Abstract: The purpose of the paper is to estimate the US small
wind turbines market potential and forecast the small wind turbines
sales in the US. The forecasting method is based on the application of
the Bass model and the generalized Bass model of innovations
diffusion under replacement purchases. In the work an exponential
distribution is used for modeling of replacement purchases. Only one
parameter of such distribution is determined by average lifetime of
small wind turbines. The identification of the model parameters is
based on nonlinear regression analysis on the basis of the annual
sales statistics which has been published by the American Wind
Energy Association (AWEA) since 2001 up to 2012. The estimation
of the US average market potential of small wind turbines (for
adoption purchases) without account of price changes is 57080
(confidence interval from 49294 to 64866 at P = 0.95) under average
lifetime of wind turbines 15 years, and 62402 (confidence interval
from 54154 to 70648 at P = 0.95) under average lifetime of wind
turbines 20 years. In the first case the explained variance is 90,7%,
while in the second - 91,8%. The effect of the wind turbines price
changes on their sales was estimated using generalized Bass model.
This required a price forecast. To do this, the polynomial regression
function, which is based on the Berkeley Lab statistics, was used. The
estimation of the US average market potential of small wind turbines
(for adoption purchases) in that case is 42542 (confidence interval
from 32863 to 52221 at P = 0.95) under average lifetime of wind
turbines 15 years, and 47426 (confidence interval from 36092 to
58760 at P = 0.95) under average lifetime of wind turbines 20 years.
In the first case the explained variance is 95,3%, while in the second
– 95,3%.
Abstract: Sometime it is difficult to determine the exact reliability for complex systems in analytical procedures. Approximate solution of this problem can be provided through discretization of random variables. In this paper we describe the usefulness of discretization of a random variable using the reversed hazard rate function of its continuous version. Discretization of the exponential distribution has been demonstrated. Applications of this approach have also been cited. Numerical calculations indicate that the proposed approach gives very good approximation of reliability of complex systems under stress-strength set-up. The performance of the proposed approach is better than the existing discrete concentration method of discretization. This approach is conceptually simple, handles analytic intractability and reduces computational time. The approach can be applied in manufacturing industries for producing high-reliable items.