Failure mode:
Aluminum electrolytic capacitors show various failure modes in different applications. (See Table 1.)

Life of Aluminum Electrolytic Capacitors
The life of aluminum electrolytic capacitor is largely dependent on environmental and electrical factors. Environmental factors include temperature, humidity, atmospheric pressure and vibration. Electrical factors include operating voltage, ripple current and charge-discharge duty cycles. The factor of temperature (ambient temperature and internal heating due to ripple current) is most critical to the life of aluminum electrolytic capacitors.
General formula to estimate lifetime:
The lifetime of non-solid aluminum electrolytic capacitors is generally expressed by using three elements, representing the effects of ambient temperature, applying voltage and ripple current, which is shown by the following equation. LX = LO * KTemp * Kvoltage * Kripple
Where:
LX = Lifetime of capacitor to be estimated
LO = Base lifetime of capacitor
Ktemp = Ambient temperature acceleration term
Kvoltage = Voltage acceleration term
Kripple = Ripple current acceleration term
Ktemp (Effects of ambient temperature on life):
Because an aluminum electrolytic capacitor is essentially an electrochemical component, increased temperatures accelerate the chemical reaction producing gas within the capacitor which is diffused through the end seal, and consequently accelerates a gradual decrease in capacitance and a gradual increase in tanδ and ESR. The following equation has been experimentally found to express the relationship between the temperature acceleration factor and the deterioration of the capacitor. LX = LO * KTemp = LO * B(TO-TX)/10 KTemp = B(TO-TX)/10
Where:
LX = Lifetime (hour) of capacitor to be estimated
LO = Base lifetime (hour) of capacitor
TO = Maximum rated category temperature(℃) of
TX = Actual ambient temperature (℃) of capacitor
B = Temperature acceleration factor (≈2)
Capacitor shown in catalog This equation is similar to Arrhenius' equation that expresses a relationship between chemical reaction rates and temperature, and called Arrhenius' rule of aluminum electrolytic capacitors. The temperature acceleration factor (B) is approximately 2 over an ambient temperature range (TX) from 40℃ to the maximum rated category temperature of each capacitor. It means that the lifetime is approximately halved with every 10℃ rise in ambient temperature and can be extended by using the capacitors at lower temperatures. For an ambient temperature range (TX) of 20℃ to 40℃, the factor B will be close to 2 and the lifetime will actually be extended. However, operating and surrounding conditions, especially the operating conditions influence ambient temperatures mutually. The ambient temperature in this range will be very changeable; therefore, lifetime estimation under 40℃ should use 40 as TX.