Refer to Table S6.1-Factors for Computing Control Chart Limits (3 sigma) for thi

Question

Refer to Table S6.1-Factors for Computing Control Chart Limits (3 sigma) for this problem. Ross Hopkins is attempting to monitor a filling process that has an overall average of 715 cc3. The average range R is 4 cc3 For a sample size of 10, the control limits for 3-sigma x chart are: Upper Control Limit (UCLcc (round your response to three decimal places) 3 Lower Control Limit (LCL,- (round your response to three decimal places. The control limits for the 3-sigma R-chart are: Upper Control Limit (UCLe (round your response to three decimal places). Lower Control Limit (LCL)ce(fround your response to three decdimal places.

Explanation / Answer

Given are ,

Xbar-bar = Overall average = 715

Rbar = Average Range = 4

Sample size = n = 10

Following are the values of relevant constants as derived from standard table for Xbar and Rbar chart for n = 10:

A2 = 0.308

D4 = 1.777

D3 = 0.223

Thus,

Control Limits for 3 Sigma Xbar chart are :

Upper Control Limit = UCLx = Xbar-bar + A2x Rbar = 715 + 0.308 x 4 = 715 + 1.232 = 716.232 CC3

Lower Control Limit = LCLx = Xbar-bar – A2xRbar = 715 – 0.308 x 4 = 715 – 1.232 = 713.768 CC3

Control Limits for 3 Sigma R chart are :

Upper Control Limit = UCLr = D4.Rbar = 1.777 x 4 = 7.108   CC3

Lower Control Limit = LCLr = D3.Rbar = 0.223 x 4 = 0.892 CC3

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