The Farley Manufacturing Company prides itself on the quality of its products. T

Question

The Farley Manufacturing Company prides itself on the quality of its products. The company is engaged in competition for a very important project. A key element is a part that ultimately goes into precision testing equipment. The specifications are 8.000 plus or minus 3.000 millimeters. Management is concerned about the capability of the process to produce that part. The accompanying data were randomly collected during test runs of the process.

The process capablity index, Cpk, is equal to ___ (3 decimal places)

Chart

Data Table Observation (millimeters) Sample 8.000 7.500 8.700 7.400 8.200 8.800 8.500 8.300 10.100 8.700 9.600 9.300 7.100 8.300 7.300 8.000 7.800 9.800 9.200 8.400 8.600 9.300 7.500 9.400 7.600 9.500 9.500 7.500 8.900 10.100 8.300 7.700 9.100 9.900 8.400 8.500 8.600 8.900 7.300 8.100 Print Done

Explanation / Answer

Mean of the sample(µ) = 8.542

Standard deviation of the sample(s) = 0.835

USL = 8 + 3 = 11

LSL = 8 - 3 = 5

Cpl = (µ – LSL)/3*s = (8.542 - 5) / (3*0.835) = 1.413

Cpu = (USL - µ)/3*s = (11 - 8.542) / (3*0.835) = 0.981

Cpk = Min(Cpu, Cpl) = 0.981

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