Question: Electrical Switches. The following scenario is taken from an aircraft engine company's training material. One hundred electrical switches are sampled from each of 25 consecutive lots. Each sampled switch is tested and the sample numbers failing are recorded in Table.

(a) Find the sample fractions of switches failing the test.

(b) What is a plausible probability model for describing the count of switches in a particular sample failing the test? Explain.

(c) Plot the number failing versus the sample period. Plot an appropriate center line and control limits on the same graph.

(d) What does your plot in (c) monitor here?

(e) Interpret your plot in (c). Identify any out-of-control points.

(f) What is the usual name of the chart you prepared in part (c)?

(g) Suppose causes for out-of-control points identified in (e) are identified and physically removed. It would then make sense to delete the out-of-control points and recalculate limits. Do this recalculation and redo (c). (You should have identified and eliminated two out-of control points.)

(h) Suppose the number of switches sampled and the number failing for the next three consecutive lots are as follows.

Using your estimated fraction failing from (g) as a standard for judging these samples, find control limits and center lines appropriate for the three new "number failing" data points. Are the three sets of control limits and center lines the same? Why is this to be expected?