Quantitative and Qualitative Forecasting

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St,r't'ts'rtt:,tt Qt rt tn ettrlrlot iltapter l3 a)a

Fr***g*fi*ntr*lwith&'ttri*:ut*l\4*frs'J}"*$}.}*il}ts: tisirtg tr"'*herts Inthecaseolthep-charl,theiternwaseithergoodorbacl.Therearetimeswhentheproduct or scrvice can have more than one defect. For example,

a boarcl sold at a lumberyard may have

muttipte knotholes ,.,r:t, O.ft.,naing on the quality giade'

'nay ol Tay'::::l*"tttvc'

When it

is desired lo monitor the number of defects per unit' thc c-chart is appropnatc'

The underlf ing distnbution lor the c-ctrart is the Poissot' which is based on the assumption

that defects n."u. .undo*if on .o.1, unit. If r: is the number of tlefects for a particular unit'

then Z is the average number o1 defects per unit, ancl the standard deviation is Vtl' For thc

putposes ()1'ouf conlrol chart we use the nrlrmal approximation to i'he Poisstxi distribution zrnd

.nn.rt*.t the chart using rhe iollowing control limits'

jffitr' tt

c : Average numbcr of defccts per unit

.r:Vc p

UCL' t':Vr'

LCL : c * zlV or 0 if less than 0

Justaswithlhep-chart.typicallyz:3(99'lpercentconfidence)or::2'58 confidence) is used.

113.81

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[13.10]

[13.11]

(99 percent

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The owners of a lumberyarcl want to rJesign a control chart to monitor the quality ttf 2 x 1

boards that come from their supplier. For their medium-qualily boards they expect an average

of four knotholes pcr S-tbot boal'd. Dcsign a control charl for use by the person rcceiving thc

boards using three-sigma (standard deviation) lirnits'

i:if,:r"{iYi!*;-t

For this Problcm. c = 4, s,, : ..'a -- Z UCL:z+2rt:4+3(2): l0

LCL : a - zx/:c : 4' 3(2) : -?'0 (Zero is used since it is

not possible to have a negative number of defects')

Fn**ess*qintr**wit$:V;ar$a[:*e{b{*asLirers"}*fitsl L3*ixg "$" *nd tr-e hnrts 1- ur6 pilrange) charts are widely used in statistical

process control'

lnattribrrtcsampling,wedetcrnrinewhcthcrsornethingisgoodorbad'fitsordoesn,tfit- itisago/no-gosituation.lnsampling'however'wemeasuretheactualweight' volume, nurrber of inchcs, or other variablc measurements,

and wc dcvclop control chatls

to determine the acceptabiiity or rejection of the process based on.tl.rose measurements' For

example, in attribute ,u*f rirg, *" Ligt, decide that if something is over l0 p.unds rve will

reject it and under t o potinos"we will iccept it. In variables sampling, we measure a sample

u,,a',uyrecordweightsofg.8poundsorl0.2pounds.Thesevaluesareusedtocreateor nrotiify control charts and to see whether tirey fall within the

acceptable limits'

There are four maiu issues ti-r address in creating a control chart: the size of the samples'

number of sanrples, frequency of sarnples' and control limits'

size of $arnples For inciustrial applicarions in process control involving the

measurementofvariables,itispret-erablctokeepthesamplesizesmall.Therearetwomun reasors. First, the sample needs to be taken rvithin a reasonable

length of time; otherwise' the

processmightchangewhilethesatnplesaretaken.second,thelargerthesanple.themoreit costs to take.

For a steptY'stcP walklfirsugn dihis

example, lri$it

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Quality characteristics that are measured in actual weight, volume, inches, centimeters, or other measure.