A manufacturer of auto windows uses a thin layer of plastic material between two layers of glass to make safety glass for windshields. The thickness of the layer of this material is important to the quality of the vision through the glass.

A constant quality control monitoring scheme is employed by the manufacturer that checks the thickness at 30-minute intervals throughout the manufacturing process by sampling five windshields. The mean thickness is then plotted on a control chart. A perfect windshield will have a thickness of 4mm. From past experience, it is known that the variance of thickness is about 0.25mm. The results of one shift’s production are given in Table 2.14.

Table 2.14 Thickness of Material (in Millimeters)

Sample Number Thickness Sample Number Thickness 1 4,3,3,4,2 10 5,4,4,6,4 2 5,4,4,4,3 11 4,6,5,4,4 3 3,3,4,4,4 12 5,5,4,3,3 4 2,3,3,3,5 13 3,3,4,4,5 5 5,5,4,4,5 14 4,4,4,3,4 6 6,4,6,4,5 15 3,3,4,2,4 7 4,4,6,5,4 16 4,3,2,2,3 8 6,5,5,6,5 17 4,5,3,2,2 9 5,5,6,5,5 18 3,4,4,3,4

(a) Construct a control chart of these data. (Hint: See Example 2.13.) Does the process stay in control throughout the shift?

(b) Does the chart indicate any trends? Explain. Can you think of a reason for this pattern? LO.1