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Question: Control charts for x‾and R are in use with the following parameters. The sample size is n = 9. Both charts exhibit control. The quality characteristic is normally distributed.

x‾ Chart                            R Chart

UCL = 363.0                   UCL = 16.18
Center line = 360.0    Center line = 8.91
LCL = 357.0                    LCL = 1.64

a) What is the α-risk associated with the x‾chart?

b) Specifications on this quality characteristic are 358 ± 6. What are your conclusions regarding the ability of the process to produce items within specifications?

c) Suppose the mean shifts to 357. What is the probability that the shift will not be detected on the first sample following the shift?

d) What would be the appropriate control limits for the x‾chart if the type I error probability were to be 0.01?

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