Question

A process is controlled with a fraction nonconforming control chart with three-sigma limits, ? = 100....

A process is controlled with a fraction nonconforming control chart with three-sigma limits, ? = 100. Suppose that the center line = 0.10.

(a) Suppose that the percentage of conforming units in sample ? is ?? . What distribution should ?? follow? Use a Normal distribution to approximate the distribution of ?? . Specify the mean and the variance of this Normal distribution.

(b) Find the upper and lower control limit for this fraction nonconforming chart.

(c) Find the equivalent control chart for the number nonconforming. Specify the plot variable, the center line and the upper and lower control limits.

(d) If the process fraction of nonconforming increases by 5% (shifts to 0.15). what out-ofcontrol distribution does the fraction of nonconforming follows? Use Normal approximation. Find the probability of type II error.

(e) If the process fraction of nonconforming decrease by 5%. Use Poisson approximation due to the small value of ?. What is the probability of type II error?

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