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Transistor Failure Rate Model

Thyristor Failure Rate Model

Example Calculation

References

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The failure rate equation for transistors [Reference 7] is:

where,

λ_P = Predicted failure rate, failures per million calendar hours
π_G = Reliability growth failure rate multiplier:

β = Growth constant. Function of transistor type (see Table 1)

λ_OB = Base failure rate, operating. Function of transistor type (see Table 1)
π_DCO = Failure rate multiplier for duty cycle, operating:

DC_1op = Constant. Function of transistor type (see Table 1)

π_TO = Failure rate multiplier for temperature, operating:

Ea_op = Activation energy, operating. Function of transistor type (see Table 1).
T_R = The junction temperature rise above the ambient operating temperature (T_AO). The junction temperature is therefore T_AO + T_R. TR can be determined in several ways:

T_Rdefault = Default temperature rise (see Table 1)

T_R = Actual (measured) temperature rise, if known

T_R = Θ_JA * P
where Θ_JA is the junction-to-ambient thermal impedance and P is the power dissipated by the transistor

T_R = Θ_JC * P
where Θ_JC is the junction-to-case thermal impedance and P is the power dissipated by the transistor

If this option is used, then T_AO should be replaced by T_C, the component case temperature, in the equation for π_TO

T_R = ∆T * S
where ∆T is the difference in junction temperature between no power dissipated and full rated power dissipated, and S is the stress ratio and is equal to the actual forward current divided by the rated forward current

For Bipolar transistors:

For all other transistor types, π_S = 1
Default V_S = Constant. Function of transistor type (see Table 1)

λ_EB = Base failure rate, environmental (see Table 1)
π_DCN = Failure rate multiplier, duty cycle – nonoperating:

DC_1nonop = Constant. Function of transistor type (see Table 1)

π_TE = Failure rate multiplier, temperature – humidity:

Ea_nonop = Activation energy, nonoperating. Function of transistor type (see Table 1)

λ_TCB = Base failure rate, temperature cycling (see Table 1)
π_CR = Failure rate multiplier, cycling rate:

CR₁ = Constant. Function of transistor type (see Table 1)

π_DT = Failure rate multiplier, delta temperature:

DT₁ = Constant. Function of transistor type (see Table 1)

λ_SJB = Base failure rate, solder joint (see Table 1)
π_SJDT = Failure rate multiplier, solder joint delta temperature:

λ_IND = Failure rate, electrical overstress (see Table 1)

NOTE: Environment-type and equipment-dependent default values for DC, TAO, TAE and CR were previously presented in Reference 1, where,

DC = Duty cycle (the percent of calendar time that the system in which the component is operating is in an operational state)

T_AO= Ambient temperature, operating (in degrees C)

T_AE = Ambient temperature, nonoperating (in degrees C)

CR = Cycling rate (the number of power cycles per year to which the system is exposed). In this case, it is assumed that the system transitions from a nonoperating environment to an operating environment at the same time that the power is applied.

The failure rate equation for thyristors [Reference 7] is:

λ_P = Predicted failure rate, failures per million calendar hours

π_G = Reliability growth failure rate multiplier

β = Growth constant. Function of thyristor type (see Table 2).

λ_OB = Base failure rate, operating (see Table 2)

π_DCO = Failure rate multiplier for duty cycle, operating

DC_1op = Constant. Function of thyristor type (see Table 2)

π_TO = Failure rate multiplier for temperature, operating

Ea_op = Activation energy, operating. Function of thyristor type (see Table 2).
T_R = The junction temperature rise above the ambient operating temperature (T_AO). The junction temperature is, therefore, T_AO+T_R.

T_R can be calculated in several ways:

T_Rdefault = Default temperature rise (see Table 2)

T_R = Actual temperature rise, if known

T_R = Θ_JA * P
where Θ_JA is the junction-to-ambient thermal impedance and P is the power dissipated by the transistor

T_R = Θ_JC * P
where ΘJC is the junction-to-case thermal impedance and P is the power dissipated by the transistor

If this option is used, then TAO should be replaced by TC, the component case temperature, in the equation for πTO

T_R = ∆T * S
where ∆T is the difference in junction temperature between no power dissipated and full rated power dissipated, and S is the stress ratio and is equal to the actual forward current divided by the rated forward current

π_S = Failure rate multiplier stress

Default VS = Constant. Function of thyristor type (see Table 2)

λ_EB = Base failure rate, environmental (see Table 2)
π_DCN = Failure rate multiplier, duty cycle – nonoperating

