1. The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the anticipated mileage to be driven next year. The miles driven during the past 5 years are as follows.
|
Year
|
Mileage
|
|
1
|
3,000
|
|
2
|
4,000
|
|
3
|
3,400
|
|
4
|
3,800
|
|
5
|
3,700
|
(a) Using a simple three-month moving average, forecast the mileage for Year 6. Please provide at least one step of calculation and the correct value for full credit.
(b) Forecast the mileage for Year 6 using a weighted moving average with weights of 0.5, 0.3, and 0.2. The weight of 0.5 is to be attached to the most recent mileage and 0.3 to the second most recent mileage. For full credit, please provide at least one step of calculation and the correct forecast.
(c) Forecast the mileage for Year 6 using exponential smoothing with α = 0.2 and the Year 5 forecast of 3,500. For full credit, please provide the formula, at least one step of calculation and the correct forecast.
(d) Estimate the regression equation using simple linear regression analysis. For both parameters a and b, please provide the formula, at least one step of calculation, and the correct value for full credit.
(e) Forecast the mileage for Year 6 using the regression equation from (d). Please provide one step of calculation and the correct answer for full credit.
2. Income at the architectural firm Spraggins and Yunes for the period February to July was as follows:
|
Month
|
February
|
March
|
April
|
May
|
June
|
July
|
|
Income
(in $1,000)
|
70.0
|
68.5
|
64.8
|
71.7
|
71.3
|
72.8
|
Use trend-adjusted exponential smoothing to forecast the firm's August income. Assume that the forecast for July without trend adjustment is $70,000 and the trend estimate for July is 0. Set smoothing constants α = 0.1 and β = 0.2. Please provide calculation steps for F8, T8, and FIT8.
3. Samples are taken to monitor a filling process. The overall mean of the samples arecc and theaverage range cc. The sample size is 10.
(a) Determine the upper and lower control limits of the chart. Please give the formulas for calculating UCL and LCL and at least one step of calculation for full credit.
(b) Determine the upper and lower control limits of the R chart. Please give the formulas for calculating UCL and LCL and at least one step of calculation for full credit.
4. The results of inspection of DNA samples taken over the past 10 days are given below. Sample size is 100.
|
Day
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
# of defectives
|
7
|
6
|
6
|
9
|
5
|
0
|
0
|
8
|
6
|
1
|
(a) Determine the fraction defective of the p chart. Please give the formula and at least one step of calculation for full credit.
(b) Determine the of the p chart. Please give the formula and at least one step of calculation for full credit.
(c) Determine the 3-sigma upper control limit and the 3-sigma lower control limit of the p chart. For each control limit, provide at least one step of calculation for full credit.
5. Suppose the difference between the upper specification and the lower specification limits is 1.2 inches. The standard deviation is 0.2 inches. What is the process capability ratio ? Please provide the formula, at least one step of calculation, and the correct answer for full credit.
6. The specifications for a plastic liner for concrete highway projects call for a thickness of 4.0 mm 0.3 mm. The standard deviation of the process is estimated to be 0.05 mm. The process is known to operate at a mean thickness of 3.8 mm.
(a) What is the of the process? Please provide the formula, at least one step of calculation, and the correct answer for full credit. (10 points)
(b) Is the process capable based on the value and why?