Stastical Quality Tools

7/31/2019 Stastical Quality Tools

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STATISTICAL

QUALITY

CONTROL


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MEANING-:

manufactured Refers to the use ofstatistical techniques in controlling thequality of goods.

Means of establishing & achievingquality specification, which requires useof tools & techniques of statistics.


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DEFINATION-:

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

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

By-:

YA LUN CHOU


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Definition-:

Statistical quality control should beviewed as a kit of tools which mayinfluence decisions to the functions ofspecification, production or inspection.

By-:

EUGENE L. GRANT


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CAUSES OF VARIATIONS INQUALITY-:

1. ASSIGNABLE CAUSES-: It refers to thosechanges in the quality of the products whichcan be assigned or attributed to anyparticular causes like defective materials,defective labour, etc.

2. CHANCE CAUSES-: These causes take placeas per chance or in a random fashion as aresult of the cumulative effect of amultiplicity of several minor causes whichcannot be identified. These causes areinherent in every type of production.


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METHODS OF S.Q.C.-:

1. PROCESS CONTROL-: Under this thequality of the products is controlled whilethe products are in the process of

production.The process control is secured with thetechnique ofcontrol charts. Control chartsare also used in the field of advertising,packing etc. They ensures that whether theproducts confirm to the specified qualitystandard or not.


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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 lowercontrol 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

3

3

Control Chart


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PURPOSE & USES OF CONTROLCHARTS

1. Helps in determining the quality standard ofthe products.

2. Helps in detecting the chance & assignablevariations in the quality standards by setting

two control limits.3. Reveals variations in the quality standards of

the products from the desired level.4. Indicates whether the production process is

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

process control.


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Types-:

Types of

ControlCharts

ControlCharts

forVariables

Chart

ControlCharts forAttributes

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


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CONTROL CHATS FORVARIABLES

CHART/ MEAN CHART-: This chart isconstructed 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 the

products in a production process.


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Chart-:This chart is constructed to get a better picture ofthe 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 withthe help of standard deviation chart. Ten items are chosen inevery sample. 18 samples in all were chosen whose S was8.28. Determine the three sigma limits of- chart. You may usethe following-:

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

Solution-: = S/K = 8.28/18 = 0.46UCL = 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 controllingthe quality standard in the average fraction defectiveof the products in a process when the observedsample items are classified into defectives & non-defectives.

np-chart-: This chart is constructed for controllingthe quality standard of attributes in a process where

the sample size is equal & it is required to plot the no.of defectives (np) in samples instead of fractiondefectives (p).


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C-Chart-: This chart is usedfor the control of no. of

defects per unit say a pieceof cloth/glass/paper/bottlewhich may contain more thanone defect. The inspectionunit in this chart will be a

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

ver small.


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USES-:

The following are the field of applicationof C-Chart-:

Number of defects of all kinds ofaircraft final assembly.

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


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ACCEPTANCE SAMPLING

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

Control or Acceptance Sampling. It is

concerned with the inspection ofmanufactured products. The items areinspected to know whether to accept alot of items conforming to standards ofquality or reject a lot as non-conforming.


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DEFINATION-:

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

to reject the mass as non-conforming toquality. The decision is reached throughsampling.

By-:

SIMPSON AND KAFKA


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Risks in Acceptance sampling

1. Producers risk-: Sometimes inspite of goodquality, the sample taken may show defectiveunits as such the lot will be rejected, suchtype of risk is known as producers risk.

2. Consumers Risk-: Sometimes the quality ofthe lot is not good but the sample results

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


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Types of Sampling Inspection Plan

Single Sampling Plan-: Under singlesampling plan, a sample of n items isfirst chosen at random from a lot of N

items. If the sample contains, say, c orfew defectives, the lot is accepted,while if it contains more than c

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


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Single 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 Plan-:

Under this sampling plan, a sample of n1 items isfirst chosen at random from the lot of sizeN. If the sample contains, say, c1 or fewdefectives, the lot is accepted; if it contains

more than c2 defectives, the lot is rejected.If however, the number of defectives in thesample exceeds c1, but is not more than c2, asecond sample of n2 items is take from thesame lot. If now, the total no. of defectives in

the two samples together does not exceedc2, the lot is accepted; otherwise it isrejected. (c1 is known as acceptance no. forthe first sample & c2 is the acceptance no. ofboth the samples taken together)

D bl S li Pl


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Double 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 d2 inthis 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 Plan-:

Under this sampling plan, a decision toaccept or reject a lot is taken afterinspecting more than two samples of

small size each. In this plan, units areexamined one at a time & afterexamining each unit decision is taken.

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


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ADVANTAGES OF S.Q.C.-:

Helpful in controlling quality of aproduct

Eliminate Assignable causes of variation

Better quality at lower inspection cost

Useful to both consumers & producers

It makes workers quality consciousHelps in earn goodwill


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LIMITATIONS-:

Does not serve as a PANACEA for allquality evils.

It cannot be used to all productionprocess.

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

Provides only an information services.


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THEEND

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