A metal-cutting operation has a target value of 20 and consistently averages 19.8 with a standard deviation of 0.5. The design engineers have established an upper specification limit of 22 and a lower specification limit of 18. Which statement concerning this process is True?
A) The process capability ratio is 1.46.
B) The process capability index is 1.33.
C) The process is in control.
D) None of these is True.

Question

Quizplus · Accepted Answer

The process capability ratio (Cp) and the process capability index (Cpk) are both measures of how well a process can meet its specification limits. Cp is calculated using the formula Cp = (USL - LSL) / (6σ), and Cpk is the minimum of [(USL - mean) / (3σ)] and [(mean - LSL) / (3σ)]. Given the data, Cp = (22 - 18) / (6*0.5) = 4 / 3 = 1.33, not 1.46, making A incorrect. For Cpk, since the process mean is 19.8, the minimum of [(22 - 19.8) / (3*0.5)] and [(19.8 - 18) / (3*0.5)] must be calculated, which would not result in 1.33 exactly, making B incorrect. The statement "The process is in control" (C) cannot be determined solely based on the given information, as being in control refers to statistical control, which requires analysis of control charts and not just capability indices. Therefore, D is the correct choice.

A Metal-Cutting Operation Has a Target Value of 20 and Consistently