11. Specification for the diameter of a metal shaft is much wider than the machi

Question

11. Specification for the diameter of a metal shaft is much wider than the machine used to make the shafts is capa- ble of. Consequently, the decision has been made to allow the cutting tool to wear a certain amount before replacement. The tool wears at the rate of .004 centime- tre per metal shaft produced. The process has a natural variation, , of .01 centimetre and is Normally distrib- uted. Specification for the diameter of the metal shafts is 15.0 to 15.2 centimetres. How many shafts can the pro- cess turn out before tool replacement becomes neces- sary (i.e., before the process makes an out-of-spec shaft)? (See diagram below.) LO3 15.2 cm. Upper specification limit Three Sigma Mean 15.0 cm. Lower specification limit Number of shafts

Explanation / Answer

Now we are given sigma = .01 so 3*sigma = .03 cm

Hence Mu (the central dotted line) when the process starts = 15.0 +.03 cm = 15.03 cm

Next Mu value after n shafts are produced = 15.2 - .03 cm = 15.17cm

Hence n = (15.17-15.03)/.004 = 35 pieces of shafts

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