Quantitative and Qualitative Forecasting

Jlo section 2 MlNt,r'tctt Bri\c ANr) Srnr icr PRor:rssi,s

fnlflEm =iR.$E!L-'*gE/r.iE

Hffi For a $t8p-by-step

walkthrough 0f this example, ui$it

wwr\r,mhhe,coml jacobsl 4e_sbs-chI 3,

t-.

An irrsurance compaily wauts to design a coutrol chalt to nronitcx' whcther insuraltce claim forms are being cor-npleted correctly. The company intends to l"lso the chart io see il improve- ments in thc design of thc lbrm are ell'ective.'lb start thc process. the company collected data on the numbLrr ol incorectly completc:d clainr {brms over the past l0 days.'lhe insurance coillpany processes thousands ol'these ibrns ear:h day, and due to the high tost til rrtspeetinS each fonn, only ii smail reprcsentative samplc was collected c,ach day. The data and anal.vsis ure shown irr Lrhihit 1.1.6.

To construct the control chart, tirst calculate the overall frae:tion delective t'rort all samples. This sets tho cenlerline {irr the control chart.

p: Total nurnber of defective units from all samples Number of samples X Sample size

Next calcuiate the sarnple standard deviation:

t{

Fo. ihc Excel templaie, v sit

www.mhhe.com/lacobsl4e

NUNiBER

Slupm TNSPECTED

:*k:03033

r l4roJlr L:-o39Ir : .ooeeo- V --300 -

Finally. calcrrlate the upper ancl lowcr prccess control lirnits. A a-valuc ol.j gives 99.7 pcrccnt conhdence that the process is within thesc liniits.

UCL : p * 3s,: .03033 + 3(.00990) : .06003

LCL : p - 3tr: .03033 - 3(.00990) : .00063

The calcularions in Exhibit 13.6. including the control chart. arc included in tlre spreadsheet ''SPC.xls."

Insurance Company Claim Form

0.06500

0 060(xi

0.05500

0.05001)

0.0.i50f)

0 0,10t)0

0.0i500

0.0.i00{:)

0 0150u

0.01000

0.01 500

0.0 1000

0.00_500

0.0u0u0

NulrgER oE

Fr ltlrs CotuP[.ETED

INa(]RRECTI.I-

FRACTIoN

DEFECTIvF,

1

2

3

4

5

10

8

I 13

7

7

6

11

12

B

91

3ULT

300

300

3tJC

300

0.0333:l

0.0?66/ 0.0300{l

0.0433;c n n)2..4

0 02333

0.02000

0 c366 / 0.04000

0.02667

0.03033

0,00990

6 303 7 30f, 3 3C0 g 30c

10 3CC Tctals 3,000

Sample slanrlarci deviatron

p(r - 0) l'L

: : ': : , , a

a: : 'uf- \, i i

i Srmple LIirp.r ctlltrol lirlit Lou er control lirnit

l0