# Hw8 - Homework 8(due April 18 1 A machine is producing...

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Homework 8 (due April 18) 1. A machine is producing shafts with a nominal diameter 5.00 mm. The actual shaft diameter is approximately normal with a standard deviation of 0.01 mm. A shaft is considered to be in-spec if its diameter is between 4.97 and 5.03 mm. When the machine is adjusted perfectly, the mean diameter of shafts it is producing is equal to the nominal diameter (so that the fraction of out-of-spec shafts produced by the machine is negligible). a) Now assume that the mean diameter shifts by 0.02 mm. Calculate the proportion of out-of-spec shafts produced by the machine after the shift. b) Suppose now that a statistical quality control procedure is used in which a sample of size 5 is taken every 2 hours. Then, provided the resulting sample mean does not fall in the interval [5 . 00 - Δ , 5 . 00 + Δ], the machine is stopped and adjusted. Shifts happen randomly, once in 50 hours on average. The cost of stopping the machine is equal to 1000. Every out-of-spec shaft incurs a cost of 10. The working machine is producing 500 shafts per hour.

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