Question

2. Each of the processes listed is noncentered with respect to the specifications for that process. Compute the appropriate capability index for each, and decide if the process is capable. Process Upper Spec Mean Standard Lower Deviation Spec 0.32 15.1 31 16 17 34 19.5 37.5 21.1 17.5

Answer 1

To calculate the process capability index, we will utilize the following formula:

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

PROCESS H

Cpk = MIN(17 - 16 / 3 * 0.32, 16 - 15.1 / 3 * 0.32)

Cpk = MIN(1.0417, 0.9375)

Cpk = 0.9375

SINCE THE Cpk < 1, THE PROCESS IS NOT CAPABLE

PROCESS K

Cpk = MIN(37.5 - 34 / 3 * 1, 34 - 31 / 3 * 1)

Cpk = MIN(1.1667, 1)

Cpk = 1

SINCE THE Cpk >= 1, THE PROCESS IS CAPABLE

PROCESS T

Cpk = MIN(21.1 - 19.5 / 3 * 0.4, 19.5 - 17.5 / 3 * 0.4)

Cpk = MIN(1.3333, 1.6667)

Cpk = 1.3333

SINCE THE Cpk >= 1, THE PROCESS IS CAPABLE

FOR PROCESS CAPABILITY, WE HAVE TO DETERMINE ITS Cpk BASED ON ITS VALUE FROM 1, IF IT IS BELOW 1, THE PROCESS IS NOT CAPABLE, IF THE PROCESS IS NEAR Cpk OF 1.3, IT IS THE MOST CAPABLE.

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