To model a physical system, we used to presume that its observed output is a sum of a systematic component representing a mix of controllable factors and an error term representing the effect of the non-controllable factors. For the goal of fitting a function through a series of observations for output and several inputs, this implies that an "average" function is obtained through minimizing the residual sum of squares of the previous model using the ordinary least squares method. However, in order to express the best product obtainable from the input combination and analyze the inefficiency of the system, we propose in this paper an original approach that consists of the decomposition of the systematic component into two terms: one representing the model function and another, called inefficiency, due to the change of some intrinsic properties of the input and/or some bad settings of the controllable factors. In attempting to estimate the parameters of the model, a procedure based on the maximization of the likelihood function has been proposed. The inefficiency has been modeled by a non-stochastic multi-step inefficiency function and the number of gaps has been optimized through the Akaike's Information Criterion. The estimation procedure is illustrated with an empirical test in which the true position of the gap is correctly estimated and a study of accuracy is done.