Answer:
Kindly check explanation
Step-by-step explanation:
Sample 1 :
Mean = (79.2 + 78.8 + 80 + 78.4 + 81) / 5 = 79.48
Range = 81 - 78.4 = 2.6
Sample 2 :
Mean = (80.5 + 78.7 + 81 + 80.4 + 80.1) / 5 = 80.14
Range = 81 - 78.7 = 2.3
Sample 3 :
Mean = (79.6 + 79.6 + 80.4 + 80.3 + 80.8) / 5 = 80.14
Range = 80.8 - 79.6 = 1.2
Sample 4 :
Mean =(78.9 + 79.4 + 79.7 + 79.4 + 80.6)/5 = 79.6
Range = 80.6 - 78.9 = 1.7
Sample 5 :
Mean = (80.5 + 79.6 + 80.4 + 80.8 + 78.8)/5 = 80.02
Range = 80.8 - 78.8 = 2
Sample 6 :
Mean =(79.7 + 80.6 + 80.5 + 80 + 81.1)/5 = 80.38
Range = 81.1 - 79.7 = 1.4
Xbar = mean of the means
Xbar = (79.48+80.14+80.14+79.6+80.02+80.38) / 6 = 79.96
Rbar = Mean of the sample ranges
Rbar = (2.6 + 2.3 + 1.2 + 1.7 + 2 + 1.4) / 6 = 1.87
n =5 ;D4 = 2.11 ; D3 = 0
From table, D4 = 2.11 ; D3 = 0
Range chart :
Upper Control limit, UCL = D4 * Rbar ; 2.11*1.87 = 3.9457 = 3.95
Lower Control limit, LCL = D3 * Rbar ; 0*1.87 = 0
Mean chart :
Xbar ± A2 * Rbar
From the table :
n = 5 ; A2 = 0.58
Lower control limit(LCL) = Xbar - A2*Rbar
LCL = 79.96 - (0.58*1.87) = 78.8754 = 78.88
Upper Control Limit (UCL) = Xbar + A2*Rbar
UCL = 79.96 + (0.58*1.87) = 81.0446 = 81.04
(78.88 ; 81.04)
The value of Each sample mean falls within the mean interval, Hence, We can conclude that process is on control.
