Suppose we use a "run of eight" rule;that is,we declare the process out of control if eight consecutive points are all above the center line of the chart or if eight consecutive points are all below the center line of the
Chart.If the process is in statistical control,what is the (approximate) probability that we declare the process out of control using this rule?

Question

Suppose we use a "run of eight" rule;that is,we declare the process out of control if eight consecutive points are all above the center line of the

chart or if eight consecutive points are all below the center line of the

Chart.If the process is in statistical control,what is the (approximate) probability that we declare the process out of control using this rule?

Quizplus · Accepted Answer

Under statistical control, each point has an equal chance of being above or below the center line. Hence, the probability of eight consecutive points being above or below the center line is (0.5)^8 = 0.0039. However, we must consider both cases (above and below). Therefore, the approximate probability of declaring the process out of control is 0.0039 + 0.0039 = 0.0078, which is closest to option C (0.008).

Suppose We Use a "Run of Eight" Rule;that Is,we Declare