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Modeling and inferring about the process using growth models are the problems of enormous practical importance. Growth behavior of melting point (MP) during hydrogenation is found to be nonlinear. The purpose of this paper is to propose a control chart based method for on-line detection of a growth process becoming dead.

The nonlinear growth kinetics of MP during hydrogenation is modeled as a random walk with drift. In earlier work, the random walk model is developed based on a linear approximation and the control chart is constructed based on this approximate model. Here, an alternative model that does not make use of any such approximation is proposed. The variable drift component of the random walk is estimated following an innovative method of instrumental variable estimation. The model thus obtained is then used to construct a new control chart.

It is shown that both the control charts are able to detect dead batches satisfactorily, but the new chart is superior to the earlier one.

The authors are not aware of any relevant literature which provides an implementable and practitioner friendly approach to model the usually cumbersome variance function using signal-to-noise ratio and then use the same for estimating the parameters of a nonlinear dynamic growth model.