MTBF-PoL Reliability Evaluation and Comparison Using Prediction Standard MIL-HDBK-217F vs. SN 29500 ^†

Abstract

In the design of military, automotive, medical, space, and professional equipment, it is essential to demonstrate that devices can operate for a specific duration with a given level of confidence. Reliability must be considered in the design process, which can involve component selection, component testing, and mitigation techniques such as redundancy and forward error correction (FEC). In modern DC–DC converters, a higher level of reliability is now a mandatory requirement—the ISO 26262, for example, acts as the guidance to provide the appropriate standardized requirements, processes and risk based approach, and it determines integrity levels (known as automotive safety integrity levels or ASILs). The purpose is to reduce risks caused by systematic and random failures to an appropriate level of acceptance. Since the release of MIL-HDBK-217F Notice 2 in 1995, newer standards for predicting failure rates have emerged in the electronic systems reliability market. These updated standards were introduced to address the limitations of the older standards, particularly in relation to advanced component technologies. Numerous studies have shown that the output capacitor bank is one of the most critical components concerning reliability. This work focuses on calculating the failure rates of an output capacitor bank and a MOSFET transistor pair used in a high-current, low-voltage buck converter. The failure rates are calculated using both the latest prediction standard, SN 29500, and the previous MIL-HDBK standard. This comparison serves as a valuable tool for selecting the output capacitor during the early stages of design. Both simulations and experimental setups were employed to measure the temperatures of the components. The SN 29500 standard is particularly beneficial for components operating in harsh environments, as it provides up-to-date failure rate data and stress models. The environmental conditions for the components were defined using a standard point of load (PoL) buck converter for both calculation methods. Results are compared by considering the impact of component temperature and by applying specific parameters such as reference and operating conditions. This kind of comparison is useful for circuit designers, especially in the field of Power electronics when the concept of designing with reliability in mind is adopted.

1. Introduction

This paper presents the comparative results of reliability calculation for a PoL converter’s output capacitor bank and is an extended version of an existing conference paper [1].

Modern power electronics need properly functioning DC–DC converters to ensure higher output quality, less energy consumption and longer lifespan. For example, reliability prediction in the automotive domain has significant implications for manufacturers, consumers, and the industry as a whole. This assures enhanced vehicle safety because predicting reliability helps identify potential failures early, reducing the risk of accidents caused by mechanical or electronic malfunctions. Additionally, it can lead to cost reductions through optimized maintenance schedules and reduce warranty costs by proactively addressing reliability concerns. Finally, reliability prediction ensures regulatory compliance in meeting stringent safety and reliability standards, which is crucial for automakers seeking to comply with industry regulations and thus avoid recalls. This paper is focused on the last requirement, analyzing the reliability of the equipment from a comparative point of view. The United States Navy’s failure rate prediction of electronic components standard, outlined in Military Handbook 217, published in 1965, has been widely accepted for decades in order to predict reliability on even industrial electronics and is still used today as a matter of priority because there have been no more updates after its latest version, MIL-HDBK-217F—Notice 2, was released in 1995 [2]. This standard includes formulae to account for environmental and usage conditions such as temperature, stress, fixed or mobile equipment, etc. In the initial stages of a design, these calculations are useful in determining the overall reliability of a design so as to compare it with the specified requirements and to determine which components are most significant in terms of system reliability so that design changes can be made if deemed necessary. Over time, this approach has been used but it does not accurately model the reliability because it does not take account a mission profile [3]. Therefore, the International Electrotechnical Commission (IEC) has provided a newer standard, named Technical Report (TR) 62380, which takes account of the temperature cycling for failure rate predictions by means of an annual mission profile [4]. As this standard has also not been updated with a data source for new device technologies, a newer standard is gaining attention for reliability engineers. This standard, which is the subject of our comparison, is named SN 29500, is from Siemens and had its latest release in 2013 [5]. Besides MIL-HDBK-217F, there are several other widely recognized reliability prediction standards, as follows:

• Telcordia SR-332 (formerly known as Bellcore)—This standard is commonly used in the telecommunications industry. It provides methods for predicting the reliability of electronic equipment, focusing on failure rates and mean time between failures (MTBF) calculations.
• 217Plus—Developed by the Reliability Information Analysis Center (RIAC), 217Plus is an updated and expanded version of MIL-HDBK-217. It incorporates additional data and methodologies to provide more accurate reliability predictions.
• ANSI/VITA 51.1—This standard is used primarily in the aerospace and defense industries. It provides guidelines for predicting the reliability of electronic systems and components, emphasizing the use of environmental and operational profiles.
• Chinese Standard GJB/z 299 [6]—This is the Chinese military standard for reliability prediction. It is similar to MIL-HDBK-217 but is tailored to the specific requirements and conditions of Chinese military applications.
• NPRD and EPRD databases—The Non-electronic Parts Reliability Data (NPRD) and Electronic Parts Reliability Data (EPRD) databases provide failure rate data for a wide range of components. These databases are often used in conjunction with other reliability prediction standards to enhance accuracy.

