Computer upgrades have a nominal time of 80 minutes. Samples of five observations each have been taken, and the results are as listed. Using A₂, D3, and D4, determine upper and lower control limits for mean and range charts, and decide if the process is in control. SAMPLE 1 2 3 4 5 6 79.2 80.5 79.6 78.9 80.5 79.7 78.8 78.7 79.6 79.4 79.6 80.6 80.0 81.0 80.4 79.7 80.4 80.5 78.4 80.4 80.3 79.4 80.8 80.0 81.0 80.1 80.8 80.6 78.8 81.1 From Excel, R=1.87, X=79.96, n=5 LCLᵣ = D₃R = 0(1.87)=0 UCLᵣ = D₄R = 2.11(1.87) = 3.9457 ≈ 3.95
LCLₓ = X-A₂R = 79.96-0.58(1.87)=78.6754 ≈ 78.88 UCLₓ = X+A₂R = 79.96+0.58(1.87) = 81.0446 ≈ 87.04