SQC MATH.(Vikas,Vaibhav,Swanand,Shree.pptx

8/10/2019 SQC MATH.(Vikas,Vaibhav,Swanand,Shree.pptx

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STATISTICAL

QUALITY

CONTROL

(S.Q.C.)

PRESENTED BY-:Vaibhav Karnawat (121416008

Vikas Patil (121416010)

Swanand Pisat (1214160)

Shrinivas Shirnewar(12141601


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CONTENTS-:

Meaning.

Definitions

CharacteristicsCauses of variations.

Methods of S.Q.C..

Process Control-:

Control Chart..

Purpose & uses of control charts.Types of control charts

Control charts for variables-:

Chart

R Chart

Chart


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Control chart for attributes-:p-chart

np-chart......C-Chart

Product Control/Acceptance Sampling-:Meaning..Definition.Risks in Acceptance Sampling-:

Producers Risk.Consumers Risk.

Types of Sampling Inspection plans-:Single Sampling planDouble Sampling Plan..Multiple Sampling Plan.

Advantages of S.Q.CLimitations of S.Q.C.


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ACKNOWLEDGEMENT -:

Mrs. Dhere Mam our Advance Mathemlecturer, without her guidance &suggestions this work is not possibl


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MEANING-:

Manufacturer Refers to the use of statitechniques in controlling the quality of go

Means of establishing & achieving quality

specification, which requires use of toolstechniques of statistics.


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DEFINITION-:

Statistical quality control can be simply dean economic & effective system of maintimproving the quality of outputs throughwhole operating process of specification

production & inspection based on continutesting with random samples.

By-:

YA LUN CH


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DEFINITION-:

Statistical quality control should be vieweof tools which may influence decisions tofunctions of specification, production orinspection.

By-:

EUGENE L. GRANT


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CHARACTERISTICS OF S.Q.C.-: Designed to control quality standard of goo

produced for marketing.

Exercise by the producers during productiassess the quality of goods.

Carried out with the help of certain statisttools like Mean Chart, Range Chart, P-CharChart etc.

Designed to determine the variations in qu

of the goods & limits of tolerance.


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CAUSES OF VARIATIONS INQUALITY-:

1. ASSIGNABLE CAUSES-: It refers to tchanges in the quality of the products wbe assigned or attributed to any particcauses like defective materials, defect

labour, etc.2. CHANCE CAUSES-: These causes takeper chance or in a random fashion as a the cumulative effect of a multiplicity minor causes which cannot be identifie

causes are inherent in every type of pr


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METHODS OF S.Q.C.-:

1. PROCESS CONTROL-: Under this the qthe products is controlled while the proare in the process of production.

The process control is secured with th

technique ofcontrol charts. Control chalso used in the field of advertising, paThey ensures that whether the producconfirm to the specified quality standa

CONTROL CHARTS


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A control chartis a time plot of a statistic, such as a sample mean, range,

standard deviation, or proportion, with a center line and upper and lower

control limits. The limits give the desired range of values for the statistic.

When the statistic is outside the bounds, or when its time plot reveals certapatterns, the process may be out of control.

A process is considered in statistical controlif it has no assignable causes

only natural variation.

UCL

LCL

Center

Line

Time

Value

This point is out of the control limits

3

3

CONTROL CHARTS-:


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PURPOSE & USES OF CONTROLCHARTS-:

1. Helps in determining the quality standaproducts.

2. Helps in detecting the chance & assignavariations in the quality standards by secontrol limits.

3. Reveals variations in the quality standarproducts from the desired level.4. Indicates whether the production proce

control or not.5. Ensures less inspection cost & time in t

process control.

TYPES


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TYPES-:

Types of

Control Charts

Control Charts

for Variables

Chart R-Chart -Chart

Control Charts

for Attributes

p-Chart np-Chart C


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CONTROL CHARTS FOR VARIAB

CHART/ MEAN CHART-: This chart iconstructed for controlling the variatioaverage quality standard of the productproduction process.

R-CHART-: This chart is constructed focontrolling the variations in the dispersvariability of the quality standards of tproducts in a production process.


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EXAMPLE-:

Sample No. Weights

1

2

3

4

5

20 15 10 11 14

12 18 10 8 22

21 19 17 10 13

15 12 19 14 20

20 19 26 12 23

Conversion factors for n=5, A2 =0.577, D3=0,D4=2.115


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SOLUTION-:

Sampleno.

Weights (X) Total

Weights(X)

=(X/5)Rang

R=(L

1

2

3

45

K=5

20 15 10 11 14

12 18 10 8 22

21 19 17 10 13

15 12 19 14 2020 19 26 12 23

70

70

80

80100

14

14

16

1620

=80

10

14

11

814

R=5


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Grand = /K = 80/5=16

Grand ChartGrand = 16 (Central line)

Control limits-:

UCL =Grand + A2

= 16 + 0.577 x 11.4= 22.577

LCL =Grand - A2= 16 0.577 x 11.4

= 9.423


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= R/K = 57/5 = 11.4

Range Chart

= 11.4 (Central line)

Control limits-:

UCL = D4.

= 2.115 x 11.4

= 24.09

LCL = D3.

= 0 x 11.4

= 0


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Chart-: This chart is constructed to get a better picture of the

variations in the quality standard in a process than that is obtained

from the range chart provided the standard deviation() of the

various samples are readily available.

Example-: Quality control is maintained in a factory with the helpstandard deviation chart. Ten items are chosen in every sample.samples in all were chosen whose S was 8.28. Determine the thrsigma limits of - chart. You may use the following-:

n = 10, B3= 0.28, B4= 1.72, K = 18.

