Question

Rudy is evaluating the capability of a process to produce candle holders with an internal diameter of 20 mm. The specification is 20 mm +/- 0.05 mm. After carefully measuring a sample of candle holders, he found that the average internal diameter is 19.98 mm with a standard deviation of 0.01 mm. Based on this information, the Cpk is:

A. 2.33
B. 1.67
C. 1.0
D. 0.6

Answer 1

The Cpk for the process is 1.0.

Step-by-step explanation:

The Cpk (Process Capability Index) is a measure of how well a process is able to produce items within the specified tolerance range. To calculate Cpk, we need to use the formula: Cpk = min((USL - mean) / 3 * standard deviation, (mean - LSL) / 3 * standard deviation), where USL is the upper specification limit and LSL is the lower specification limit.

In this case, the specification is 20 mm +/- 0.05 mm. So, the USL would be 20 + 0.05 = 20.05 mm and the LSL would be 20 - 0.05 = 19.95 mm.

Now, plugging in the values: Cpk = min((20.05 - 19.98)/(3 * 0.01), (19.98 - 19.95)/(3 * 0.01)) = min(0.07/0.03, 0.03/0.03) = min(2.33, 1) = 1

Therefore, the Cpk is 1, so the answer is C. 1.0.