Question

Given the following measurements representing 10 samples of size 3. find the s-bar, UCL and LCL for a S-bar chart. Is the process in control 2 3 4 5 6 7 8 9 | 10A 10 5 10 8 9 88 892 | 102 103 104 105 101 103N00EUBU 9.94 0.9 103 10.8 || 10 H104 10. 610103 0 19.79 10 3 102 s-bar 027 UCL 0.68 LCL 0 1 The process is in control s-bar 0.27 UCL 0.65 LCLLO The process is in control s-bar 0.29 UCL 0.51 LCLLO The process in control s-bar 10351 UCLEOS L The procent is not in control

Answer 1

The correct answer is option (i)

First we calculate sbar.

sbar=Average of all sample standard deviations

Sample standard deviation of sample 1=STDEV(B3:B5)=0.10

(Drag this cell formula to right to the rest of the samples till sample 10)

sbar=AVERAGE(B7:K7)=0.27

For n=3,from the control constants table,we have,B3=0 ;B4=2.568

UCLs=B4*sbar=0.69

LCL=B3*sbar=0

All the sample standard deviation values lie within the control limits.Hence,the process is in control.

fac =AVERAGE(B7:K7) D E Α C F G H I J K 10.2 234|| 10.5 10.8 9.88 10.1 10.5 9.94 10.6 10.11 9.39| 6 10.21 10.9 10.11 9.92 9.94 9.39| 7 10.71 10.3 9.79 8 10.1 10.8 10.3 10.3 10.4 10.3 10.2 10.2 10.1 10.2 10.3 Sample Standard 7 dev 8 9 sbar 0.10 0.26 0.35 0.30 0.31 0.44 0.46 0.36 0.06 0.10 0.27! 10 11 Forn 12 B3 13 B4 2.568 0.69 15 UCL | 16 LCL