9a. statistical quality control

8/8/2019 9a. Statistical Quality Control

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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

9a. statistical quality control

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