# Process Performance Maximization through Input Parameters Optimization using Taylor Series Expectation Approximation

###### Process Performance Maximization through Input Parameters Optimization using Taylor Series Expectation Approximation

**Abstract**

In several industrial settings or manufacturing units the process output is expressed as a function of several inputs and such relationships can be expressed in the form of the equation based on the prior data or known truth. It is desirable in such a setting that the output is within a specified threshold for acceptance of the quality of the product. It is not always possible to operate the industrial plant under several settings and then evaluate the one that maximizes the performance. Besides such experiments/tests can be expensive as well as time consuming. Given that the output-input relationship in the form of an equation and that the probability distribution of the inputs is known from the prior data the process performance at the current setting can be evaluated by randomly sampling inputs as per the input distributions and then checking the proportion of samples for which the output values are outside the specified threshold. If the process performance is not satisfactory there are generally two ways that one can optimize the performance. One can i) optimize the input parameters mean/mode, etc. keeping the variance of the input distributions constant (or/and) ii) optimize the variances of the inputs keeping the other parameters of the distribution constant. Generally, in such settings controlling the variances of the inputs is often difficult and harder to implement as opposed to varying the mean or other parameters that don’t influence the variances. This paper attempts to illustrate an efficient technique to find the best mean of the input probability distributions (keeping the input variances, skewness and kurtosis constant) that maximize or minimize the output mean so that the proportion of output beyond the threshold is minimized.

** The entire paper can be located in the link - **