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In order to discover the optimum process conditions and to supply basic data for process control, it is necessary to determine, at least approximately, the process lawη=f(ξ1…ξk;Θ1…Θp) ….(1)connecting a response η (such as yield of product) with levels of the variables ξ1…ξk(such as temperature, time, pressure, etc.),Θ1…Θp being unknown parameters.The problem is discussed of using an electronic digital computer for fitting the function eqn. (1), to a set of observed data,(a) when the functional form is unknown but can be locally represented by a multivariate polynomial, and(b) when the functional form is not known explicitly, but is thought to be the solution of s simultaneous differential equations.In case (b), starting with any guessed values of the parameters Θ1…Θp the electronic computer is caused to follow a series of trial values which result in progressively smaller discrepancies between observed and calculated values of η. The procedure provides the least-squares estimates of the parameters and their standard errors; it also gives a criterion from which the adequacy of the form of the assumed sets of differential equations may be judged.An example of the application of the method is described.
Box et al. (Sun,) studied this question.