Singleterry Products makes rods and piston housings for various types of motors. Having a perfect fit is critical if an engine is going to work properly and not leak oil. If it is too tight a fit, the rod will wear down the piston housing, causing early failure (freezing up) of the engine. If the fit is too loose, oil leaks and compression is lost. For one model of rod and piston housing, the circumference of the rod needs to be 0.495 inches, while the circumference of the piston housing needs to be 0.5 inches to ensure a perfect fit. These measures can only vary by 0.005 or leaving a gap of 0.005 between the rod and piston housing circumferences. The gap can only be between 0.004 and 0.007 before problems occur. The company uses Shewhart control charts to keep track of this vital characteristic of its rods and pistons. The data collected on the line yesterday is contained in the table below.

REQUIRED:

a. Make a Shewhart control chart for the circumference variable. Plot each of the observations on your control chart by time.

b. Make a Shewhart control chart for the size of the piston housing circumference variable. Again plot each observation by time.

c. Make a Shewhart control chart for the size of the gap, again plotting each observation by time.

d. When should Singleterry shut down the line and make adjustments? Specifically, should it focus on only one of these metrics, and if so, which one is critical? Why?

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Singleterry Products Rod Circumference Piston Housing Circumference Time of Sample Gap 7 a.m. 0.495 0.500 0.005 8 a.m. 0.495 0.502 0.007 9 a.m. 0.496 0.508 0.012 10 a.m. 0.498 0.512 0.014 11a.m. 0.495 0.495 0.000 12:30 p.m. 0.494 0.505 0.011 130 р.m. 0.487 0.512 0.025 2:30 р.m. 0.482 0.515 0.033