You manage the quality for the production line of your company's running shoes. A salesperson for an equipment producer is trying to sell you on a new machine designed to cut the insoles for your shoes. Your company specifies that the thickness of the insoles must be 0.250 inches and can not be more than 0.001 of an inch from that specification (either above or below). The salesperson insists that the new machine will outperform your current machine because, through extensive testing, they have determined that the new machine has a production standard deviation of only 0.0005 inches for any chosen average thickness. Calculate Cpk for the salesperson's machine. Enter your answer two decimal places.
Upper specification limit (USL) = 0.250 + 0.001 = 0.251
Lower specification limit (LSL) = 0.250 - 0.001 = 0.249
Mean = 0.250
Standard deviation (SD) = 0.0005
Cpl = (Mean - LSL) / (3 x SD) = (0.250-0.249)/(3x0.0005) = 0.001/0.0015 = 0.67
Cpu = (USL - Mean) / (3 x SD) = (0.251-0.250)/(3x0.0005) = 0.001/0.0015 = 0.67
Process capability index (Cpk) = Minimum of (Cpu, Cpl)
= Minimum of (0.67, 0.67)
= 0.67
You manage the quality for the production line of your company's running shoes. A salesperson for...
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