Control Charts v Good

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STATISTICALSTATISTICAL

QUALITYQUALITY

CONTROLCONTROL

(S.Q.C.)(S.Q.C.)


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ContentsContents--::

Meaning.Meaning.

Definitions Definitions CharacteristicsCharacteristicsCauses of variations.Causes of variations.Methods of S.Q.C..Methods of S.Q.C..

Process ControlProcess Control--::Control Chart..Control Chart..Purpose & uses of control charts.Purpose & uses of control charts.Types of control chartsTypes of control charts

Control charts for variablesControl charts for variables--::

ChartChartR Chart R Chart ChartChart


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Control chart for attributesControl chart for attributes--::pp--chartchart

npnp--chart......chart......CC--ChartChart

Product Control/Acceptance SamplingProduct Control/Acceptance Sampling--::Meaning..Meaning..Definition.Definition.

Risks in Acceptance SamplingRisks in Acceptance Sampling--::Producers Risk.Producers Risk.Consumers Risk.Consumers Risk.

Types of Sampling Inspection plansTypes of Sampling Inspection plans--::Single Sampling planSingle Sampling plan

Double Sampling Plan..Double Sampling Plan..Multiple Sampling Plan.Multiple Sampling Plan.

Advantages of S.Q.CAdvantages of S.Q.CLimitations of S.Q.C.Limitations of S.Q.C.


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MEANINGMEANING--::

manufactured Refers to the use ofmanufactured Refers to the use ofstatistical techniques in controlling thestatistical techniques in controlling the

quality of goods.quality of goods.

Means of establishing & achievingMeans of establishing & achieving

quality specification, which requires usequality specification, which requires useof tools & techniques of statistics.of tools & techniques of statistics.


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DEFINATIONDEFINATION--::

Statistical quality control can be simplyStatistical quality control can be simplydefined as an economic & effective system ofdefined as an economic & effective system ofmaintaining & improving the quality of outputsmaintaining & improving the quality of outputs

throughout the whole operating process ofthroughout the whole operating process ofspecification, production & inspection basedspecification, production & inspection basedon continuous testing with random samples.on continuous testing with random samples.

ByBy--::

YA LUN CHOUYA LUN CHOU


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DefinitionDefinition--::

Statistical quality control should beStatistical quality control should beviewed as a kit of tools which mayviewed as a kit of tools which may

influence decisions to the functions ofinfluence decisions to the functions ofspecification, production or inspection.specification, production or inspection.

ByBy--::EUGENE L. GRANTEUGENE L. GRANT


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CHARACTERISTICS OF S.Q.C.CHARACTERISTICS OF S.Q.C.--::

Designed to control quality standard of goodsDesigned to control quality standard of goodsproduced for marketing.produced for marketing.

Exercise by the producers during production toExercise by the producers during production toassess the quality of goods.assess the quality of goods.

Carried out with the help of certain statistical toolsCarried out with the help of certain statistical toolslike Mean Chart, Range Chart, Plike Mean Chart, Range Chart, P--Chart, CChart, C--Chart etc.Chart etc.

Designed to determine the variations in quality of theDesigned to determine the variations in quality of thegoods & limits of tolerance.goods & limits of tolerance.


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CAUSES OF VARIATIONS INCAUSES OF VARIATIONS IN

QUALITYQUALITY--::1.1. ASSIGNABLE CAUSESASSIGNABLE CAUSES--:: It refers to thoseIt refers to thosechanges in the quality of the products whichchanges in the quality of the products whichcan be assigned or attributed to anycan be assigned or attributed to any

particular causes like defective materials,particular causes like defective materials,defective labour, etc.defective labour, etc.2.2. CHANCE CAUSESCHANCE CAUSES--:: These causes take placeThese causes take place

as per chance or in a random fashion as aas per chance or in a random fashion as a

result of the cumulative effect of aresult of the cumulative effect of amultiplicity of several minor causes whichmultiplicity of several minor causes whichcannot be identified. These causes arecannot be identified. These causes areinherent in every type of production.inherent in every type of production.


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METHODS OF S.Q.C.METHODS OF S.Q.C.--::

1.1. PROCESS CONTROLPROCESS CONTROL--:: Under this theUnder this thequality of the products is controlled whilequality of the products is controlled whilethe products are in the process ofthe products are in the process of

production.production.The process control is secured with theThe process control is secured with thetechnique oftechnique of control chartscontrol charts.. Control chartsControl chartsare also used in the field of advertising,are also used in the field of advertising,packing etc. They ensures that whether thepacking etc. They ensures that whether theproducts confirm to the specified qualityproducts confirm to the specified qualitystandard or not.standard or not.


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A control chart is 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 certain

patterns, the process may be out of control.

