Question

An chart with three-sigma limits has parameters as follows: Suppose the process quality characteristic being controlled is normally distributed with a true mean of 98 and a standard deviation of 8. What is the probability that the control chart would exhibit lack of control by at least the third point plotted?

Answer 1

Ok now I am going to solve this BIG question just for sake of brotherhood of industrial Engineers \m/

Now amount of output falling outside of Control Limits.

Above z=(104-98)/8/root(5) = 1.677

amount of output falling outside of Upper Control Limits =1-P(z=1.67) = 5% from normal tables

below Z= (96-98)/8/root(5) = -0.56 = P(z=-0.56) = 28.7%

amount of output falling outside of Lower Control Limits =28.7%

totaloutput falling outside of Control Limits =33.7%

so Probability that CL would exibit lack of control for at least third poit plotted = 0.663*0.663*0.337 = 0.148 = 14.8%

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