DC_1nonop = Constant. Function of thyristor type (see Table 2)
π_TE = Failure rate multiplier, temperature – environment

Ea_nonop = Activation energy, nonoperating. Function of thyristor type (see Table 2)
λ_TCB = Base failure rate, temperature cycling (see Table 2)
π_CR = Failure rate multiplier, cycling rate

CR₁ = Constant. Function of thyristor type (see Table 2)

π_DT = Failure rate multiplier, delta temperature

DT₁ = Constant. Function of thyristor type (see Table 2)

λ_SJB = Base failure rate, solder joint (see Table 2)
π_SJDT = Failure rate multiplier, solder joint delta temperature:

λ_IND = Failure rate, induced (see Table 2)

As with the Transistor model, the environment-type and equipment-dependent default values for DC, TAO, TAE and CR were previously presented in Reference 1.

What is the predicted failure rate of a field effect, high frequency microwave transistor manufactured in 2006. The transistor operates in a “Ground, Mobile, Heavy-wheeled” vehicle with an assumed operating temperature of 55°C, a dormant temperature of 14°C and a relative humidity of 40%. The temperature rise of the FET is unknown. The operating profile of the equipment is typical of military ground equipment, with a duty cycle of 45% and a cycling rate of 263 cycles per year.

The failure rate equation for a transistor [Reference 7] is:

where,

π_G = e^{(-Β (Y-1993) )} = 0.005736
where β = 0.397 (from Table 1) and Y = 2006 (given)

λ_OB = 0.001049 (from Table 1)

π_DCO = DC / DC_1op = 1.966

DC = 0.45 (given as 45%)
DC_1op = 0.23 (from Table 1)

Ea_op = 0.20 (from Table 1)
T_AO = 55 (given)
T_Rdefault = 60 (from Table 1)

π_S = 1 (Field effect transistor)

λ_EB = 0.0004674 (from Table 1)

DC = 0.45 (given as 45%)
DC_1nonop = 0.77 (from Table 1)

Ea_nonop = 0.30 (from Table 1)
T_AE = 14 (given)

λ_TCB = 0.000225 (from Table 1)

CR = 263 (given)
CR₁ = 754.38 (from Table 1)

T_AO = 55 (given)
T_Rdefault = 60 (from Table 1)
T_AE = 14 (given)
DT₁ = 80 (from Table 1)

λ_SJB = 0.0015 (see Table 1)

π_SJDT = Failure rate multiplier, solder joint delta temperature:

T_AO = 55 (given)
T_Rdefault = 60 (from Table 1)
T_AE = 14 (given)

λ_IND = 0.04541 (from Table 1)

λ_p = (0.005736)((0.001049)(1.966)(6.090)(1)+(0.0004674)(0.7143)
(0.6390)+(0.000225)(0.3486)(1.594))+0.0015)(6.540)+(0.04541)

λp = 0.05529 f/10⁶ calendar hours

1. "An Introduction to the RIAC 217PlusTM Component Failure Rate Models", Journal of the Reliability Information Analysis Center, First Quarter 2007, available for PDF download from the RIAC at http://theRIAC.org


2. "The 217PlusTM Capacitor and Diode Failure Rate Models", Journal of the Reliability Information Analysis Center, Second Quarter 2007, available for PDF download from the RIAC at http://theRIAC.org


3. "The 217PlusTM Integrated Circuit and Inductor Failure Rate Models", Journal of the Reliability Information Analysis Center, Third Quarter 2007, available for PDF download from the RIAC at http://theRIAC.org


4. "The 217PlusTM Transformer and Optoelectronic Device Failure Rate Models", Journal of the Reliability Information Analysis Center, Fourth Quarter 2007, available for PDF download from the RIAC at http://theRIAC.org


5. "The 217PlusTM Switch and Relay Failure Rate Models", Journal of the Reliability Information Analysis Center, First Quarter 2008, available for PDF download from the RIAC at http://theRIAC.org


6. "The 217PlusTM Connector and Resistor Failure Rate Models", Journal of the Reliability Information Analysis Center, Second Quarter 2008, available for PDF download from the RIAC at http://theRIAC.org


7. Denson, W.K., "Handbook of 217PlusTM Reliability Prediction Models", Reliability Information Analysis Center (RIAC), 26 May 2006, ISBN 1-933904-02-X


8. "An Overview of the 217PlusTM System Reliability Assessment Methodology", Journal of the Reliability Information Analysis Center, Fourth Quarter 2006, available for PDF download from the RIAC at http://theRIAC.org