Question

Design specifications require that a key dimension on a product measure 100+ 10 units. A process being considered for producing this product has a mean of 100 and a standard deviation of four units. Calculate the process capability index for this example. Keep two decimals!

Answer 1

To calculate the process capability index, we need to use the formula:

Process Capability Index (Cpk) = (USL - µ) / (3 * σ)

Where:
- USL is the upper specification limit, which is given as 100+10 units (110 units)
- µ is the mean of the process, given as 100 units
- σ is the standard deviation of the process, given as 4 units

Let's calculate the process capability index step by step:

Step 1: Substitute the given values into the formula:
Cpk = (110 - 100) / (3 * 4)

Step 2: Simplify the equation:
Cpk = 10 / 12

Step 3: Divide to get the final answer:
Cpk = 0.83 (rounded to two decimal places)

Therefore, the process capability index for this example is 0.83.

In summary, the process capability index is a measure of how well a process can meet the design specifications. In this case, the process capability index is 0.83, indicating that the process has some capability to produce the product within the specified dimensions.