划分产品生命周期期段的双对数算法

本文定义了关于产品生命周期的期段、期段曲线和期段组合曲线,并以Gompertz曲线为模式,提出了一种划分期段与预测的算法——双对数算法。文中给出了计算程序,计算结果表明了本算法的正确性和有效性。

Double Logarithm for Division of Product Life Cycle

For a long time in the past, the data y,(t = [1,n]) are usually put into a mathematical model to perform calculation when the life cycle of a product is analyzed. Obviously, it is supposed that all the products are in the same cycle all the while. But this is not in conformity with reality, Some basic concepts such as the interval, the interval curve, the combinatorial curve of intervals as well as a double logarithm method are proposed by the author to determine the number of the intervals covered by all the data and the beginning and ending point of individual interval. The basic concept of the method is, by double logarithm transformation of Gompertz curve y = f(t, R) =Kabt(R= (K,a,b)T), each interval on the curve on the double logarithm plane is transformed into a regression line segment. Now let r0 and r1 be respectively the correlation coefficients of one regression line, and the combination of two neighbouring regression lines There must be the relationship |r0|>|r1|. We may take three data(m = 3)from the final point(t = n)and calculate its correlation coefficient r0, then add another data of a new point and calculate again the coefficient r1. If |k0|>|r1|, then the beginning time of the interval is t = t*. Otherwise, m m + 1. Further search will have to be made until t = 1.By substituting R* obtained above into f(t,R), forecast can be made.Actual examples are calculated using the algorithm described in this paper and the results are all satisfactory.