Solution-: = S/K = 8.28/18 = 0.46

UCL = B4. LCL = B3.

= 1.72 x 0.46 = 0.28 x 0.46

= 0.7912 = 0.1288


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Control Charts for Attributes

p-chart-: This chart is constructed for

controlling the quality standard in the

fraction defective of the products in awhen the observed sample items are

into defectives & non-defectives.

np-chart-: This chart is constructed for

controlling the quality standard of atta process where the sample size is eq

required to plot the no. of defectives

samples instead of fraction defectives


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Example-:

Sample No. Size of sample(n)

No. ofdefectives (d)

Fractiondefectives (d/

12

3

4

5

6

7

8

9

10

100100

100

100

100

100

100

100

100

100

53

3

6

5

6

8

10

10

4

0.050.03

0.03

0.06

0.05

0.06

0.08

0.1

0.1

0.04

K = 10 d = 60


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= Total no. of defectives/Total no. of units 60/1000 = 0.06q= 1- = 1- 0.06 = 0.94

= 0.06 (central line)

UCL = + 3 . q/n= 0.06 + 30.06x0.94/100= 0.1311

LCL = - 3 . q/n= 0.06 - 3 0.06x0.94/100= -0.0111 = 0


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Example-: A i ti f 10 l f i 400 h f 10 l t l th


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Example : An inspection of 10 samples of size 400 each from 10 lots reveal thefollowing number of defectives:

17, 15, 14, 26, 9, 4, 19, 12, 9, 15

Calculate control limits for the no. of defective units.

Solution-: n = 400, k (No. of samples) = 10, d (total no. of defective140

n = d/k = 140/10 = 14

Now, = n /n = 14/400 = 0.035,

q= 1- = 1- 0.035 = 0.965

n = 14 (central line)

UCL= n + 3 n q LCL= n - 3 n q

= 14 + 3400x0.035x0.965 = 14 - 3400x0.035x0.965

= 25.025 = 2.975


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C-Chart-:

This chart is used for the control ofno. of defects per unit say a piece ofcloth/glass/paper/bottle which maycontain more than one defect. Theinspection unit in this chart will be a single

unit of product. The probability ofoccurrence of each defect tends to remainvery small.


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USES-:

The following are the field of application of C-Cha

Number of defects of all kinds of aircraft finassembly.

Number of defects counted in a roll of coatedsheet of photographic film, bale of cloth etc.


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ACCEPTANCE SAMPLING-:

Meaning-:Another major area of S.Q.C. is Product Control

Acceptance Sampling. It is concerned with thof manufactured products. The items are inspeknow whether to accept a lot of items conformistandards of quality or reject a lot as non- conf


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DEFINITION-:

Acceptance Sampling is concerned with the deciaccept a mass of manufactured items as conforstandards of quality or to reject the mass as noconforming to quality. The decision is reached tsampling.

By-:

SIMPSON AND KAFKA


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Risks in Acceptance sampling-:

1. Producers risk-: Sometimes inspite of good qusample taken may show defective units as suchwill be rejected, such type of risk is known as risk.

2. Consumers Risk-: Sometimes the quality of thgood but the sample results show good qualitysuch the consumer has to accept a defective lrisk is known as consumers risk.


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Types of Sampling Inspection Pla

Single Sampling Plan-: Under single sampling plan, n items is first chosen at random from a lot ofIf the sample contains, say, c or few defectiveaccepted, while if it contains more than c defelot is rejected (c is known as acceptance numb


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Single Sampling Plan-:

Count the no. of

defectives,

d in the sample of size

n

Is d c

If yes, then accept the

lotIf no, then reject the lot


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Double Sampling Plan-:

Under this sampling plan, a sample of n1 items is firchosen at random from the lot of size N. If thesample contains, say, c1 or few defectives, the lot iaccepted; if it contains more than c2 defectives, thlot is rejected. If however, the number of defectivin the sample exceeds c1, but is not more than c2, asecond sample of n2 items is taken from the same lIf now, the total no. of defectives in the two sampletogether does not exceed c2, the lot is accepted;

otherwise it is rejected. (c1 is known as acceptanceno. for the first sample & c2 is the acceptance no. oboth the samples taken together)

Double Sampling Plan-:C unt th n


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p gCount the no.

of defectives,

d1in the first

sample of size

n1

Is d1 c1 ?

If No, then

check

If c1 d1 c2?

Draw another

sample of size

n2

Count the no.

of defectives

d2 in this

sample

Is d1 + d2 c2

If No,then

reject the lot

If yes, then

accept the lot.

If yes, accept

the lot


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ADVANTAGES OF S.Q.C.-:

Helpful in controlling quality of a product

Eliminate Assignable causes of variation Better quality at lower inspection cost

Useful to both consumers & producers

It makes workers quality conscious

Helps in earn goodwill It leads to more uniform quality of production

Benefits of Statistical Quality Control-:) d f d


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1) It provides a means of detecting error at inspection.

2) It leads to more uniform quality of production.

3) It improves the relationship with the customer.

4) It reduces inspection costs.

5) It reduces the number of rejects and saves the cost of m

6) It provides a basis for attainable specifications.

7) It points out the bottlenecks and trouble spots.

8) It provides a means of determining the capability of themanufacturing process.

9) It promotes the understanding and appreciation of qualitcontrol.


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LIMITATIONS-:

Does not serve as a PANACEA for all quality ev It cannot be used to all production process.

It involves mathematical & statistical problems process of analysis & interpretation of variationquality.

Provides only an information services.


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THANK YOU!!

SQC MATH.(Vikas,Vaibhav,Swanand,Shree.pptx

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