Question

Two machines are currently in use in a process at the Dennis Kira Mfg. Co. The standards for this process are LSL=.320 " and USL = .323". Machine One is currently producing with mean = .321" and standard deviation .0006". Machine Two is currently producing with mean .3205" and standard deviation .0007". Which machine has the higher capability index? Machine One has an index of ____________

Answer 1

Capability index (Cpk) is calculated for each machine using their respective means and standard deviations along with the given USL and LSL. The machine with the higher Cpk value will have the higher capability index.

Step-by-step explanation:

When comparing the capability indexes of two different machines with specified upper and lower specification limits (USL and LSL), we use the formula for the capability index (Cpk), which is the minimum of two ratios: (USL - mean) / (3 * standard deviation) or (mean - LSL) / (3 * standard deviation).

For Machine One, with a mean of .321" and a standard deviation of .0006", the Cpk can be calculated. The USL is .323" and LSL is .320".

For Machine Two, with a mean of .3205" and a standard deviation of .0007", the Cpk can also be calculated using the same limits.

To answer the question, we need to calculate the Cpk for each machine and compare them to find out which machine has the higher capability index. However, the question is asking to fill in the value for Machine One, which can be done by performing the necessary calculations based on the formula given above.