p & np control charts (2)

8/4/2019 p & Np Control Charts (2)

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Submitted to:Er. Rupen Trehan

(Lect. In mech.Deptt.)

MMEC

Submitted by:Rocky Garg

11081030Mech. 7th sem.


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Control charts are first described by Walter A.Shewhart while working for Bell Labs in the1920s.

They are also known as Shewhart charts orprocess-behaviour charts.

In statistical process control, these are toolsused to determine whether or not a

manufacturing or business process is in astate of statistical control.


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To determine whether a process shouldundergo a formal examination for quality-related problems.

Shewhart framed the problem in terms ofCommon & Special causes of variation.

If only commoncauses arepresent

If only specialcauses arepresent

Process understatisticalcontrol

Process notunder statisticalcontrol


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CommonCauses

Special Causes


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Points represents measurements of a qualitycharacteristic in samples taken from theprocess at different times.
http://en.wikipedia.org/wiki/File:ControlChart.svg


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The mean of this statistic using all thesamples is calculated.

A center line is drawn at the value of themean of the statistic.

The standard error (e.g., standarddeviation/sqrt(n) for the mean) of the

statistic is also calculated using all thesamples.

Upper and lower control limits

(sometimes called "natural processlimits") that indicate the threshold atwhich the process output is consideredstatistically 'unlikely' are drawn.


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If the process is in control, almost all(99.73%) points will plot within the controllimits. Any observations outside the limits,or systematic patterns within, suggest the

introduction of a new (and likelyunanticipated) source of variation, known asa special cause variation. Since increasedvariation means increased quality costs, a

control chart "signaling" the presence of aspecial-cause requires immediateinvestigation


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Originally proposed byWalter A.Shewhart

Used for Rational subgroup size, n > 1Quality characteristic type: Attributes

data

p-chart is used to monitor theproportion ofnonconforming units ina sample, where the sample

proportion nonconforming is definedas the ratio of the number ofnonconforming units to the samplesize, n.
http://en.wikipedia.org/wiki/Walter_A._Shewharthttp://en.wikipedia.org/wiki/Walter_A._Shewharthttp://en.wikipedia.org/wiki/Nonconformity_(quality)http://en.wikipedia.org/wiki/Nonconformity_(quality)http://en.wikipedia.org/wiki/Walter_A._Shewharthttp://en.wikipedia.org/wiki/Walter_A._Shewharthttp://en.wikipedia.org/wiki/Walter_A._Shewhart


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Formula:p = np / nwhere p= proportion or fraction NC inthe sample or subgroup, n= numberin the sample or subgroup, np=number NC in the sample or subgroup

The fraction nonconforming, p, is

usually small, say, 0.10 or less.

Because the fraction nonconforming is

very small, the subgroup sizes must be

quite large to produce a meaningful

chart.


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During the first shift, 450 inspection are made

of book-of the month shipments and 5 nc

units are found. Production during the shiftwas 15,000 units. What is the fraction nc?

p = (np)/n = 5/450 = 0.011

Thep, is usually small, say 0.10 or less.

Ifp > 0.10, indicate that the organization is in

serious difficulty.


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Select the quality characteristics.

Determine the subgroup size andmethod

Collect the data.Calculate the trial central line and control

limits.

Establish the revised central line and

control limits.Achieve the objective.


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The quality characteristic?

A single quality characteristic

A group of quality characteristics A part

An entire product, or

A number of products.


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The size of subgroup is a function of theproportion nonconforming.

If p= 0.001, and n= 1000, then theaverage number nc, np= 1. Not good,

since a large number of values would bezero.

If p =0.15, and n= 50, then np= 7.5,would make a good chart.

Therefore, the selection subgroup sizerequires some preliminary observations toobtain a rough idea of the proportionnonconforming.


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Control limits =

n

npp

subgroupsmanyforpofaveragep


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Sub-

group

Number

Number

Inspected

n

np p

1 300 12 0.040

2 300 3 0.010

3 300 9 0.030

4 300 4 0.013

5 300 0 0.0

6 300 6 0.020

7 300 6 0.020

8 300 1 0.003

19 300 16 0.053

25 300 2 0.007

Total 7500 138

018.07500

138

n

npp

0.0005.0

300

)018.01(018.03018.0

LCL

041.0

300

)018.01(018.03018.0

UCL

Negative value of LCL is possible in a theoritical result, butnot in practical (proportion of nc never negative).


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p-bar

LCL

UCL

Subgroup

p

5 10 15 2025

0

0.01

0.02

0.03

0.04

0.053


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Originally proposed byWalter A. ShewhartUsed for Rational subgroup size, n > 1Quality characteristic type: Attributes dataMeasurement type: Number

nonconforming per unit The np-chart is a type of control chart

used to monitor the number ofnonconforming units in a sample. It is an

adaptation of the p-chart and used insituations where personnel find it easierto interpret process performance in termsof concrete numbers of units rather than

the somewhat more abstract proportion
http://en.wikipedia.org/wiki/Walter_A._Shewharthttp://en.wikipedia.org/wiki/Nonconformity_(quality)http://en.wikipedia.org/wiki/P-charthttp://en.wikipedia.org/wiki/P-charthttp://en.wikipedia.org/wiki/P-charthttp://en.wikipedia.org/wiki/P-charthttp://en.wikipedia.org/wiki/Nonconformity_(quality)http://en.wikipedia.org/wiki/Walter_A._Shewharthttp://en.wikipedia.org/wiki/Walter_A._Shewhart


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The np-chart differs from the p-chartin only the three following aspects :

The control limits( )are established during control-chartsetup.

The number nonconforming (np),rather than the fraction nonconforming(p), is plotted against the controllimits.

The sample size, n, is constant.


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Subgroup n np UCL np-bar LCL1 300 3 12.0 5.24 0.0

2 300 6 12.0 5.24 0.0

3 300 4 12.0 5.24 0.0

4 300 6 12.0 5.24 0.0

5 300 20 12.0 5.24 0.0

21 300 2 12.0 5.24 0.0

22 300 3 12.0 5.24 0.023 300 6 12.0 5.24 0.0

24 300 1 12.0 5.24 0.0

25 300 8 12.0 5.24 0.0


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0

0 0 0

Central Line =

Control Limits = 3 (1 )

np

np np p

p & np control charts (2)

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