In some situations, the sizes of sampled specimens vary, and larger specimens are expected to have more defects than smaller ones. For example, sizes of fabric samples inspected for flaws might vary over time. Alternatively, the number of items inspected might change with time.

Let ui

g xi i



where “size” might refer to area, length, volume, or simply the number of items inspected. Then a u chart plots u1, u2, . . . , has center line u, and the control limits for the ith observations are u  3u/gi

.

Painted panels were examined in time sequence, and for each one, the number of blemishes in a specified sampling region was determined. The surface area (ft2

) of the region examined varied from panel to panel. Results are given below. Construct a u chart.

Area No. of Panel Examined Blemishes 1 .8 3 2 .6 2 3 .8 3 4 .8 2 5 1.0 5 6 1.0 5 7 .8 10 8 1.0 12 9 .6 4 10 .6 2 11 .6 1 12 .8 3 13 .8 5 14 1.0 4 15 1.0 6 16 1.0 12 17 .8 3 18 .6 3 19 .6 5 20 .6 1