Rationality of alarm systems enormously impacts safety and economic performances of process plants, which definitely demands for process alarm threshold optimization. In this work, first, we analyze the assignable causes of missed alarms and false alarms from the probability theory perspectives before formulating corresponding calculation metrics based on Bayesian Inference. Then, we minimize missed alarm probability (MAP) and false alarm probability (FAP) in a multidimensional space, where the kernel density estimation method is invoked to estimate joint probability density functions using process historical data. Mathematical models associated with multivariable process alarm threshold optimization are established on the basis of density functions, and gradient descent algorithms are employed to achieve advisable alarm thresholds. An industrial application shows that this approach effectively reduces MAP of the plant, as well as lowers FAP to a relatively reasonable level. (c) 2014 American Institute of Chemical Engineers