Question

# You're the operations manager at a regional hospital and your management has set the goal that...

 You're the operations manager at a regional hospital and your management has set the goal that no one should wait more than 3 minutes to see a nurse in the Emergency Room.  You've collected 40 samples of the average wait times at five different times during the day over 40 days as shown below. a. construct an x-bar chart for this data.  Is the process in control? b. using 3 minutes as the upper tolerance limit and zero as the lower tolerance limit, calculate the process capability statistics ( Cp, Cpk, Cpu and Cpl).  Is your process capable of achieving management's goal, based on the data? c.  What percentage of ER visits would you expect to exceed the Upper Tolerance Limit? Day 1 1.22 1.54 1.53 1.86 1.49 2 1.48 1.18 1.41 1.29 1.61 3 2.12 1.76 1.29 1.78 1.74 4 1.34 1.22 1.29 1.69 1.42 5 1.11 1.21 3.60 1.95 1.22 6 0.73 1.97 1.51 1.67 1.77 7 1.20 1.46 1.05 3.55 1.80 8 1.72 1.58 1.79 1.95 0.83 9 1.23 3.10 1.57 1.49 1.58 10 0.70 0.94 1.14 1.54 1.81 11 1.50 1.83 1.60 1.15 1.79 12 1.72 1.61 1.63 1.84 1.95 13 1.64 1.13 1.60 1.87 1.36 14 0.73 1.39 1.39 1.85 1.86 15 1.72 1.42 1.59 0.70 1.55 16 1.91 2.08 1.64 2.05 1.60 17 1.63 1.57 0.95 2.02 1.69 18 1.53 1.47 2.05 1.19 1.52 19 1.18 1.78 3.20 1.53 1.30 20 1.74 2.14 1.24 0.92 1.34 21 1.47 1.89 1.53 2.28 1.84 22 1.68 1.35 1.26 3.20 1.63 23 0.99 1.57 1.45 1.50 1.98 24 1.92 1.01 0.93 1.68 1.96 25 3.13 1.57 1.75 1.72 1.63 26 1.13 0.99 1.27 1.35 1.37 27 1.87 1.74 0.89 1.61 1.77 28 0.99 1.36 0.89 1.54 3.30 29 1.75 1.96 1.57 1.67 2.31 30 1.59 2.15 3.10 1.42 1.50 31 0.93 1.65 1.29 1.02 1.48 32 1.40 1.98 1.54 0.97 1.62 33 1.69 1.62 1.47 1.81 0.97 34 1.98 1.26 1.32 1.17 1.39 35 3.25 1.42 2.06 1.27 1.34 36 1.45 1.57 1.70 1.32 1.26 37 1.98 1.61 1.45 1.46 2.19 38 1.46 1.46 1.70 1.56 1.93 39 1.80 1.34 1.46 3.40 1.10 40 1.04 1.29 1.30 1.77 1.13

(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 %

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