To calculate the reduction in failure rate for operation at 50% voltage and 50% rated temperature, you would typically use the Arrhenius equation, which relates the failure rate of a component to the temperature at which it operates.
The Arrhenius equation is given by:
λ2 = λ1 * e^((Ea/R) * ((1/T2) - (1/T1)))
Where: λ1 is the initial failure rate at temperature T1. λ2 is the failure rate at temperature T2. Ea is the activation energy (a constant specific to the component/material). R is the gas constant (8.314 J/(mol·K)). T1 is the initial temperature (20 degrees Celsius in this case). T2 is the reduced temperature (50% of the rated temperature, which would be 10 degrees Celsius in this case).
Since the question also mentions a 50% voltage, it's important to note that voltage can affect the failure rate of some components, but the specific relationship depends on the type of component. The Arrhenius equation only considers temperature, so if voltage is a factor, additional information would be needed to calculate the reduction in failure rate accurately.
Without further information about the type of component and its voltage characteristics, it's not possible to provide a specific calculation for the reduction in failure rate based on voltage alone.