A process is considered in statistical control if it has no assignable causes,

only natural variation.

UCL

LCL

Center

Line

Time

Value This point is out of the control limits

3W

3W

Control ChartControl Chart


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PURPOSE & USES OF CONTROLPURPOSE & USES OF CONTROL

CHARTSCHARTS1.1. Helps in determining the quality standard ofHelps in determining the quality standard ofthe products.the products.

2.2. Helps in detecting the chance & assignableHelps in detecting the chance & assignable

variations in the quality standards by settingvariations in the quality standards by settingtwo control limits.two control limits.3.3. Reveals variations in the quality standards ofReveals variations in the quality standards of

the products from the desired level.the products from the desired level.4.4. Indicates whether the production process isIndicates whether the production process is

in control or not.in control or not.5.5. Ensures less inspection cost & time in theEnsures less inspection cost & time in the

process control.process control.


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TypesTypes--::

Types of

ControlCharts

ControlCharts

forVariables

Chart

ControlCharts forAttributes

R-Chart -Chart p-Chart np-Chart C-Chart


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CONTROL CHATS FORCONTROL CHATS FOR

VARIABLESVARIABLESCHART/ MEAN CHARTCHART/ MEAN CHART--:: This chart is

constructed for controlling the variations inthe average quality standard of the products

in a production process. R-CHART-: This chart is constructed for

controlling the variations in the dispersion orvariability of the quality standards of theproducts in a production process.


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EXAMPLEEXAMPLE--::

Sample No.Sample No. WeightsWeights

11

2233

44

55

2020 15 10 11 1415 10 11 14

1212 18 10 8 2218 10 8 222121 19 17 10 1319 17 10 13

1515 12 19 14 2012 19 14 20

20 19 26 12 2320 19 26 12 23

Conversion factors for n=5, AConversion factors for n=5, A22 =0.577, D=0.577, D33 =0,=0,DD44=2.115=2.115


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SolutionSolution--::SampleSampleno.no.

Weights (X)Weights (X) TotalTotal

WeightsWeights((X)X)

=(=(X/5)X/5)

RangeRange

R=(LR=(L--S)S)

11

22

33

44

55

K=5K=5

2020 15 10 11 1415 10 11 14

1212 18 10 8 2218 10 8 22

2121 19 17 10 1319 17 10 13

1515 12 19 14 2012 19 14 20

20 19 26 12 2320 19 26 12 23

7070

7070

8080

8080

100100

1414

1414

1616

1616

2020

=80=80

1010

1414

1111

88

1414

R=57R=57


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GrandGrand == /K = 80/5=16/K = 80/5=16

GrandGrandChartChartGrandGrand= 16 (Central line)= 16 (Central line)

Control limitsControl limits--::

UCL =UCL = GrandGrand + A+ A22= 16 + 0.577 x 11.4= 16 + 0.577 x 11.4= 22.577= 22.577

LCL =LCL = GrandGrand -- AA22= 16= 16 0.577 x 11.40.577 x 11.4= 9.423= 9.423


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== R/K = 57/5 = 11.4R/K = 57/5 = 11.4

Range ChartRange Chart= 11.4 (Central line)= 11.4 (Central line)

Control limitsControl limits--::UCL = DUCL = D44.. = 2.115 x 11.4= 2.115 x 11.4= 24.09= 24.09

LCL = DLCL = D33..= 0 x 11.4= 0 x 11.4= 0= 0


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ChartChart--:: This chart is constructed to get a better picture ofThis chart is constructed to get a better picture ofthe variations in the quality standard in a process than that isthe variations in the quality standard in a process than that is

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

of the various samples are readily available.of the various samples are readily available.

ExampleExample--:: Quality controlismaintainedin a factory withQuality controlismaintainedin a factory withthehelp ofstandarddeviation chart. Ten itemsare chosen inthehelp ofstandarddeviation chart. Ten itemsare chosen in

everysample. 18 samplesin all were chosen whoseeverysample. 18 samplesin all were chosen whoseS wasS was8.28. Determinethethreesigmalimits of8.28. Determinethethreesigmalimits of-- chart.chart. You may useYou may usethe followingthe following--::

n = 10, Bn = 10, B33 = 0.28, B= 0.28, B44 = 1.72, K = 18.= 1.72, K = 18.

SolutionSolution--:: == S/K = 8.28/18 = 0.46S/K = 8.28/18 = 0.46UCL = BUCL = B44.. LCL = BLCL = B33..

