Reverse-current readings (in nanoamperes) are made at the location of a transistor on an integrated circuit. A sample of size 10 is taken every half hour. Since some of the units may prove to be "shorts" or "opens," it is not always possible to obtain 10 readings. The following table shows the number of readings made at the end of each half-hour interval during an 8-hour shift, and the mean reverse currents obtained:

(a) Find the central line for an \(\bar{x}\) chart by taking the weighted mean of the \(16 \bar{x}\) 's, weighting each value with the size of the corresponding sample.

(b) Construct a table showing the central line in part (a) and three-sigma control limits corresponding to \(n=6,7,8,9\), and 10 . Use \(R=4.0\), a value based on prior data.

(c) Plot the data on a control chart like the one in Figure 15.15 and interpret the results.

Data From Figure 15.15

Transcribed Image Text:

Sample 2 3 4 10 5 6 7 8 n 10 6 9 8 8 10 7 9 R 12.5 11.1 10.2 11.6 21.9 12.3 9.7 15.6 Sample 9 10 II 12 13 14 15 16 n 7 8 10 9 7 8 9 10 R 16.7 9.8 11.6 17.2 10.1 9.5 13.1 14.2