An in-control, centered process that follows a normal distribution has a $\mathrm { C } _ { \mathrm { p } } = 0.6667$. How many standard deviations away from the process mean is the upper specification limit?
A) $2 \sigma$
B) $4 \sigma$
C) $\frac { 2 \sigma } { 3 }$
D) $3 \sigma$

Question

Quizplus · Accepted Answer

The process capability index $ C_p $ is defined as $ C_p = \frac{USL - LSL}{6\sigma} $. Given $ C_p = 0.6667 $, it implies $ \frac{USL - LSL}{6\sigma} = 0.6667 $. Solving for $ USL - LSL $ gives $ 4\sigma $, so the USL is $ 2\sigma $ from the mean.

An In-Control, Centered Process That Follows a Normal Distribution Has Cp=0.6667\mathrm { C } _ { \mathrm { p } } = 0.6667Cp​=0.6667

An In-Control, Centered Process That Follows a Normal Distribution Has $\mathrm { C } _ { \mathrm { p } } = 0.6667$