Question

Calculate Xbar, R, and S for each subgroups, then calculate Central lines and control limits for all three plots (Xbar,R,S). These are 3 subgroups but calculate it assuming these are regular long run SPC in chapter 6. (show your calculations step by step) 10:30 AM 11:30 AM 12:30 PM Subgroup 1 Subgroup 2 Subgroup 3 7.0 7.0 6.9 6.9 Sample Recor ding 7.1 6.8 7.0 7.1 7.2 6.9 6.9 Xbar 7.080 7.000 0.300 0.300 0.130 0.205

Answer 1

If x₁,x₂,...……..,xn are samples from each subgroups then,

xbar=sum(xi)/n , range(R)=X(maximum)-X(minimum) & S=square root of((xi-xbar)^2/n-1)

1) for subgroup I

xbar=(7+6.9+7.1+7.2+6.9)/5

xbar=35.1/5=7.020

2) for subgroup II

R=7.4-6.9=0.500

3) for subgroup III

S=square root (0.015/4)    ; where sum(xi-xnbar)^2=0.015

S =0.1224