The RIAC 217Plus™ Transistor and Thyristor Failure Rate Models

In a previous edition of the RIAC Journal [Reference 1], we provided a high-level introduction to the 217Plus™ component failure rate prediction models, and in the last five editions we presented the 217Plus™ capacitor and diode failure rate models [Reference 2], the integrated circuit and inductor failure rate models [Reference 3], the transformer and optoelectronic device models [Reference 4], the switch and relay models [Reference 5] and the connector and resistor models [Reference 6].

In this edition of the Journal, we present the Transistor and Thyristor component models in their entirety. A brief example will be provided at the end of the article.

217Plus™ Transistor Failure Rate Model

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

where,

λP = Predicted failure rate, failures per million calendar hours
πG = Reliability growth failure rate multiplier:

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

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

DC1op = Constant. Function of transistor type (see Table 1)

πTO = Failure rate multiplier for temperature, operating:

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

TRdefault = Default temperature rise (see Table 1)

TR = Actual (measured) temperature rise, if known

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

TR = ΘJC * 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

TR = ∆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

πS = Failure rate multiplier stress

For Bipolar transistors:

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

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

DC1nonop = Constant. Function of transistor type (see Table 1)

πTE = Failure rate multiplier, temperature – humidity:

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

λTCB = Base failure rate, temperature cycling (see Table 1)
πCR = Failure rate multiplier, cycling rate:

πCR = CR / CR1

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

πDT = Failure rate multiplier, delta temperature:

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

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

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

Table 1: Transistor Parameters

Part Type

λOB

λEB

λTCB

λIND

λSJB

β

Bipolar,
Germanium

0.001586

0.0007359

0.000965

0.02954

.0015

0.281

Bipolar, High Frequency,
Microwave

0.000106

0.0005206

0.000054

0.003106

.0015

0.269

Bipolar, Low Frequency

0.000235

0.0001657

0.00016

0.008899

.0015

0.281

Bipolar, Multiple

0.000621

0.0004759

0.000648

0.00754

.0015

0.281

Field Effect, High
Frequency, Microwave

0.001049

0.0004674

0.000225

0.04541

.0015

0.397

Field Effect, Low Frequency,
Silicon

0.000195

0.000333

0.000255

0.01099

.0015

0.397

Field Effect, Multiple

0.00022

0.0004209

0.00076

0.01618

.0015

0.269

Field Effect, Unijunction

0.000143

0.0002657

0.000023

0.002462

.0015

0.397

General

0.000078

0.00002607

0.000019

0.03433

.0015

0.397

Part Type

DC1op

Eaop

TRdefault

VSdefault

DC1nonop

Eanonop

CR1

DT1

Bipolar,
Germanium

0.23

0.2

60

.5

0.77

0.3

754.38

80

Bipolar, High Frequency,
Microwave

0.23

0.2

60

.5

0.77

0.3

754.38

80

Bipolar, Low Frequency

0.23

0.2

60

.5

0.77

0.3

754.38

80

Bipolar, Multiple

0.23

0.2

60

.5

0.77

0.3

754.38

80

Field Effect, High
Frequency, Microwave

0.23

0.2

60

N/A

0.77

0.3

754.38

80

Field Effect, Low Frequency,
Silicon

0.23

0.2

60

N/A

0.77

0.3

754.38

80

Field Effect, Multiple

0.23

0.2

60

N/A

0.77

0.3

754.38

80

Field Effect, Unijunction

0.23

0.2

60

N/A

0.77

0.3

754.38

80

General

0.23

0.2

60

.5

0.77

0.3

754.38

80

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)

TAO= Ambient temperature, operating (in degrees C)

TAE = 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.

217Plus™ Thyristor Failure Rate Model

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

λP = Predicted failure rate, failures per million calendar hours

πG = Reliability growth failure rate multiplier

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

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

πDCO = Failure rate multiplier for duty cycle, operating

DC1op = Constant. Function of thyristor type (see Table 2)

πTO = Failure rate multiplier for temperature, operating

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

TR can be calculated in several ways:

TRdefault = Default temperature rise (see Table 2)

TR = Actual temperature rise, if known

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

TR = ΘJC * 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

TR = ∆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

πS = Failure rate multiplier stress

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

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

DC1nonop = Constant. Function of thyristor type (see Table 2)
πTE = Failure rate multiplier, temperature – environment

Eanonop = Activation energy, nonoperating. Function of thyristor type (see Table 2)
λTCB = Base failure rate, temperature cycling (see Table 2)
πCR = Failure rate multiplier, cycling rate

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

πDT = Failure rate multiplier, delta temperature

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

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

λIND = 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.

Table 1: Transistor Parameters

Part Type

lOB

lEB

lTCB

lIND

lSJB

β

General

0.000393

0.004602

0.001756

0.01219

.00087

0.2

SCR

0.000324

0.001011

0.00203

0.02001

.00087

0.2

Triac

0.000576

0.007286

0.00199

0.01636

.00087

0.2

Part Type

DC1op

Eaop

TRdefault

VSdefault

DC1nonop

Eanonop

CR1

DT1

General

0.26

0.4

60

.37

0.74

0.4

508.77

73

SCR

0.26

0.4

60

.37

0.74

0.4

508.77

73

Triac

0.26

0.4

60

.37

0.74

0.4

508.77

73

Example Calculation

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,

πG = e(-Β (Y-1993) ) = 0.005736
where β = 0.397 (from Table 1) and Y = 2006 (given)

λOB = 0.001049 (from Table 1)

πDCO = DC / DC1op = 1.966

DC = 0.45 (given as 45%)
DC1op = 0.23 (from Table 1)

Eaop = 0.20 (from Table 1)
TAO = 55 (given)
TRdefault = 60 (from Table 1)

πS = 1 (Field effect transistor)

λEB = 0.0004674 (from Table 1)

DC = 0.45 (given as 45%)
DC1nonop = 0.77 (from Table 1)

Eanonop = 0.30 (from Table 1)
TAE = 14 (given)

λTCB = 0.000225 (from Table 1)

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

TAO = 55 (given)
TRdefault = 60 (from Table 1)
TAE = 14 (given)
DT1 = 80 (from Table 1)

λSJB = 0.0015 (see Table 1)

πSJDT = Failure rate multiplier, solder joint delta temperature:

TAO = 55 (given)
TRdefault = 60 (from Table 1)
TAE = 14 (given)

λIND = 0.04541 (from Table 1)

λp = (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

References:

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