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12-51.

A glass factory makes a continuous ribbon of glass by pouring a continuous stream of hot liquid silicon on a lake of molten tin. The liquid silicon spreads out evenly on the tin and then cools into glass. It is a process that must continue uninterrupted $24$ hours a day, so adjustments to equipment and materials are ongoing. Assume that inspectors work eight-hour shifts, watching the glass ribbon as it flows from the lake of tin, marking and counting the number of defects on the new glass. The number of defects identified by the inspectors for a $24$-hour period is shown below: Homework Help ✎

 Hour $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $11$ $12$ Defects $43$ $40$ $42$ $40$ $38$ $39$ $36$ $38$ $44$ $41$ $45$ $42$

 Hour $13$ $14$ $15$ $16$ $17$ $18$ $19$ $20$ $21$ $22$ $23$ $24$ Defects $40$ $37$ $39$ $39$ $43$ $40$ $42$ $42$ $38$ $41$ $38$ $37$

1. Create an $x$-bar process control chart with a UCL of $45$ and an LCL of $35$.

Make a graph where the $x$-axis is Hours, the $y$-axis is Defects.
The $y$-axis should range from $35$ to $45$.

2. What do you notice about the process control chart that might concern you as a quality control engineer?

Answers will vary, but notice that there appears to be a cycle every $8$ hours.