Ways other than the trapezoidal rule for F calc

Please do not provide commercial information with your data.

 

An interesting post and a question that I have never heard from a student. I sincerely hope that you are not trying to find a way out of a production problem; being able to sleep at night is important.

 

The trapezoidal rule is a commonly used method for estimating the area under the lethality -time graph using simple numerical integration. Generally it gives an acceptable result. This is dependant upon an acceptable number of data points and the use of a constant and small delta time value e.g. 1-5 minutes; smaller is better.

 

However there are other more accurate ways of obtaining the area under a curve, Simpson's rule and Romberg integration are probably the best known. Of the three methods, Romberg integration gives the most accurate result but Simpson's rule (there are 2 actually) is generally more commonly used.

 

The differences in the F value calculated by the three methods are often too small to be of any practical significance in food processing;the errors inherent in the trapezoidal rule are small compared with other errors involved in thermal processing e.g.  temperature measurement. When one considers how easy it is to use the trapezoidal rule it is easy to understand why it has become so widely used. However on occasions there can be significant differences.

 

It is very easy to set up a spreadsheet to calculate F values using the three methods.