This paper describes, and gives a mathematical analysis of, the performance of two makes of CRT bleed resistors which exhibit markedly different characteristics under heat soak conditions. By examining the observed resistance changes with temperature, and relating these to the Arrhenius equation, the reaction activation energies can be determined. Further analysis of the power consumption characteristics of the resistors leads to the establishment of resistance‐time curves for both makes of resistor. These indicate very different conclusions than might otherwise have been drawn from initial test data. Finally the Monte Carlo' simulation technique is used to determine the most likely survival characteristics in a field situation, and a quantitative assessment of the reliability of CRTs using these bleed resistors is given. The construction of the resistor body is common to both makes and comprises a resistor substrate enclosed within an overcoat which is in turn encapsulated in epoxy. One make (type A) is a glass thick film structure, whereas the other is a polymer thick film system. Copyright © 1986 John Wiley & Sons, Ltd.