## Answers

(a) Xbar and R chart are constructed as under:

Calculate sample Average (Xbar) and Range (R = difference of MAX and MIN value) for each day.

Calculate the Average of Xbars and R vaues of 40 days to get Xbarbar and Rbar

(b) Process standard deviation, = Rbar/d2 , where d2 is control chart constant = 2.326

= 1.12/2.326 = 0.4817

Cp = (USL-LSL)/6 = (3-0)/(6*0.4817) = **1.038**

Cpu = (USL - )/3 = (3 - 1.6)/(3*0.4817) = 0.9688

Cpl = ( - LSL)/3 = (1.6 - 0)/(3*0.4817) = 1.1072

Cpk = MIN(Cpu, Cpl) = MIN(0.9608, 1.1072) = **0.9688**

Cp and Cpk are less than 1.33. Therefore, the process is not capable of meeting specifications on 3 sigma quality.

c) z = (3-1.6)/0.4817 = 2.9064

P(z) = NORMSDIST(2.9064) = 0.9982

Percentage of ER visits expected to exceed the tolerance limit = 1 - 0.9982 = 0.0018 or **0.18** %