SAMPLING
(b)Biased sample
2.Position of the individual in the population.
3.Subconscious bias of the personal
●Yarn
●Fabric
#Theory and method of fibre sampling:-
(b)Length Bias fibre sample
(c)Extent bias fibre simple
Proportion of fibres having different properties is equal to the proportion in the population called numerical proportion.
Let us assume a homogeneous of fibres having strength and parallel fibres and is composed of a number superimposed stream of fibres having different fibre lengths. Each stream have a particular fibre length.
Q.What is sampling?
It is the act of collecting small quantity of material from the total bulk/population for the purpose of testing.#knowledge needed for sampling for sampling:-
(a)Sample size/quantity:- Depends on the type of test and the degree of variations in the property to be tested.
(b)Number of samples:- Depends on the degree of variation and degree of accuracy required in the result.
Q.why sampling?
●It is physically/practically impossible to test the total population due to the large labour and time required.
●Destructive nature of the test leads to destruction of the total population.
#Types of Sample
(a)Numerical sample(b)Biased sample
(a)Numerical Sample:-
It is sample where every individual in the population has equal chance of being selected.
It is sample where every individual in the population has equal chance of being selected.
It is representative sample. Representative sample:- It represents the total sample and the value of any property tested from the sample is equal to the value of total population. The population of different individual in the sample is equal to the proportion in the population.
(b).Biased sample:-
It is the sample where the selection of any individual from the population is not random but in instead.It is influenced by factors other than chance.
It is not a representative sample and the value of any property tested from the sample does not match with the population.
The proportion of different individual in the sample is not equal to the proportion in the population.
It is the sample where the selection of any individual from the population is not random but in instead.It is influenced by factors other than chance.
It is not a representative sample and the value of any property tested from the sample does not match with the population.
The proportion of different individual in the sample is not equal to the proportion in the population.
#Probable causes of biasness:-
1.Physical appearance of the individuals2.Position of the individual in the population.
3.Subconscious bias of the personal
#sampling in textile
●Fibre●Yarn
●Fabric
#Theory and method of fibre sampling:-
Types of fibre sample:-
(a)Numerical fibre sample(b)Length Bias fibre sample
(c)Extent bias fibre simple
(a)Numerical fibre simple:-
It is a fibre sample where every fibre in the population has equal chance of being selected and included in the sample.
It is a representative sample.Proportion of fibres having different properties is equal to the proportion in the population called numerical proportion.
Let us assume a homogeneous of fibres having strength and parallel fibres and is composed of a number superimposed stream of fibres having different fibre lengths. Each stream have a particular fibre length.
For any stream,
n=L/d
Proportion of fibres of different length
=n1/Σn, n2/Σn, n3/ΣN........
................( Σn=n1+n2+n3+.......)
=Numerical proportion
n=L/d
Proportion of fibres of different length
=n1/Σn, n2/Σn, n3/ΣN........
................( Σn=n1+n2+n3+.......)
=Numerical proportion
Hence, in a numerical sample proportion of different length is proportional to the number of fibres in the population.
The proportion of fibres of different length is different from the proportion in the population.
From the given strand let us select in "K" attempts fibres from different places at random and combine them to form a sample.
The probability of selecting a fibre of a given length in each attempt is given by
l/d
Q2. The sliver containing a total of 10000 fibres have the following composition of different fibre length.
(b)Length bias sample:-
It is a fibre sample where there is a higher proportion of longer length fibres then shorter fibres as compared to a numerical sample.
It is not a representative sample.The proportion of fibres of different length is different from the proportion in the population.
From the given strand let us select in "K" attempts fibres from different places at random and combine them to form a sample.
The probability of selecting a fibre of a given length in each attempt is given by
l/d
Problems:-
Q1. The population of 2000 fibres have 1000 fibres of length 50 mm and rest 1000 fibres of length 25 mm. calculate the proportion that is likely to the obtained in a numerical sample in a length Biased sample and calculate the average fibre length obtained in each case.
Solution:-
Population=2000 fibres
n1=1000 fibres l1=25mm
n2=1000fibres l2=50mm
Population=2000 fibres
n1=1000 fibres l1=25mm
n2=1000fibres l2=50mm
Numerical bias
=(1000/2000,1000/2000)=(1/2:1/2)
Average fibre length in numerical bias
=(1/2×25)+(1/2×50)=37.8mm
=(1000/2000,1000/2000)=(1/2:1/2)
Average fibre length in numerical bias
=(1/2×25)+(1/2×50)=37.8mm
Length bias
=(25/75,50/75)=(1/3:2/3)
Average fibre length in length bias
=(1/3×25)+(2/3×50)=41.75mm
=(25/75,50/75)=(1/3:2/3)
Average fibre length in length bias
=(1/3×25)+(2/3×50)=41.75mm
Q2. The sliver containing a total of 10000 fibres have the following composition of different fibre length.
Sampling is carried out to generate go to the numerical length bias samples. Calculate the fraction of different fibres likely to be obtained in each sample along with the average fibre length.
Solution:-
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