Six Sigma Black Belt Certified Practice Exam

To calculate the upper control limit for the process, we use the formula for the control limits in a control chart. Specifically, the upper control limit (UCL) can be determined using the average of the process (X) plus a factor times the standard error of the mean.

The formula for the upper control limit is:

UCL = X + Z * (σ / √n)

Where:

- X is the process mean,

- Z is the z-score that corresponds to the desired level of confidence (typically for a control chart, this is 3 for three sigma),

- σ is the standard deviation of the process,

- n is the size of the subgroup.

In this case, we have:

- X = 35.0

- σ = 5.00

- n = 5

First, we need to calculate the standard error of the mean (SEM):

SEM = σ / √n = 5.00 / √5 ≈ 2.24

Next, applying the three-sigma control chart method, we use Z = 3. Therefore:

UCL = 35.0 + (3 * 2.24) = 35.0 + 6.72 = 41.