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Abstract
Parvin and Grammas defined the technical progress as a learning process and examined this view in the context of the theory of learning in psychology. They developed interesting models for the production of a service or goods where man and machine are input factors. In particular, they offered a mathematical model in which they assumed that an operator makes an error changes from trial to trial. The details of some interesting results which lead to the generalized of the Stirling numbers of the first and second kind which presented in several authors. Also some probability distributions are presented.
The main objective of this thesis is to find the generalization of Bernoulli learning models and derive some applications.