18 quality control

8/8/2019 18 Quality Control

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STATISTICAL QUALITY

CONTROL


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STATISTICSStudy of

Collection

Presentation

Analysis

Interpretation

of data


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QUALITY

The extent to which the products meetthe specifications


4/41

CONTROL

Involves

Assessing product quality

Assessing process deviations


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CENTRAL TENDENCY OF DATA

Mean (average)

x/n

MedianThe central value after arranging data

in ascending or descending order

Mode

The value occurring most frequently

M


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MEASURES OF VARIATION

Range Xmax - Xmin

Standard deviation

(X - X)

n-1

Variance SD

2

2


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COEFFICIENT OF VARIATION

SD

X

Used when the averages of two sets of

data are far apart

The average and standard deviation of two

sets of data are contradictory


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FREQUENCY CURVE

parameter

frequen

cy


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PROCESS UNDER STATISTICAL

CONTROL

A process is said to be in a state of

statistical control if it is governed onlyby random causes of variation and there

is no assignable variation in it


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NORMAL CURVE

68.26%95.45%99.73%

freque

ncy


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STANDARD NORMAL VARIATE

(X X) / SD

The normal curve using standard normal

variate instead of original data is calledstandard normal curve

The standard normal curve has a mean of

0 and a standard deviation of 1


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CHARACTERISTICS OF NORMAL CURVE

It does not touch x axis on either side

It is symmetrical

The total area under the normal curve is1.0

The mean is at the point of highest

frequency

Mean = median = mode


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CONTROL CHARTS

A tool for monitoring and thereby controlling

the process characteristics

Control charts for variables X - R chart

Control charts for attributes p chart

c chart


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GENERAL LAYOUT OF A CONTROL

CHART

UCL

LCL

USL

LSL

X

+ 3 SD

- 3 SD


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PRE REQUISITES FOR A CONTROL CHART

Define the characteristic

Frequency of sample

Sample size

Place of control chart


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X - R chart

X chart

X X / n

Central line X / m

UCL X + A2 R

LCL X - A2 R

Controls within sample and between samplesvariation

R chart

Central line R / m

UCL D4 R

LCL D3 R

M M

M


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n A2 D3 D4 n A2 D3 D4

2 1.880 0 3.267 14 0.235 0.328 1.672

3 1.023 0 2.574 15 0.223 0.347 1.653

4 0.729 0 2.282 16 0.212 0.363 1.637

5 0.577 0 2.114 17 0.203 0.379 1.622

6 0.483 0 2.004 18 0.194 0.391 1.608

7 0.419 0.076 1.294 19 0.187 0.403 1.597

8 0.373 0.136 1.864 20 0.180 0.415 1.585

9 0.337 0.184 1.816 21 0.173 0.425 1.575

10 0.308 0.223 1.776 22 0.167 0.434 1.566

11 0.285 0.256 1.744 23 0.162 0.443 1.557

12 0.266 0.283 1.717 24 0.157 0.451 1.548

13 0.249 0.307 1.693 25 0.153 0.459 1.541


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P chart (fraction defective chart)

p number defective / number inspected

p total number defective / total inspected

Control limits

Central line p

UCL p + 3 p (1-p)

n

LCL p -3 p (1-p)

n


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c chart (defects chart)

Sample size is defined

Sampling frequency is defined

c c / n

Control limits

Central line c

UCL c + 3 c

LCL c - 3 c


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Normal behaviour

Interpretation of control chart


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.

One point out above

Investigate the cause of poor performance



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.

One data point out below

Investigate the cause of improvement



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Two data points near upper limit

Investigate cause of poor performance

..



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..

Two data points near lower limit

Investigate the cause of improvement



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. . . . .

Five successive data points above central line

Investigate the cause of sustained poor performance



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. .

. ..

Five successive points below central line

Investigate the cause of sustained improvement



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.

.

..

.

....

.

Five successive data points on increasing ordecreasing trend

Investigate the cause of progressive change



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Erratic behaviour

Investigate



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Sudden change in level

investigate



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Process capability

The ability of a process to produce within

specifications


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Process capability index

Cp (USL LSL) / 6 SD

Cpk (USL X) / 3 SD

(X LSL) / 3 SD

(which ever is lower)

Process is capable if

Cp and Cpk are greater than 1


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Cp and Cpk greater than 1


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Cp greater than 1

Cpk less than 1


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Cp and Cpk less than 1


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ACCEPTANCE SAMPLING

Deciding the acceptability or otherwise of a lot

on the basis of inspecting a sample


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Sampling inspection is necessary if

The inspection is destructive

The inspection is costly

The inspection takes too much time

The lot size is too large


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SAMPLING RISK

Producers risk

Suppliers risk

Good bad

ba

d

goo

d

sample

lo

t


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Acceptable quality level

The limit of defectives % acceptable in

the lot


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A SAMPLING PLAN INCLUDES

Lot size

Sample size

Acceptance number

At a specific AQL


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NN

c

P r o

b a

b i l i

t y

o f

a c c e p

t a n c e

Lot defective %

18 quality control

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