with absolute certainty thus the ideal control scheme is a step function referring now to the prior art scheme and the embodiment 200 the embodiment 200 is generally closer to the ideal scheme than the prior art scheme for example when the true percentage of the bed greater than 500 degrees celsius is one half percent the probability that the prior art scheme will falsely indicate that the maximum fraction has been exceeded is about 45 as compared to 10 for the embodiment 200 the exception in the one to one and one half percent range where the prior art scheme enjoys an advantage in accuracy as compared to the embodiment 200 is not significant due to generosity in safety factors the embodiment 200 significantly reduces risk of production and sales loss which occurs when the true fraction of the bed is less than the maximum fraction but the prior art scheme falsely indicates otherwise conversely the embodiment 200 provides greater protection against unknowingly operating the reactor with an excessive fraction of the bed above the upper temperature limit fig2 assumes 108 thermocouples are present as the number of thermocouples increases the embodiment 200 will be closer to the ideal scheme fig3 illustrates another comparison between the prior art hot spot scheme and a scheme 200 according to an embodiment of the present invention as with fig2 these curves were created by a monte carlo simulation of a maleic anhydride reactor having 31 000 to 35 000 tubes and 108 thermocouples in the catalyst bed and having a maximum temperature limit of 500 degrees celsius and a maximum fraction of one percent the actual fraction of the.