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Question: 1 / 400

The hardness specification for a material is 100 BHN or greater. If the process for that material has a mean of 105.0 and a standard deviation of 1.0, what is the Cpk for this process?

1.00

1.33

1.67

To calculate the Cpk (Process Capability Index), it is necessary to understand how this metric evaluates the capability of a process to meet specified limits, particularly in relation to the mean and standard deviation of the process.

The formula for Cpk is expressed as:

Cpk = min(Cpu, Cpl)

Where:

- Cpu = (USL - Mean) / (3 * Standard Deviation)

- Cpl = (Mean - LSL) / (3 * Standard Deviation)

In this case, the hardness specification has a lower specification limit (LSL) of 100 BHN and no upper specification limit (USL), which complicates the calculation of Cpu. However, we can directly use the available information to find Cpl, since that pertains to the limit we care about.

Given:

- Mean = 105.0

- Standard Deviation = 1.0

- LSL = 100.0

Calculating Cpl:

Cpl = (105.0 - 100.0) / (3 * 1.0) = 5.0 / 3 = 1.67

Since there is no upper limit to consider, Cpu is irrelevant for this scenario. Therefore, the

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