Six samples of five observations each have been taken and the results are listed

Question

Six samples of five observations each have been taken and the results are listed below. Using the factors from the attached table 10-2, determine the upper and lower control limits for both of the X-bar and R charts,

1 2 3 4 5 6
79.20 80.50 79.60 78.90 80.50 79.70
78.80 78.70 79.60 79.40 79.60 80.60
80.00 81.00 80.40 79.70 80.40 80.50
78.40 80.40 80.30 79.40 80.80 80.00
81.00 80.10 80.80 80.60 78.80 81.10
X - BAR 79.48 80.14 80.14 79.60 80.02 80.38
RANGE 2.60 2.30 1.20 1.70 2.00 1.40

What is the X-bar CL?

a. 80.44

b. 79.96

c. 78.88

c. 81.04

Explanation / Answer

Xbar-Bar = Mean of Xbar values = ( 79.48 + 80.14+ 80.14+79.60+80.02 + 80.38) / 6 = 79.96

Rbar = Nean of Range values = ( 2.6 + 2.3 + 1.2+ 1.7 + 2 + 1.40 ) / 6 = 1.866

Sample size = n = 5

Relevant values of constants for n= 5 as derived from standard table for Xbar and Range charts :

A2 = 0.577

D4 = 2.114

D3 = 0

Control Limits for Xbar chart :

Upper control Limit = Xbar-bar + A2.Rbar = 79.96 + 0.577x1.866 = 79.96 + 1.076 = 81.036

Lower Control Limit = Xbar-bar – A2.Rbr = 79.96 – 0.577 x 1.866 = 79.96 – 1.076 = 78.884

Control Limit for Range chart:

Upper Control Limit = D4.Rbar = 2.114 x 1.866 = 3.944

Lower Control Limit = D3.Rbar = 0

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