Adaptive measurement control for calorimetric assay

The performance of a calorimeter is usually evaluated by constructing a Shewhart control chart of its measurement errors for a collection of reference standards. However, Shewhart control charts were developed in a manufacturing setting where observations occur in batches. Additionally, the Shewhart control chart expects the variance of the charted variable to be known or at least well estimated from previous experimentation. For calorimetric assay, observations are collected singly in a time sequence with a (possibly) changing mean, and extensive experimentation to calculate the variance of the measurement errors is seldom feasible. These facts pose problems in constructing a control chart. In this paper, the authors propose using the mean squared successive difference to estimate the variance of measurement errors based solely on prior observations. This procedure reduces or eliminates estimation bias due to a changing mean. However, the use of this estimator requires an adjustment to the definition of the alarm and warning limits for the Shewhart control chart. The authors propose adjusted limits based on an approximate Student`s t-distribution for the measurement errors and discuss the limitations of this approximation. Suggestions for the practical implementation of this method are provided also.