Question

Process Capability MKS Inc., produces meter sticks that have a target length of 100 centimeters with upper and lower specification limits of 100.05 and 99.95 centimeters respectively. Their existing process produces meter sticks with an average length of 99.97 centimeters and a standard deviation of 0.015 centimeters. They are considering the purchase of a new machine that can hold a process output average exactly to target with a standard deviation of 0.02. Which machine will provide better process capability and why? (Show all your work in order to receive the full credit.) 1. Calculate capability index for the old machine. (8 points) 2. Calculate capability index for the new machine. (8 points) 3. Compare capabilities, decide which is better, and explain why. (4 points)

Answer 1

MACHINE 1

UPPER SPECIFICATION = 100.05
LOWER SPECIFICATION = 99.95
PROCESS MEAN = 99.97
STANDARD DEVIATION = 0.015

Cpk = MINIMUM((UPPER SPECIFICATION - MEAN) / 3 * STANDARD DEVIATION), (MEAN - LOWER SPECIFICATION) / 3 * STANDARD DEVIATION)

Cpk = MINIMUM((100.05 - 99.97) / 3 * 0.015), (99.97 - 99.95) / 3 * 0.015)
Cpk = MINIMUM(1.777778, 0.444444)
Cpk = 0.4444

NEW MACHINE

UPPER SPECIFICATION = 100.05
LOWER SPECIFICATION = 99.95
PROCESS MEAN = 100
STANDARD DEVIATION = 0.02

Cpk = MINIMUM((UPPER SPECIFICATION - MEAN) / 3 * STANDARD DEVIATION), (MEAN - LOWER SPECIFICATION) / 3 * STANDARD DEVIATION)

Cpk = MINIMUM((100.05 - 100) / 3 * 0.02), (100 - 99.95) / 3 * 0.02)
Cpk = MINIMUM(0.833333, 0.833333)
Cpk = 0.8333

3. WE SHOULD CHOOSE THE NEW MACHINE BECAUSE IT HAS A HIGHER PROCESS CAPABILITY. A HIGHER CAPABILITY WOULD MEAN THAT THE PROCESS IS MORE LIKELY TO PRODUCE THE OUTPUT WITHIN THE SPECIFICATIONS.