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Statistical Quality
Control
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Quality Definition
Quality is defined as the totality of features and
characteristics of a product or service that bears
on its ability to satisfy given needs. Organizations recognize that to be competitive in
todays global economy, they must strive for high
levels of quality.
As a result, an increased emphasis falls on
methods for monitoring and maintaining quality.
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Quality Assurance
Quality assurance refers to the entiresystem of policies, procedures, and
guidelines establish by an organization toachieve and maintain quality. Quality assurance consists of two principal
functions:Quality engineeringQuality control
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The objective of quality engineering is to
include quality in the design of theproducts and processes and to identify
potential quality problems prior to
production. Quality control consists of making a series
of inspections and measurements to
determine whether quality standards arebeing met.
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If quality standards are not being met ,
corrective and/ or preventive action can be
taken to achieve and maintainconformance.
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Statistical Process Control
Despite high standards of quality inmanufacturing and production operations,
machine tools will invariably wear out,vibrations will throw machines settings outof adjustment, purchased materials will bedefective, and human operators will make
mistakes. Any or all of these factors canresult in poor quality output.
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Fortunately, procedures are available for
monitoring production output so that poor
quality can be detected early and theproduction process can be adjusted or
corrected.
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If the variation in the quality of the
production output is due to assignablecauses such as tools wearing out,incorrect machine settings, poor qualityraw materials, or operator error, the
process should be adjusted or correctedas soon as possible.
Alternatively, if variation is due to
common causes that is, temperature,humidity and so on, which themanufacturer cannot possibly control- theprocess does not need to be adjusted.
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The main objective of the statistical
process control is to determine whether
variations in the output are due toassignable causes or common causes.
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Control Charts
Control charts show a step by step
approach to statistical process control.
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Major Parts of Control Chart
Value
Average
Quality
Scale(Upper Control Limit)
(Central Line)
(Lower Control Limit)
3 sigma
3 sigma
Out of Control
Out of Control
UCL
LCL
1 2 3 4 5 6 7Sample (Sub-group) Number
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CHARTS: Control charts for Process Means
In order to ascertain whether the process
is in control or out of control, - charts are
connected. In regard to the process output, there is an
assumption of normality where and
are known, though in many situations thisassumption may not hold good.
x
x
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The construction of - chart needs the
value of and and also a sample sizen.
There are three lines in a control chart.
The center line, The upper Control Limit (UCL),
The Lower Control Limit (LCL),
x
x
x
3+x
3x
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Example A company is engaged in the manufacture of
battery cells in its plant. The process is said to
be under control if the mean life of battery cells
is 1,200 hrs with a standard deviation of 75 hrs.
Considering these values to be the processaverage and process dispersion.
You are required to determine the 3 sigma
control limits for - chart for samples of size 16.
x
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Solution:
16751200 === nandhrshrsGiven
75.1143
)163(75/1200
/3
25.1256
)163(75/1200
/3
==
=
=+=
+=
nLCL
nUCL
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CHARTS: when are not knownx and
nd
RxLCL
nd
RxUCL
2
2
3
3
=
+=
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Example
A company manufactures tyres. A qualitycontrol engineer is responsible to ensure
that the tyres turned out are fit for use up
to 40,000 km. He monitors the life of the output from the
production process.
From each of the 10 batches of 900 tyres,he has tested 5 tyres and recorded the
following data, with measured in
thousands of km.Randx
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Batch 1 2 3 4 5 6 7 8 9 10
40.2 43.1 42.4 39.8 43.1 41.5 40.7 39.2 38.9
41.9
1.3 1.5 1.8 0.6 2.1 1.4 1.6 1.1 1.3 1.5
x
R
26.405326.2
)42.1(308.41
3
9.415326.2
)42.1(308.413
08.41
42.110
2.14
08.4110
8.410
2
2
=
+==
=
+=+=
=
===
===
nd
RxLCL
nd
RxUCL
CL
k
RR
k
xx
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R-Charts: Control Charts for Process
Variability R-chart can be used to control the
variability of a process.
To develop the R-chart, we need to thinkof the range of a sample as a random
variable with its own mean and standard
deviation.
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==
+=+=
2
3
2
3
2
3
2
3
31
3
31
3
d
dR
d
RdRUCL
d
d
Rd
Rd
RUCL
It may be noted as these limits are also calculated as:
2
333
2
344
31,
31,
d
dDwhereDRLCL
d
dDwhereDRUCL
==
+==
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We have to determine the UCL and LCL
by applying the formula:
0)astakenbe(to156.0326.2
)864.0(311.42
31
3996.2326.2
)864.0(311.42
31
2
3
2
3
=
=
=
=
+=
+=
d
dRLCL
approxor
d
dRUCL