A manager wants to build 3-sigma x-bar control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 3. If samples of size 9 are to be taken, what will be the upper and lower control limits, respectively?
A) 19 and 1
B) 16 and 4
C) 13 and 7
D) 4 and 16
E) 7 and 13

Question

Quizplus · Accepted Answer

The upper and lower 3-sigma control limits for an x-bar chart are calculated using the formula: UCL = μ + Z(σ/√n) and LCL = μ - Z(σ/√n), where μ is the process mean, σ is the process standard deviation, Z is the Z-value for the desired sigma level (for 3-sigma, Z=3), and n is the sample size. Here, μ=10, σ=3, Z=3, and n=9. Thus, UCL = 10 + 3*(3/√9) = 10 + 3 = 13, and LCL = 10 - 3*(3/√9) = 10 - 3 = 7.

A Manager Wants to Build 3-Sigma X-Bar Control Limits for a Process