Question

Two machines are currently in use in a process at the Dennis Kira Mfg. Co. The standards for this process are LSL = 430 and USL = .435. Machine One is currently producing with mean = 432 and standard deviation .0005. Machine Two is currently producing with mean .4315 and standard deviation .0004. Which machine has the higher capability index? Machine One has an index of ?(round your response to two decimal places).

Answer 1

Machine One has a higher capability index of 1.33, when compared to Machine Two's index, indicating that Machine One performs better relative to the standards set for the process.

Step-by-step explanation:

The question involves calculating the capability index for two machines to determine which machine has the higher capability index. The capability index can be calculated using the formula Cpk = min(USL - μ, μ - LSL) / (3σ), where μ is the mean of the process, σ is the standard deviation, USL is the upper specification limit, and LSL is the lower specification limit.

For Machine One:
Cpk = min(0.435 - 0.432, 0.432 - 0.430) / (3 * 0.0005)
≈ min(0.003, 0.002) / 0.0015
≈ 0.002 / 0.0015
≈ 1.33 (rounded to two decimal places)

For Machine Two, we would calculate:
Cpk = min(0.435 - 0.4315, 0.4315 - 0.430) / (3 * 0.0004)
≈ min(0.0035, 0.0015) / 0.0012
≈ 0.0015 / 0.0012
≈ 1.25 (rounded to two decimal places)

Hence, comparing the Cpk values, Machine One has a higher capability index than Machine Two.