Post on 04-Jun-2018
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Quality Control Charts
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Control Charts
Primary purpose of control charts is toindicate at a glance when productionprocesses might have changed sufficientlyto affect product quality.
If the indication is that product quality hasdeteriorated, or is likely to, then corrective istaken.
If the indication is that product quality isbetter than expected, then it is important tofind out why so that it can be maintained.
Use of control charts is often referred to as
statistical process control (SPC).
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Constructing Control Charts
Vertical axis provides the scale for the
sample information that is plotted on the
chart.
Horizontal axis is the time scale.
Horizontal center line is ideally determined
from observing the capability of theprocess.
Two additional horizontal lines, the lower
and upper control limits, typically are 3standard deviations below and above
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Constructing Control Charts
If the sample information falls within thelower and upper control limits, the qualityof the population is considered to be incontrol; otherwise quality is judged to beout of control and corrective actionshould be considered.
Two versions of control charts will be
examined Control charts for attributes
Control charts for variables
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Control Charts for Attributes
Inspection of the units in the sample is
performed on an attribute
(defective/non-defective) basis.
Information provided from inspecting a
sample of size n is the percent
defective in a sample, p, or the numberof units found to be defective in that
sample divided by n.
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Control Charts for Attributes
Although the distribution of sampleinformation follows a binomialdistribution, that distibution can beapproximated by a normal distribution
with a
mean of p
standard deviation of
The 3scontrol limits are
)/np(100p
)/np(100p3-/p
-
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Example: Attribute Control Chart
Every check cashed or deposited atState Bank of India must be encodedwith the amount of the check before it
can begin the clearing process. Theaccuracy of the check encodingprocess is of upmost importance. Ifthere is any discrepancy between theamount a check is made out for andthe encoded amount, the check isdefective.
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Example: Attribute Control Chart
Twenty samples, each consisting of250 checks, were selected and
examined. The number of defective
checks found in each sample is shownbelow.
4 1 5 3 2 7 4 5 2 3
2 8 5 3 6 4 2 5 3 6
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Example: Attribute Control Chart
The manager of the check encodingdepartment knows from past
experience that when the encoding
process is in control, an average of1.6% of the encoded checks are
defective.
She wants to construct a p chart with
3-standard deviation control limits.
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Example: Attribute Control Chart
s
(1 ) .016(1 .016) .015744.007936
250 250p
p p
n
UCL = 3 =.016+3(.007936)= .039808 or 3.98%p
p s
LCL = 3 =.016-3(.007936)=-.007808= 0%p
p s
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Example: Attribute Control Chart
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
0.045
0 5 10 15 20SampleProportion
p
Sam le Number
p Chart for State Bank of IndiaU
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Control Charts for Variables
Inspection of the units in the sample isperformed on a variable basis.
The information provided from inspecting
a sample of size n is:
Sample mean, x, or the sum of measurement
of each unit in the sample divided by n
Range, R, of measurements within the
sample, or the highest measurement in the
sample minus the lowest measurement in the
sample
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Control Charts for Variables
In this case two separate control chartsare used to monitor two different
aspects of the processsoutput:
Central tendency Variability
Central tendency of the output is
monitored using the x-chart. Variability of the output is monitored
using the R-chart.
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x-Chart
The central line is x, the sum of a
number of sample means collected
while the process was considered to bein control divided by the number of
samples.
The 3slower control limit is x - AR The 3supper control limit is x + AR
Factor A is based on sample size.
=
=
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R-Chart
The central line is R, the sum of a
number of sample ranges collected while
the process was considered to be in
control divided by the number ofsamples.
The 3slower control limit is D1
R.
The 3supper control limit is D2R.
Factors D1and D2 are based on sample
size.
3 C t l Ch t F t f
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3sControl Chart Factors for
Variables
Control Limit Factor Control Limit FactorSample for Sample Mean for Sample Range
Size n A D1 D2
2 1.880 0 3.267
3 1.023 0 2.575
4 0.729 0 2.282
5 0.577 0 2.116
0.308 0.223 1.777
15 0.223 0.348 1.65220 0.180 0.414 1.586
25 0.15310 0.459 1.541
Over 25 0.45+.001n 1.55-.0015n0.75(1/ )n
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Statistical Process Control
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Quality Control (QC)
Controlthe activity of ensuringconformance to requirements and
taking corrective action when
necessary to correct problems Importance
Daily management of processes
Prerequisite to longer-term improvements
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Designing the QC System
Quality Policy and Quality Manual Contract management, design control and
purchasing
Process control, inspection and testing
Corrective action and continual improvement
Controlling inspection, measuring and test
equipment (metrology, measurement system
analysis and calibration)
Records, documentation and audits
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Commonly Used Control
Charts
Variables data
x-bar and R-charts
x-bar and s-charts Charts for individuals (x-charts)
Attribute data
For defectives (p-chart, np-chart) For defects (c-chart, u-chart)
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Inspection/Testing Points
Receiving inspection
In-process inspection
Final inspection
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Receiving Inspection
Spot check procedures
100 percent inspection
Acceptance sampling
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Acceptance Sampling
Lot received for inspection
Sample selected and analyzed
Results compared with acceptance criteria
Accept the lot
Send to production
or to customer
Reject the lot
Decide on disposition
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In-Process Inspection
What to inspect? Key quality characteristics that are related
to cost or quality (customer requirements)
Where to inspect? Key processes, especially high-cost and
value-added
How much to inspect?All, nothing, or a sample
St ti ti l P C t l
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Statistical Process Control
(SPC)
A methodology for monitoring aprocess to identify special causes of
variation and signal the need to take
corrective action when appropriate SPC relies on control charts
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Common
Causes
Special Causes
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Histograms do
not take intoaccount changes
over time.
Control charts
can tell us
when aprocess
changes
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Control Chart Applications
Establish state of statisticalcontrol
Monitor a process and signalwhen it goes out of control
Determine process capability
C l U d C t l
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Commonly Used Control
Charts
Variables data
x-bar and R-charts
x-bar and s-charts Charts for individuals (x-charts)
Attribute data
For defectives (p-chart, np-chart)
For defects (c-chart, u-chart)
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SPC Implementation
Requirements
Top management commitment
Project champion
Initial workable projectEmployee education and training
Accurate measurement system