The instrumental transient

Melting is an endothermic process since the sample absorbs energy in order to melt. Integrating the peak area gives the heat of fusion A Hf and this can be a simple process but often requires careful choice of cursor positions for the integration. 

Many materials do not contain single crystals but a range of crystals of varying stability that melt over a broad temperature range. Typical of these are polymeric systems, including 

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Alternative models may be developed to include additional covariates which are not measured with error, e.g., X = f(R,Z). The classical model is used when an attempt to measure x is made but cannot be done so due to various measurement errors. An example of this is the measurement of blood pressure. There is only one true blood pressure reading for a subject at a particular point in time, but due to minor calibration errors in the instrument, transient increases in blood pressure due to diet, etc., possible recording errors and reading errors by the nurse, etc., blood pressure is a composite variable that can vary substantially both within and between days. In this case it makes sense to try and model the observed blood pressure using Eq. (2.84). Under this model, the expected value of X is x. In regression calibration problems, the focus is on the distribution of x given X. For purposes herein, the focus will be on the classical error model. The reader is referred to Fuller (1987) and Carroll et al. (1995) for a more complete exposition of the problem. 

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