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Process or Product Monitoring and Control_7

Tham khảo tài liệu 'process or product monitoring and control_7', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 6.4.3.5. Triple Exponential Smoothing Complete season needed To initialize the HW method we need at least one complete season s data to determine initial estimates of the seasonal indices I t-L. L periods A complete season s data consists of L periods. And we need to estimate the in a season trend factor from one period to the next. To accomplish this it is advisable to use two complete seasons that is 2L periods. Initial values for the trend factor How to get initial estimates for trend and seasonality parameters The general formula to estimate the initial trend is given by Ậ VỉẠ-l Vl . VL- -2 V2 . VL- -L Vl iA L L H L Initial values for the Seasonal Indices As we will see in the example we work with data that consist of 6 years with 4 periods that is 4 quarters per year. Then Step 1 compute yearly averages Step 1 Compute the averages of each of the 6 years Step 2 Step 2 Divide the observations by the appropriate yearly mean divide by yearly 1 2 3 4 5 6 averages y1 A1 y5 A2 y9 A3 y13 A4 y17 A5 y21 A6 y2 A1 y6 A2 y10 A3 y14 A4 y18 A5 y22 A6 y3 A1 y7 A2 y11 A3 y15 A4 y19 A5 y23 A6 y4 A1 y8 A2 y12 A3 y16 A4 y20 A5 y24 A6 http www.itl.nist.gov div898 handbook pmc section4 pmc435.htm 2 of 3 5 1 2006 10 35 16 AM 6.4.3.5. Triple Exponential Smoothing Step 3 form seasonal indices Step 3 Now the seasonal indices are formed by computing the average of each row. Thus the initial seasonal indices symbolically are h y1 A1 y5 A2 y9 A3 y13 A4 y 17 A5 y21 A6 6 h y2 A1 y6 A2 y10 A3 y14 A4 y 18 A5 y22 A6 6 3 y3 A1 y7 A2 y11 A3 y15 A4 y19 A5 y22 A6 6 I4 y4 Ai y8 A2 y12 A3 y16 A4 y20 A5 y24 A6 6 We now know the algebra behind the computation of the initial estimates. The next page contains an example of triple exponential smoothing. The case of the Zero Coefficients Zero Sometimes it happens that a computer program for triple exponential coefficients smoothing outputs a final coefficient for trend 99 or for seasonality Ợ of for trend zero. Or worse both are outputted as zero and .