lecture_no._2.pptx

7/29/2019 Lecture_No._2.pptx

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Copyright 2013 M. Naveed Akhtar,UMT

Email: mnab k mail.com

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2Lecture

Statistics in TextileEngineeringBy

M. Naveed Akhtar, UMTPH. +92 321 6682395

E-Mail [email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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SAMPLING IN TEXTILES

MA-310 Statistical Methods for Textile Engineers

By

M. NAVEED AKHTARContact: 0306-7122490

E-Mail: [email protected]

Copyright 2013 M. Naveed Akhtar,UMT

Email: [email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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Reference Books:

1. Physical testing of Textiles by B. P. Saville2. Principles of Textile Testing by J. E. Booth


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POPULATION AND SAMPLE

POPULATION

The whole bulk of the material available for testing

is termed the population

In Textiles population may be fibre bales, loose fibremass, laps, sliver, roving, yarn bobbins, yarn cones,

fabric or garments


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POPULATION AND SAMPLE

SAMPLE

A relatively small number of individual

members which is selected to represent the

whole population is termed sample


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OBJECTIVE OF SAMPLING

The aim of sampling is to produce an unbiased

sample in which the proportions of, forexample, the different fibre lengths in the

sample are the same as those in the bulk


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UNITS OF SAMPLE

The units for the sample will be the same as

the population

The units may be numbers or weight measure

in textiles such as grams, kilograms etc


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IMPORTANT TERMS

Consignment: Quantity of material delivered atthe same time

Test Lot or Batch: All containers of textilematerial of one defined type and quality,delivered to one customer according to one

dispatch note. It is equivalent to statisticalpopulation

Laboratory Sample: A sample derived from thetest lot by random sampling for being tested in

the laboratory


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IMPORTANT TERMS

Test Specimen: Specimen actually derived fromthe Laboratory Sample for individual

measurement.

Container or Case: A shipping unit identified onthe dispatch note, eg, carton, box, bale etc. It

may or may not contain packages. Package: Elementary units of material present in

each container of the consignment which can beunwound.


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FIBRE SAMPLING

Zoning

Zoning is a method that is used for selectingsamples from raw cotton or wool or other loose

fibre where the properties may vary considerably

from place to place (ie heterogeneous).

At least 40 small samples of fibres (approx 50

gram each) are taken randomly from differently

widely spaced places of the whole lot.


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FIBRE SAMPLING (zoning)

Each sample is divided into two halves- onlyone half is retained at random and is againdivided into two halves.

The procedure is repeated until n/x fibresremain in the sample where

n = total number of fibres required insample and

x = number of original samples taken


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Fibres from all the samples are then united

together to get final test sample of correct sizecontaining n fibres


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FIBRE SAMPLING

Core Sampling

A tube with a sharpened tip is forced into the bale ofcotton or raw wool and a core of fibres is withdrawn

The tubes are 600mm long so as to penetrate halfwayinto the bale

A detachable cutting tip with internal diameter slightlysmaller than that of tube is used

14 to 18mm diameter cores used for varying samplesize

All cores combined to get required sample size


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FIBRE SAMPLING

Fibre Sampling from Sliver, Roving and Yarn

Problems of length and extent bias faced in suchsampling

Length Bias: That is longer fibres will have morechance of being selected

Extent: It is the distance parallel to the strand axisthrough which a fibre extends

Extent Bias: The chance of a fibre being selectedfrom a strand is proportional to its extent


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FIBRE SAMPLING (extent bias)


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FIBRE SAMPLING (sliver, roving)

Fibre extent instead of fibre length determines

chance of selection

Length bias must be avoided is testing fibre

length, but also has effect while testing fibre

fineness, strength etc.

To avoid bias- prepare a numerical sample

Prepare a length biased sample so that its bias

can be taken care of during calculation


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FIBRE SAMPLING

Numerical Sample

The percentage by numbers of fibres is each lengthgroup should be the same in the sample as it is in thebulk

A and B represent two planes. Solid circles show allthose fibres whose left ends lay between A and B

If all fibres left to A are removed- all those fibresmarked with solid circles will be selected

Similarly by drawing another plane right to B andrepeating the activity- similar samples are prepared


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FIBRE SAMPLING (numerical)


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FIBRE SAMPLING

Length Biased Sample

The percentage of fibres in any length group is

proportional to the product of length and the

percentage of fibres of that length in the bulk

Removal of one such sample changes the

composition of remaining bulk- as sample

removed contains higher proportion of longer

fibres


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FIBRE SAMPLING(Length Bias)

If A and B are two planes through the sliver thenchance of a fibre crossing these lines isproportional to its length.

