Question

Two machines are currently in use in a process at the Dennis Kira Mfg.Co. The standards for this process are LSL = 300" and USL = 303". Machine One is currently producing with mean = 301" and standard deviation .0005". Machine Two is currently producing with mean 3005" and standard deviation .0004". Which machine has the higher capability index? Machine One has an index of (round your response to two decimal places)

Answer 1

Cpk = MIN(UPPER LIMIT - MEAN / 3 * STANDARD DEVIATION, MEAN - LOWER LIMIT / 3 * STANDARD DEVIATION)

UPPER SPECIFICATION = 0.303

LOWER SPECIFICATION = 0.300

MEAN = 0.301

STANDARD DEVIATION = 0.0005

Cpk = MIN(0.303 - 0.301 / 3 * 0.0005, 0.301 - 0.3 / 3 * 0.0005)

Cpk = MIN(1.333, 0.667)

Cpk = 0.667

The process is not capable since the Cpk < 1

MACHINE 2

UPPER SPECIFICATION = 0.303
LOWER SPECIFICATION = 0.3
MEAN = 0.3005
STANDARD DEVIATION = 0.0004

Cpk = MIN(0.303 - 0.3005 / 3 * 0.0004, 0.3005 - 0.3 / 3 * 0.0004)
Cpk = MIN(2.083, 0.417)
Cpk = 0.417

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