Question

Problem 5 [Pencil version] An X-bar chart is to be established with u= 100, o=8 (i.e., process standard deviation = 8), and n = 4. Note that European countries use the 0.002 probability limits instead of the 3-sigma limits. Obtain their corresponding 0.002 probability limits (i.e., obtain their UCL, CL, and LCL). This exercise was done in class, but redo it and show your work.

Answer 1

Answer:

Given that:

An X-bar chart is to be established with µ= 100, $\sigma$   = 8 (i.e., process standard deviation = 8), and n = 4. Note that European countries use the 0.002 probability limits instead of the 3-sigma limits.

$\sigma =8 , \mu =100, n=4$

0.002 probability limits $\alpha =0.002$

confidence level = 0.998

$Z_{\alpha /2} = \pm 3.09$

$\mu = \bar{x}\pm Z_{\alpha /2}(\sigma /\sqrt{n})$

$\mu = 100\pm 3.09(8/\sqrt{4})$

$\mu = 100\pm 3.09(8/2)$

$\mu = 100\pm 3.09(4)$

$\mu = 100\pm 12.36$