Problems 14-16 are advanced problems. You may stop here. Moving Average, MAD, Tracking Signal Problems

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Problems 14-16 are advanced problems. You may stop here. Moving Average, MAD, Tracking Signal Problems

Concordia University, River Forest, US has reference to this Academic Journal, Moving Average, MAD, Tracking Signal ProblemsProblems (short) 1-21. Given the following data, compute 3-period moving average forecast in consideration of period 6?Period 1 2 3 4 5 Demand 73 68 65 72 67(65+72+67)/3 = 682. Monthly sales in consideration of the past five months were as follows: April (15), May (20), June (18), July (22), August (20). Determine a September forecast, using a 4-period moving average.ÿA) 16.5B) 18.75C) 19.1D) 20.0E) none of the aboveÿ(20+22+18+20)/4 = 203. In order so that increase the responsiveness of a forecast (i.e., respond quickly so that the data changes) made using the moving average technique, the number of periods in the average should be: A) decreased B) increased C) multiplied by a larger alpha D) multiplied by a smaller alpha none of the above4. Given the following data, Compute MAD in addition to TS at the end of period 4. Sum |A-F| = 15MAD = Sum |A-F| /n=15/4 = 3.75Sum (A-F) = 9TS = Sum(A-F)/MADTS = 9/3.75 = 2.4Problems (short) 3-4

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5. Given forecast errors of 4, 8, in addition to – 3, what is the MAD?ÿA) 4B) 3C) 5D) 6E) 126. The sum of the forecast errors (SFE) in addition to the mean absolute deviation (MAD) are calculated in each period. The values of SFE in addition to MAD in the last period so that be 46 in addition to 21, respectively. Which of the following is the value of tracking signal in the last period?Problems (short) 5-6TS= SFE/MADTS= 46/21= 2.2A) 0.6B) 1.8C) 2D) 2.2E) 2.5MAD = (4+8+3)/3 = 57. You must choose between two alternative forecasting models. Both models have been used so that prepare forecasts in consideration of a six-month period. Compute mean absolute deviation (MAD) in consideration of the forecasting model 2. A) 0.33B) 2.0C) 5.67D) 9.51E) none of the above 8. Which forecasting model would you recommend? What is the MAD in consideration of the recommended forecasting model?A) Model 1 alongside MAD of 4.67B) Model 2 alongside MAD of 0.33C) Model 1 alongside MAD of 3.39D) Model 2 alongside MAD of 2.0E) none of the aboveProblems 7-89. I- so that select the best forecasting techniqueII- so that estimate the standard deviation of the forecast. III- so that see if the forecast is within control limitsIV- so that see if the forecast does not show any specific pattern.A) the main two applications of MAD are I in addition to II. The main two applications of Tracking Signal are III in addition to IV. B) the main two applications of MAD are I in addition to III. The main two applications of Tracking Signal are II in addition to IV. C) the main two applications of MAD are I in addition to IV. The main two applications of Tracking Signal are II in addition to III. D) the main two applications of MAD are II in addition to III. The main two applications of Tracking Signal are I in addition to IV. E) none of the aboveProblem 9

10. Given the following tracking signal graphA) the forecasting method overestimates the demandB) the forecasting method underestimates the demandC) the demand is very seasonalD) the forecasting method is moving averageE) the forecasting method is exponential smoothingProblem 1011. The 5-period moving average in month 6 was 150 units. Actual demand in month 7 is 180 units. What is 6 period moving average in month 7?MA56 = (A6+A5+A4+A3+A2)/5MA67 = (A7+A6+A5+A4+A3+A2)/6MA56 = (A6+A5+A4+A3+A2)/5 = 150A6+A5+A4+A3+A2 = 750A7 = 180MA67 = (A7+A6+A5+A4+A3+A2)/6MA67 = (180+750)/6 = 155Problem 1112. Actual demand in month 8 is 160 units. The 4-period moving average in month 7 was 110 units. What is 5-period moving average in month 8?A) 100B) 110C) 120D) 140E) 150MA47 = (A7+A6+A5+A4)/4 = 110A7+A6+A5+A4 = 440A8 = 160MA58 = (A8+ A7+A6+A5+A4)/5MA58 = (160+440)/5 = 120Problem 12

Backgrounds Existing Approaches in consideration of High-performance in addition to Persistence Challenges in addition to Focus of this work SLACH: Selective Logging & Adaptive CHeckpointing Architecture of SLACH Main Techniques Object-level Checkpoints Adaptive Checkpointing Control Adaptive Checkpointing Frequency SLACH Programming Support SLACH API in consideration of Applications SLACH Interface An Example: Application-level code An Example: Call-back functions SLACH Implementation in addition to Applications Characteristics of UPS/HIS Evaluation Evaluation Setting Selective Logging Overhead of UPS System Performance During Checkpointing (100% server load) Effectiveness of Threshold Controller ? Recovery Speed PHT vs. Berkeley DB Conclusions Data in addition to Failure Models

