ABSTRACT
A chemical reactor has 1250 sections and it is possible to calculate a theoretical temperature for each section. These have a distribution across sections with mean 452 °C and standard deviation 22 °C; the distribution is closely approximated by a normal distribution in the range 390–520 °C. For a variety of reasons, measured temperatures depart from the theoretical ones, the discrepancies being partly random and partly systematic. The temperature is measured in 20 sections. Special interest attaches to the number of channels in the reactor with 'true' temperature above 490 °C. The theoretical temperatures tTH are in principle known for the whole population and are the result of solving the appropriate partial differential equations for an idealized model of the reactor. The 'true' temperatures depart from the theoretical temperatures for a variety of reasons, partly random, partly systematic.
