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Probability of signaling

Quality control: when the output of a production process is stable at an acceptable standard, it is said to be "in control?. Suppose that a production process has been in control for some time and that the proportion of defectives has been 0.5. as a means of monitoring the process, the production staff decides to consider the process “out of control” if 2 or more defectives are found in a sample of 15 items.

a) Find α, the probability of signaling “out of control,” when the process is at p =0.05

b) Graph the power curve for this control scheme from the values at p = 0.05, 0.1, 0.2, 0.3, 0.4

(Note: in quality control terminology, one usually works with the operating characteristic whose values are equal to 1 –(power), or the probability of accepting H0.)

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