sigma curve
3 Sigma curve
3 Sigma Vs 6 Sigma
In a 3 sigma process the values are widely spread along the center line,
showing the higher variation of the process. Whereas in a 6 Sigma
process, the values are closer to the center line showing
less variation in the process.
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Why 6 sigma?
LSL USL1.5SD
By shifting 3 sigma
process 1.5 SD, we
create 66,807 defects
per billion
opportunities
By shifting 6 sigma
process 1.5 SD, we
create 3.4defects per
billion opportunities
1.5SD
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Sigma Level
Sigma level DPMO PercentdefectivePercentage
yield Cp
1 691,462 69% 31% 0.33
2 308,538 31% 69% 0.67
3 66,807 6.7% 93.3% 1.00
4 6,210 0.62% 99.38% 1.33
5 233 0.023% 99.977% 1.67
6 3.4 0.00034% 99.99966% 2.00
7 0.019 0.0000019% 99.9999981% 2.33
http://en.wikipedia.org/wiki/Defects_per_million_opportunitieshttp://en.wikipedia.org/wiki/Defects_per_million_opportunities -
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