Question

The manager of an organic yogurt processing plant desires with a mean of 16 ounces +/- 0.5 ounces. The process has a mean of 15.9 ounces and a standard deviation of 1 ounce.

1. Determine the Cp and Cpk of the process. Is the process capable of meeting specifications?

Now the management has redesigned the system and so the standard deviation of the process is reduced to 0.1 ounces.

2. What is the Cp and Cpk of the new process? Is the new process capable of meeting specifications?

3. What happens to Cp as the process slides to the right? (the mean of the system increases?)

4. What happens to Cpk as the process slides to the right? (the mean of the system increases?)

5. What is the maximum value of Cpk?

Answer 1

1. UPPER = 16.6
LOWER = 15.5
PROCESS MEAN = 15.9
STANDARD DEVIATION = 1

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

CPK = MIN((16.6 - 15.9) / 3 * 1), (15.9 - 15.5) / 3 * 1)
CPK = MIN(0.2333, 0.1333)
CPK = 0.133

SINCE CPK = 0.133 < 1, THE PROCESS IS NOT CAPABLE.

PROCESS CAPABILITY RATIO

UPPER = 16.6
LOWER = 15.5
STANDARD DEVIATION = 1

CP = (UPPER - LOWER ) / (6 * STANDARD DEVIATION)

CP = (16.6 - 15.5) / (6 * 1)
CP = 0.183

CP = 0.183 < 1, THE PROCESS IS NOT CAPABLE

2. A. UPPER = 16.6
LOWER = 15.5
PROCESS MEAN = 15.9
STANDARD DEVIATION = 0.1

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

CPK = MIN((16.6 - 15.9) / 3 * 0.1), (15.9 - 15.5) / 3 * 0.1)
CPK = MIN(2.3333, 1.3333)
CPK = 1.333

SINCE CPK = 1.333 > 1, THE PROCESS IS CAPABLE

2. UPPER = 16.6
LOWER = 15.5
STANDARD DEVIATION = 0.1

CP = (UPPER - LOWER ) / (6 * STANDARD DEVIATION)

CP = (16.6 - 15.5) / (6 * 0.1)
CP = 1.833

CP = 1.833 > 1, THE PROCESS SHOWS HIGH CAPABILITY

B. CP, BEING A CENTERED PROCESS WOULD NOT BE AFFECTED BY THE CHANGE IN THE MEAN VALUE SINCE CP IS CALCULATED BY THE DIFFERENCE IN THE UPPER LIMIT / 6 * SIGMA

C. AS THE MEAN INCREASES, THE CPK WOULD FIRST INCREASE, THEN STABILIZE THEN START DECREASING AS THE PROCESS MOVES TOWARD THE UPPER CONTROL LIMIT.

D. THERE IS NO MAXIMUM VALUE THAT LIMITS THE CPK VALUE, BUT AN EXTREMELY HIGH OR NEGATIVE VALUE OF CPK WOULD SUGGEST THAT THE PROCESS OF MEASURING THE OBSERVATIONS AND SAMPLES WAS INACCURATE. THE CPK VALUE IS HIGHLY STANDARD DEVIATION DEPENDENT. THE MORE NARROWER THE DEVIATION, THE HIGHER CPK WILL INCREASE.

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