Most of diffusion literature has the origin on Bass(1969). Over 300 research and application papers have been published under the issue of a diffusion or a new product growth model. See Mahajan et al.(1990).

In these researches, they have, seperatively or integratively, incorporated (1) repeat-purchasing, (2) competition, (3) exogenous market factors, and (4) marketing mix variables, into a diffusion model.

Heeler and Hustad(1980) and Kamakura and Balasubramanian(1987), showed the importance of replacement purchases within a diffusion framework. That is, this demand component contaminates forecasts when total sales data are used to generate long-term sales prediction based on a diffusion model.

If environmental conditions change, the impact of these changes on diffusion process must be reflected in modeling procedure. Furthermore, if we want to model brand sales growth, competitive phenomena of marketing mix variables should be considered.

The above four factors are integrated into the proposed model in this thesis with new product growth model. We present the model including a replacement demand and marketing mix variables for two firms introducing competing brands of a new durable product.

Thus, the proposed model is not completely different or new, in comparison to the previous models. However, it has been attempted to be as complete as possible in reflecting real situations. To attain this goal, numerous contributions from consumer behavior, advertising research, research on competition, reliability analyis, and stochastic optimal control theory, are utilized.

Nevertheless, it is thought that the current model still possess some limitations. It is desirable to address these four critics.

(1) It might be addressed about the complexity of the proposed model, at first. More than 10 variables must be estimated, by statistical procedures, as well as managerial judgements.

(2) This model can hardly be useful for a diagnostic purpose to test the possibility of market success of new product during the early stage of product life cycle.

(3) In proposed model, it is implicitly assumed exponential growth of total market size. Although the estimated values for this rate makes it approximately linear, this assumption should be refined to reflect exogenous market factors that can impact diffusion rate.

(4) Much laborious works are required to estimate parameters for the proposed model, and the significance or validity of statistically-determined parameters can hardly be evaluated. Furthermore, this procedures requires sufficient experiences and knowledge about managerially-determined variables. Frequently, absurd values for these variables severely deterioriates fittng results and sales forecasts.

Possible future research directions are

(1) to incorporate multi-ownership into the proposed model, the research by Chung and Park(1989) might give an insight to this approach,

(2) to develop a managerially-usable algorithm and packages based on Kalman filter method, and

(3) to make plausible assumptions and design mathematical representations of these assumptions,