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 %
You're the operations manager at a regional hospital and your management has set the goal that...
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3.75 3.68 1466 6
1.1 1.54 706 4
3 3.32 1160 5
0.05 0.33 756 3
1.38 0.36 1058 2
1.5 1.97 1008 7
1.38 2.03 1104 4
4.01 2.05 1200 7
1.5 2.13 896 7
1.29 1.34 848 3
1.9 1.51 958 5
3.11 3.12 1246 6
1.92 2.14 1106 4
0.81 2.6 790 5
1.01 1.9 954 4
3.66 3.06 1500 6
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Table 12.1 (below)TABLE 12.1 Year-to-Year Total Returns: 1926–2019YearLarge-Company StocksLong-Term Government BondsU.S. Treasury BillsConsumer Price Index192611.62%7.77%3.27%–1.49%192737.498.933.12–2.08192843.61.103.56–.971929–8.423.424.75.201930–24.904.662.41–6.031931–43.34–5.311.07–9.521932–8.1916.84.96–10.30193353.99–.07.30.511934–1.4410.03.162.03193547.674.98.172.99193633.927.52.181.211937–35.03.23.313.10193831.125.53–.02–2.781939–.415.94.02–.481940–9.786.09.00.961941–11.59.93.069.72194220.343.22.279.29194325.902.08.353.16194419.752.81.332.11194536.4410.73.332.251946–8.07–.10.3518.1619475.71–2.62.509.0119485.503.40.812.71194918.796.451.10–1.80195031.71.061.205.79195124.02–3.931.495.87195218.371.161.66.881953–.993.641.82.62195452.627.19.86–.50195531.56–1.291.57.3719566.56–5.592.462.861957–10.787.463.143.02195843.36–6.091.541.76195911.96–2.262.951.501960.4713.782.661.48196126.89.972.13.671962–8.736.892.731.22196322.801.213.121.65196416.483.513.541.19196512.45.713.931.921966–10.063.654.763.35196723.98–9.184.213.04196811.06–.265.214.721969–8.50–5.076.586.1119703.8612.116.525.49197114.3013.234.393.36197219.005.693.843.411973–14.69–1.116.938.801974–26.474.358.0012.20197537.239.205.807.01197623.9316.755.084.811977–7.16–.695.126.7719786.57–1.187.189.03197918.61–1.2310.3813.31198032.50–3.9511.2412.401981–4.921.8614.718.94198221.5540.3610.543.87198322.56.658.803.8019846.2715.489.853.95198531.7330.977.723.77198618.6724.536.161.1319875.25–2.715.474.41198816.619.676.354.42198931.6918.118.374.651990–3.106.187.816.11199130.4719.305.603.0619927.628.053.512.90199310.0818.242.902.7519941.32–7.773.902.67199537.5831.675.602.54199622.96–.935.213.32199733.3615.855.261.70199828.5813.064.861.61199921.04–8.964.682.682000–9.1021.485.893.392001–11.893.703.831.552002–22.1017.841.652.38200328.681.451.021.88200410.888.511.203.2620054.917.812.983.42200615.791.194.802.5420075.499.884.664.082008–37.0025.871.60.09200926.46–14.90.102.72201015.0610.14.121.5020112.1127.10.042.96201216.003.43.061.74201332.39–12.78.021.51201413.6924.71.02.7620151.38–.65.02.73201611.961.75.202.07201721.836.24.802.112018–4.38–.571.811.91201931.4912.162.142.29Questions:a.Calculate the arithmetic average returns for large-company stocks and T-bills over this period. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)b.Calculate the standard deviation of the returns for large-company stocks and T-bills over this period. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)c-1.Calculate the observed risk premium...