Question

We have m = 5 preliminary samples of size n = 3 (some numbers have unfortunately been erased by accident by a clumsy co-op student): ri Si 1.3 1.07 1.9 Ti.1 11,2 1 27.1 29.4 2 30.6 32.5 3 25.7 35.5 4 31.1 23.2 5 24.1 34.2 11,3 27.9 32.4 31.83 30 30.4 25 26.43 27.4 28.57 total: 145.13 4.91 7.9 10.1 32 5.15 16.57 What is the control chart (give the interval) for X from S?

Answer 1

sah Hese Mis & n=3 Table sl -- si X;,2 Xe Eik 22 29.4 27.2 27.9 27-) 30.6 32.4 31.83 bil 2 3215 3SS s.s 4.91 25.7 20 3 30.4 23.2 25 26.43 361 bit 4.14 24.1 34.2 SIS 1.01 27.4 28.57 S Total Eloshl 32 16.54 1 = Enlig = 27.9x3 - 27,1 f 29,4 tdi? [!X+ 5.95 = t.88 dis 5.95-t.E8 = 2.t2 =E! x1 = 29.4-29-2 = mod-min 83 35.5 - 30 2/sos Su = 16.57- Sifh 2+53 +55 su = 16.54-12.43 4.14 X Sd Chast formula CL = 5 = 16.57 = 3.314 5 UCL = Buš, whese Bu = constant =2-089 = 2.089 X 3-314 = 6.922996 LeL = B35 whese B320 LCL 20 CS Scanned with CamScanner

for a chast UCL =ř +A; whese Az is constant T = Exi Elishi - ero.be کے 5 & A 3=1.427 UCL = 29.026 +1.427 3.314 A SEASSE EEF LCL = H - Az 5 = 29.026-4-729078 24.2969221 control chast for å from 5 is (24.296922 , 33. 286.78 g- CS Scanned with CamScanner

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