Question: A process is under control and follows a normal distribution with mean 100 and standard deviation 10. In constructing a standard x-chart for this process,

A process is under control and follows a normal with mean 100 and standard deviation 10. In constructing a standard x̅-chart for this process, the control limits are set 3 standard deviations from the mean-that is, 100 ± 3(10/ √n). The probability of observing an x outside the control limits is (.00135 + .00135) = .0027.
Suppose it is desired to construct a control chart that signals the presence of a potential special cause of variation for less extreme values of x. How many standard deviations from the mean should the control limits be set such that the probability of the chart falsely indicating the presence of a special cause of variation is .10 rather than .0027?

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