If fibres crossing this area are selected- longerfibres will have more chance of being selected

Fibres are gripped along narrow line of contact,loose fibres removed by combing both sides ofcontact.

Such sample is also known as tuft sample

Such samples used for length measurement byFibrograph


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FIBRE SAMPLING (length bias)


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FIBRE SAMPLING (tuft sample)

The histograms show the mean fibre length

from both the numerical sample and tuft

sample


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FIBRE SAMPLING


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FIBRE SAMPLING

Random Draw Method

Used for sampling sliver and top

Sliver is parted by hand and placed on two

velvet boards with the parted end near thefront of the first board.

The opposite end of the sliver is weighed

down with a glass plate to stop it moving Discard a 2mm fringe of fibres from the parted

end using a wide grip


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FIBRE SAMPLING (Random Draw) This procedure is repeated until a distance

equal to that of the longest fibre in the sliverhas been removed

All succeeding draws will be used as sample asthese will be representing all fibre lengths

They represent a numerical sample where all

the fibres with ends between two lines aretaken as the sample

All the fibres of the sample must be measured


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FIBRE SAMPLING (Random Draw)


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FIBRE SAMPLING

Cut Square Method

Used for sampling of yarn

A length of the yarn being tested is cut off andthe end untwisted by hand

The end is laid on a small velvet board andcovered with a glass plate

The untwisted end of the yarn is then cut about5mm from the edge of the plate

All the fibres that project in front of the glassplate are removed one by one with a pair offorceps and discarded


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FIBRE SAMPLING (Cut Square)

All the cut fibres are removed, leaving only fibres withtheir natural length

The glass plate is then moved back a few millimetres,exposing more fibre ends

These are then removed one by one and measured

When these have all been measured the plate is movedback again until a total of 50 fibres have beenmeasured

In each case once the plate has been moved allprojecting fibre ends must be removed and measured


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The whole process is then repeated on fresh

lengths of yarn chosen at random from the

bulk, until sufficient fibres have been

measured


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YARN SAMPLING

Ten packages are selected at random from theconsignment

If the consignment contains more than five

cases, five cases are selected at random fromit

Test sample will consist of two packages

selected at random from each case The appropriate number of tests are then

carried out on each package


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FABRIC SAMPLING

Fabric samples are always taken from the

warp and weft separately

The warp direction should be marked on each

sample before it is cut out

No two specimens should contain the same

set of warp or weft threads

Samples should not be taken from within

50mm of the selvedge


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FABRIC SAMPLING


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MEASUREMENT

A quantitative comparison between a predefined

standard and the object being measured

The actual process of measurement is always

subject to errors

Error is the difference between the measured

value and the 'true' value

Precision is the quality that characterises theability of a measuring instrument to give the

same value of the quantity measured


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MEASUREMENT (Accuracy)

Precision of any measurement is obtained bymaking a number of identical measurementsand estimating the dispersion of the results

about the mean by calculating StandardDeviation or Coefficient of Variation

Accuracy is nearness to the 'true value ofthe quantity being measured

It is obtained by calibration of the measuringsystem against the appropriate standards


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MEASUREMENT (Sensitivity)

Sensitivity is the least change in the measured

quantity that will cause an observable change

in the instrument reading

It can be increased by amplifying the output

or by using a magnifying lens to read the scale

Errors will also amplify if there is no increase

in accuracy of the calibration and a reduction

in sources of variation


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STATISTICAL TERMS


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STATISTICAL TERMS


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STATISTICAL TERMS


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STATISTICAL TERMS

Coefficient of variation (CV): It is often used as

a measure of dispersion

It is the standard deviation expressed as apercentage of the mean


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STATISTICAL TERMS

Standard error of the mean: It is a measure of

the reliability of the mean value obtained

from a sample of a particular size. It is the standard deviation of the means that

would be obtained if repeated samples of the

given size were measured


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STATISTICAL TERMS

The standard error is used to place confidence

limits on the mean that has been measured


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STATISTICAL TERMS

There is 95% probability that the population

mean lies within (tx standard error) of the

measured mean value.

For large samples or parent universe the value

oftis 1.96

For smaller samples (less than 30 size) the

value oftis greater and can be calculatedfrom t-tables

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