= 1.72 x 0.46 = 0.28 x 0.46= 1.72 x 0.46 = 0.28 x 0.46= 0.7912 = 0.1288= 0.7912 = 0.1288


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Control Charts for AttributesControl Charts for Attributes--::

pp--chartchart--:: This chartis constructed for controllingThis chartis constructed for controllingthe qualitystandardin theaverage fraction defectivethe qualitystandardin theaverage fraction defectiveoftheproductsin aprocess when the observedoftheproductsin aprocess when the observed

sampleitemsare classifiedinto defectives & nonsampleitemsare classifiedinto defectives & non--defectives.defectives.

npnp--chartchart--:: This chartis constructed for controllingThis chartis constructed for controllingthe qualitystandard ofattributesin aprocess wherethe qualitystandard ofattributesin aprocess where

thesamplesizeisequal & itisrequiredto plotthe no.thesamplesizeisequal & itisrequiredto plotthe no.ofdefectives (np) in samplesinstead of fractionofdefectives (np) in samplesinstead of fractiondefectives (p).defectives (p).


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ExampleExample--::

Sample No.Sample No. Size ofsampleSize ofsample(n)(n)

No. ofNo. ofdefectives (d)defectives (d)

FractionFractiondefectives (d/n)defectives (d/n)

11

22

3344

55

66

77

8899

1010

100100

100100

100100100100

100100

100100

100100

100100100100

100100

55

33

3366

55

66

88

10101010

44

0.050.05

0.030.03

0.030.030.060.06

0.050.05

0.060.06

0.080.08

0.10.10.10.1

0.040.04

K= 10K= 10 d= 60d= 60


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== Total no. of defectives/Total no. of units =Total no. of defectives/Total no. of units =6060//10001000 == 00..0606qq == 11-- == 11-- 00..0606 == 00..9494

== 00..0606 (central line)(central line)

UCL =UCL = ++ 33 .. qq/n/n== 00..0606 ++ 3300..0606xx00..9494//100100

== 00..13111311LCL =LCL = -- 33 .. qq/n/n== 00..0606 -- 33 00..0606xx00..9494//100100== --00..01110111 == 00


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ExampleExample--::An inspection ofAn inspection of 1010 samples of sizesamples of size 400400 each fromeach from 1010 lots reveallots reveal

the following number of defectives:the following number of defectives:

1717,, 1515,, 1414,, 2626,, 99,, 44,, 1919,, 1212,, 99,, 1515Calculate control limits for the no. of defective units.Calculate control limits for the no. of defective units.

SolutionSolution--:: n =n = 400400, k (No. of samples) =, k (No. of samples) = 1010,, d (total no. ofd (total no. ofdefectives) =defectives) = 140140

nn == d/k =d/k = 140140//1010 == 1414

Now,Now, == nn/n =/n = 1414//400400 == 00..035035,,

qq == 11-- == 11-- 00..035035 == 00..965965

nn == 1414 (central line)(central line)

UCL=UCL= nn ++ 33 n n qq LCL=LCL= nn -- 33 nn qq == 1414 ++ 33400400xx00..035035xx00..965965 == 1414 -- 33400400xx00..035035xx00..965965

== 2525..025025 == 22..975975


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CC--ChartChart--:: This chart is usedThis chart is usedfor the control of no. offor the control of no. ofdefects per unit say a piecedefects per unit say a pieceof cloth/glass/paper/bottleof cloth/glass/paper/bottle

which may contain more thanwhich may contain more thanone defect. The inspectionone defect. The inspectionunit in this chart will be aunit in this chart will be a

single unit of product. Thesingle unit of product. Theprobability of occurrence ofprobability of occurrence ofeach defect tends to remaineach defect tends to remain

very small.very small.


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USESUSES--::

The following are the field of applicationThe following are the field of applicationof Cof C--ChartChart--::

Number of defects of all kinds ofNumber of defects of all kinds ofaircraft final assembly.aircraft final assembly.

Number of defects counted in a roll ofNumber of defects counted in a roll ofcoated paper, sheet of photographiccoated paper, sheet of photographicfilm, bale of cloth etc.film, bale of cloth etc.


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ACCEPTANCE SAMPLINGACCEPTANCE SAMPLING

MeaningMeaning--::Another major area of S.Q.C. is ProductAnother major area of S.Q.C. is Product

Control or Acceptance Sampling. It isControl or Acceptance Sampling. It isconcerned with the inspection ofconcerned with the inspection ofmanufactured products. The items aremanufactured products. The items areinspected to know whether to accept ainspected to know whether to accept a

lot of items conforming to standards oflot of items conforming to standards ofquality or reject a lot as nonquality or reject a lot as non--conforming.conforming.


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DEFINITIONDEFINITION--::

Acceptance Sampling is concerned with the Acceptance Sampling is concerned with thedecision to accept a mass of manufactureddecision to accept a mass of manufactureditems as conforming to standards of quality oritems as conforming to standards of quality or

to reject the mass as nonto reject the mass as non--conforming toconforming toquality. The decision is reached throughquality. The decision is reached throughsampling.sampling.

