pp 44-55 (Vol 12 2019)

A. Wee and
A. Nocon
*

Mathematics and Statistics Department, De La Salle University, Manila, Philippines

Corresponding Author: ederlina.nocon@dlsu.edu.ph

ABSTRACT

The mathematical model called the process-based strategy (or PBS) model describes a situation wherein a particular end goal is obtained by undergoing an n-step process. As this describes some practical applications in real-life situations, it is of great interest to focus on other relevant and valid scenarios that treat the process as an iterative model. In this research study, we give an insightful extension of the results found in the paper “Success Probability of an n-Step Process with n Independent Step Probabilities.” More specifically, we extend the results of the paper by showing new applications of the PBS model pertaining to the concept of saturations as introduced in the paper. We consider various exposure scenarios and introduce the concept of prime agents acting as producers of new agents out of the success cases, which in turn also become catalysts for the succeeding cycles. In this sense, the PBS model becomes iterative. The interest is shifted to determining the number of prime agents that each cycle produces. Also discussed in this paper is the consideration of exposure scenarios where attrition is present. Lastly, the concept of critical points is also discussed, which examines conditions that determine whether the number of prime agents in the iterative PBS model will exponentially increase, remain constant, or be reduced to zero. It is perceived that the iterative PBS model can describe real-life situations such as multilevel marketing tactics and personnel training and development with the aim of using it for practical purpose of optimizing the results of such schemes.