A Belt working in a supply chain environment has to make a decision to change suppliers of critical raw materials for a new product upgrade. The…

The standard process Z score measures the distance between the specification limit and the process mean in terms of standard deviation units. Given an Upper Specification Limit ($\text{USL}$) of $2,800, a mean ($\mu$) of $2,240, and a standard deviation ($\sigma$) of $120, the Z-value is computed as:

$$Z = \frac{\text{USL} - \mu}{\sigma} = \frac{2,800 - 2,240}{120} = \frac{560}{120} = 4.67$$

A: 2.33 results from incorrectly doubling the standard deviation divisor or miscalculating the specification margin.

C: 6.48 is a mathematical error not matching the standard score ratio $(2800 - 2240) / 120$.

D: 8.28 results from incorrectly dividing by the standard error of the mean instead of the sample standard deviation.

- Breyfogle, F. W. (2003). Implementing Six Sigma: Smarter Solutions Using Statistical Methods (2nd ed.). Wiley. Chapter 12: Process Capability and Z-value, pp. 185–189. https://doi.org/10.1002/9781118320495

- Pyzdek, T., & Keller, P. (2014). The Six Sigma Handbook (4th ed.). McGraw-Hill Education. Chapter 9: Process Capability, pp. 335–340.