A method of controlling a temperature of a chemical reaction, comprising: injecting a reactant stream into a reactor and through a catalyst bed of the reactor, the reactant stream comprising a hydrocarbon and oxygen, thereby causing an exothermic chemical reaction; circulating a coolant through the reactor, thereby removing heat from the catalyst bed; measuring temperature at a plurality of locations in the catalyst bed; and calculating a fraction of the catalyst bed greater than a predetermined maximum temperature limit using a probability distribution generated using the temperature measurements wherein calculating the fraction comprises: subtracting a temperature of the catalyst bed adjacent an inlet of the reactor or a control temperature of the coolant from each of the temperature measurements, thereby obtaining temperature differences, and subtracting a temperature of the catalyst bed adjacent an inlet of the reactor or a temperature of the coolant from the maximum temperature limit, thereby obtaining a maximum temperature limit difference; wherein: calculating the fraction further comprises calculating a logarithm of each temperature difference, thereby obtaining log temperature differences, and the probability distribution is generated using the log temperature differences; wherein: calculating the fraction further comprises calculating an average and a standard deviation of the log temperature differences, and the probability distribution is generated using the average and the standard deviation of the log temperature differences; wherein calculating the fraction further comprises calculating an integral of the lognormal probability distribution from the maximum temperature limit difference to infinity and;comparing the calculated fraction to a predetermined maximum fraction; and taking remedial action if the calculated fraction exceeds the maximum fraction. injecting a reactant stream into a reactor and through a catalyst bed of the reactor, the reactant stream comprising a hydrocarbon and oxygen, thereby causing an exothermic chemical reaction; circulating a coolant through the reactor, thereby removing heat from the catalyst bed; measuring temperature at a plurality of locations in the catalyst bed; and calculating a fraction of the catalyst bed greater than a predetermined maximum temperature limit using a probability distribution generated using the temperature measurements subtracting a temperature of the catalyst bed adjacent an inlet of the reactor or a control temperature of the coolant from each of the temperature measurements, thereby obtaining temperature differences, and subtracting a temperature of the catalyst bed adjacent an inlet of the reactor or a temperature of the coolant from the maximum temperature limit, thereby obtaining a maximum temperature limit difference; calculating the fraction further comprises calculating a logarithm of each temperature difference, thereby obtaining log temperature differences, and the probability distribution is generated using the log temperature differences; calculating the fraction further comprises calculating an average and a standard deviation of the log temperature differences, and the probability distribution is generated using the average and the standard deviation of the log temperature differences; wherein calculating the fraction further comprises calculating an integral of the lognormal probability distribution from the maximum temperature limit difference to infinity and;comparing the calculated fraction to a predetermined maximum fraction; and taking remedial action if the calculated fraction exceeds the maximum fraction.