Final answer:
The capability index (Cp) for the process that produces computer chips with a mean of 0.04 defective chips and a standard deviation of 0.003 chips, with allowable variation from 0.037 to 0.043, is calculated to be 0.333 when rounded to three decimal places.
Step-by-step explanation:
The capability index (Cp) for the process is computed using the formula Cp = (USL - LSL) / (6σ), where USL is the upper specification limit, LSL is the lower specification limit, and σ is the standard deviation. In this case, the mean is 0.04 defective chips, the standard deviation is 0.003 chips, the USL is 0.043 defective chips, and the LSL is 0.037 defective chips.
Using the provided data:
- USL = 0.043
- LSL = 0.037
- σ = 0.003
Plugging the values into the formula:
Cp = (0.043 - 0.037) / (6 * 0.003)
Cp = 0.006 / 0.018
Cp = 0.333
Therefore, the capability index (Cp) for this process is 0.333 when rounded to three decimal places, which indicates a process that may not be capable since Cp < 1 suggests that the process variation is greater than the width of the specification range.