Answer to Question #154628 in Statistics and Probability for Zanny

Question

1. What should the control limits be placed in the design of the process sets alpha = 0.01 with the following parameters (assume that the sample size condition has been verified)?

(a) = 100,= 20, and n = 25 cases per batch

(b) = 2000,= 2000, and n = 100 cases per batch

 

Answer 1

a)

$UCL = \mu+Z_{\alpha/2}\frac{\sigma}{\sqrt{25}}=100+2.58*20/5=110.32\\ LCL = 100-2.58*20/5=89.68$

b)

$UCL = 2000+2.58*2000/10=2516\\ LCL = 2000-2.58*2000/10=1484$