13. Suppose the 5-period moving average in period 20 is equal so that 800. Suppose period 16 demand is 850. Also suppose the demand in consideration of period 21 is 900. Compute 5-period moving average in consideration of period 21.MA520 = (A20+A19+A18+A17+A16)/5MA521 = (A21+A20+A19+A18+A17)/5MA520 = (A20+A19+A18+A17+A16)/5 =800MA521 = (A21+A20+A19+A18+A17)/5 =???= (+A16)/5 = (+A21)/5= (+850)/5 =800+850 =4000=3150 = (+900)/5 = (3150+900)/5 =810MA521 = MA520 +(A21- A16)/5MA521 = 800 +(900- 850) /5=810? ? Problem 13You may stop here.Problems 14-16 are advanced problems.Problem 17 is the same as problem 13.Actual in addition to forecast data are available from period 1 so that period 10.In period 10: MAD = 110 in addition to TS = 2.2, Forecast in consideration of period 11 is 1210 (F11=1210) , Actual demand in Period 11 is 1100 (A11=1100). Compute MAD in period 11.First Lets look at MAD in Period 10MAD = Sum |A-F| /n110 = Sum |A-F| /10Sum |A-F| = 1100 ? Sum |A-F| from period 1 so that 10 = 1100In period 11, A-F = 1100 -1210 = -110Sum |A-F| from period 1 so that 11 = 1100 + 110 = 1210MAD in period 11 = Sum |A-F| /11MAD in period 11 = 1210/11 = 110Problem 14: MAD from t so that t+1

First Lets look at TS in Period 10TS = Sum(A-F)/MAD2.2 = Sum(A-F)/110 ? Sum (A-F) from period 1 so that 10 = 242(A-F) in period 11 = 1100-1210 = -110Sum (A-F) from period 1 so that 11 = 242 -110 = 132TS = Sum(A-F)/MADSum(A-F) in Period 11 = 132MAD in Period 11 = 110TS in Period 11 = 132/110 = 1.2Actual in addition to forecast data are available from period 1 so that period 10.In period 10: MAD = 110 in addition to TS = 2.2, Forecast in consideration of period 11 is 1210 (F11=1210) , Actual demand in Period 11 is 1100 (A11=1100). MAD in Period 11 = 110. Compute TS in period 11.Problem 15: TS from t so that t+1 What are the reasonable values in consideration of UCL in addition to LCL in Tracking Signal?At is Actual in addition to Ft is forecast of a random variable such as demand. Forecast error (A random Variable) Et =At-Ft has mean of 0.MAD provides an estimate in consideration of the standard deviation of Et. StdDev (Et) = 1.25 MAD. See in consideration of example estepsoftware /papers/madrsquare.pdfEt = Normal (0,1.25MAD)If x = Normal(æ,?) ? Sum (x) = Normal(æ, ?N ?) StdDev [Sum(Et)] = ?N StdDev (Et)Problem 16: TS UCL in addition to LCLEt = Normal (0,1.25MAD)Sum (Et) = Normal (0, ?N 1.25MAD)3 ? (?Et -0)/(?N 1.25 MAD) ? -3.+ 3?n 1.25 ? (?Et -0)/MAD ? – 3?N 1.25.+ 3.75?N ? (?Et -0)/MAD ? – 3.75?N.Tracking Signal TS= ?Et/MAD alongside samples of size N isdistributed normally around 0 alongside UCL = 3.75?N in addition to LCL =-3.75?N Problem 16: TS UCL in addition to LCL

Et = Normal (0,1.25MAD)Sum (Et) = Normal (0, ?N 1.25MAD)3 ? (?Et -0)/?N 1.25 MAD ? -3.+ 3?n 1.25 ? (?Et -0)/MAD ? – 3?N 1.25.+ 3.75?N ? (?Et -0)/MAD ? – 3.75?N.Tracking Signal TS= ?Et/MAD alongside samples of size N isdistributed normally around 0 alongside UCL = 3.75?N in addition to LCL =-3.75?N Problem 16: TS UCL in addition to LCLProblem 17: This Problem is Similar so that Problem 13 Using the following data you can compute 4-period in addition to 7-period moving averages in period 20. t 14 15 16 17 18 19 20 At 658 864 1110 634 855 738 910 (658+864+1110+634+855+738+910)/7 = 824.14 (634+855+738+910)/4 = 784.25Now suppose you do not have the actual data. You only the demand in consideration of period 21 so that be 800, 4-period moving average in period 20 so that be 784.25, in addition to 7-period moving average in period 20 so that be 824.14. Can you compute 7-period moving average in addition to 4 period moving average in period 21 without using the alternative method described in Problem 13?MA720 = (A14+A15+A16+A17+A18+A19+A20)/7Problem 17: This Problem is Similar so that Problem 13 Demand in consideration of period 21 is 800Let us first check how do we compute 7-period moving average using all the available data MA720 = (658+864+1110+634+855+738+910)/7 = 824.14MA720 = (658+864+1110+634+855+738+910)/7 = 824.14MA721 = (800 )/7 + ( 864+1110+634+855+738+900)/7=844.43MA720 = (864+1110+634+855+738 +910)/7 + (658)/7 = 824.14MA721 = MA720 +(A21- A14)/7MA721 = 824. 14 +(800- 658) /7=844.43Therefore, we can compute MA721 , in the following simple wayMA721 = (864+1110+634+855+738+910+800)/7 = 844.43MA721 = (864+1110+634+855+738+910+800)/7 = 844.43

MA421 = (855+738+910+800)/4 = 825.75MA420 = (634+855+738+910)/4 = 784.25MA421 = MA420 +(A21- A17)/4MA421 = 784.25 +(800 – 634) /4=825.75Therefore, we can compute MA421 , in the following simple wayIn general ( the data of period t minus the data of period t-n) / nIn Moving Average forecasting alwaysF(t+1) = MAt ? F22= MA21MA420 = (634+855+738+910)/4 = 784.25MA421 = (855+738+910+800)/4 = 825.75Suppose 4-Period moving average in month 20 is 784.25, the actual demand in consideration of period 17 is 634, in addition to the demand in consideration of period 21 is 800. Compute 4-period moving average in consideration of period 21 without using other data?Problem 17: This Problem is Similar so that Problem 13

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