ByBy--::

SIMPSON AND KAFKASIMPSON AND KAFKA


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Risks in Acceptance samplingRisks in Acceptance sampling

1.1. Producers riskProducers risk--:: Sometimes inspite of goodSometimes inspite of goodquality, the sample taken may show defectivequality, the sample taken may show defectiveunits as such the lot will be rejected, suchunits as such the lot will be rejected, such

type of risk is known as producers risk.type of risk is known as producers risk.

2.2. Consumers RiskConsumers Risk--:: Sometimes the quality ofSometimes the quality ofthe lot is not good but the sample resultsthe lot is not good but the sample results

show good quality units as such the consumershow good quality units as such the consumerhas to accept a defective lot, such a risk ishas to accept a defective lot, such a risk isknown as consumers risk.known as consumers risk.


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Types of Sampling Inspection PlanTypes of Sampling Inspection Plan

Single Sampling PlanSingle Sampling Plan--:: Under singleUnder singlesampling plan, a sample of n items issampling plan, a sample of n items isfirst chosen at random from a lot of Nfirst chosen at random from a lot of Nitems. If the sample contains, say, c oritems. If the sample contains, say, c orfew defectives, the lot is accepted,few defectives, the lot is accepted,while if it contains more than cwhile if it contains more than c

defectives, the lot is rejected (c isdefectives, the lot is rejected (c isknown as acceptance number).known as acceptance number).


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Single Sampling PlanSingle Sampling Plan

Count the no. of defectives,d in the sample of size n

Is d c

If yes, than accept the lot If no, then reject the lot


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Double Sampling PlanDouble Sampling Plan--::

Under this sampling plan, a sample of nUnder this sampling plan, a sample of n11 items is items isfirst chosen at random from the lot of sizefirst chosen at random from the lot of sizeN. If the sample contains, say, cN. If the sample contains, say, c11 or few or fewdefectives, the lot is accepted; if it containsdefectives, the lot is accepted; if it contains

more than cmore than c22 defectives, the lot is rejected. defectives, the lot is rejected.If however, the number of defectives in theIf however, the number of defectives in thesample exceeds csample exceeds c11, but is not more than c, but is not more than c22, a, asecond sample of nsecond sample of n22 items is take from the items is take from thesame lot. If now, the total no. of defectives insame lot. If now, the total no. of defectives in

the two samples together does not exceedthe two samples together does not exceedcc22, the lot is accepted; otherwise it is, the lot is accepted; otherwise it isrejected. (crejected. (c11 is known as acceptance no. for is known as acceptance no. forthe first sample & cthe first sample & c22 is the acceptance no. of is the acceptance no. ofboth the samples taken together)both the samples taken together)


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Double Sampling PlanDouble Sampling Plan--::Count the no. of defectives,

d1in the first sample of size n1

Is d1 c1 ?

Draw another sample ofsize n2

If No, then checkIf c1 d1 c2 ?

Count the no. of defectives d2in

this sample

Is d1 + d2 c2

If No, reject the lot

If yes, accept the lot

If yes, then accept

the lot.


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Multiple Sampling PlanMultiple Sampling Plan--::

Under this sampling plan, a decision toUnder this sampling plan, a decision toaccept or reject a lot is taken afteraccept or reject a lot is taken afterinspecting more than two samples ofinspecting more than two samples ofsmall size each. In this plan, units aresmall size each. In this plan, units areexamined one at a time & afterexamined one at a time & afterexamining each unit decision is taken.examining each unit decision is taken.

However, such plan are veryHowever, such plan are verycomplicated & hence rarely used incomplicated & hence rarely used inpractice.practice.


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ADVANTAGES OF S.Q.C.ADVANTAGES OF S.Q.C.--::

Helpful in controlling quality of aHelpful in controlling quality of aproductproduct

Eliminate Assignable causes of variationEliminate Assignable causes of variationBetter quality at lower inspection costBetter quality at lower inspection cost

Useful to both consumers & producersUseful to both consumers & producers

It makes workers quality consciousIt makes workers quality consciousHelps in earn goodwillHelps in earn goodwill


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LIMITATIONSLIMITATIONS--::

Does not serve as a PANACEA for allDoes not serve as a PANACEA for allquality evils.quality evils.

It cannot be used to all productionIt cannot be used to all productionprocess.process.

It involves mathematical & statisticalIt involves mathematical & statisticalproblems in the process of analysis &problems in the process of analysis &interpretation of variations in quality.interpretation of variations in quality.

Provides only an information services.Provides only an information services.


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