Since then, several other standards have been developed, especially for telecommunication systems [6,7,8,9,10,11]. These standards offer various methodologies and datasets to help predict the reliability of electronic and mechanical systems, each with its own strengths and applications.

None of the alternative proposed standards have managed to become well accepted, with all of them being criticized or defended. The reliability technologies and the methods for calculating their failure rates are subject to continuous development and thus to continuous change.

Ensuring that designs meet industry reliability standards and regulations is crucial. Reliability comparisons help in verifying that the designs comply with these standards, avoiding potential legal and regulatory issues.

The research gap and contributions of this work, as well as the existing limitations and the advancements of this paper, speak to the way in which the technical literature does not provide sufficient examples in this regard. This work presents, for the first time, a comparison between two standards used for reliability prediction, one being a well-known reference standard and the other a newer one, predominantly used in industry, especially in Europe. Additionally, calculating reliability using these two types of predictive standards is based on the use of data obtained from hands-on work, or, more precisely, by determining the temperature of the capsules of active devices and passive components using the method of infrared photography.

2. Brief Description of the Reliability Concept and the Metrics to Express It

What is the use of reliability predictions? Reliability predictions can be used to assess whether reliability goals e.g., MTBF can be reached; the identification of potential design weaknesses; the evaluation of alternative designs and life-cycle costs; the provision of data for system reliability and availability analysis; logistic support strategy planning; and to establish objectives for reliability tests [12,13].

What are the conditions that have a significant effect on reliability? Important factors affecting reliability include the following:

• Temperature stress
• Electrical and mechanical stress
• Environment
• Duty cycle
• Quality of components

Reliability is the ability of an item to perform a specific function under given conditions but in a specific period of time, often expressed by the failure rate λ:

R(t) = e^−λt

(1)

A more practical and commercial way to express reliability is mean time between failure (MTBF), which is the average length of time before the first failure appears and the item no longer being able to continue functioning in normal operation. This is expressed by the integral of (1), as follows:

$$\mathrm{MTBF}={\int }_0^{\infty }R\left(t\right)dt$$

(2)

a simpler form results in the following:

MTBF = 1/λ

(3)

at the moment of time t = 1/λ, we find the following:

R = 1/e = 0.367

(4)

where the mathematical mean of R(t) is the amount of time that should elapse until the first failure occurs, here signifying that 37% of the items within a large group will last as long as the MTBF number. Thus, λ signifies the intrinsic failure rate, excluding early failures and wear-out failures, which is assumed to be constant during the lifetime period, as shown in the bath tub curve (Figure 1) and expressed in [F/10⁶ h], i.e., failures per one million component hours or [FIT], i.e., failures in time or one failure per one billion component hours. The term failure in time (FIT) is defined as a failure rate of 1 per billion hours. A component having a failure rate of 1 FIT is equivalent to having an MTBF of 1 billion hours. Most components have failure rates measured in 100’s and 1000’s of FITs. For components such as transistors and ICs, the manufacturer will test a large number over a period of time to determine the failure rate. If 1000 components are tested for 1000 h, then that is considered to be equivalent to 1,000,000 h of test time. There are standard formulas that convert the number of failures in a given test time to the MTBF for a selected confidence level. For a system of components, one method of predicting the MTBF is to add the failure rates of each component and then take the reciprocal. Therefore, all of the standards provide a constant failure rate for a system’s components during its useful lifetime.

The bathtub model in reliability engineering describes the failure rate of a product over its lifecycle using a characteristic curve that resembles the shape of a bathtub. This model is widely used to understand and predict system failures, helping engineers design more reliable products. The bathtub curve consists of three distinct phases, as follows:

Early Failure (Infant Mortality) Phase: This phase occurs at the beginning of a product’s life. The failure rate is initially high due to manufacturing defects, poor material quality, or improper assembly. Over time, defective units are identified and removed, leading to a decrease in the failure rate. Burn-in testing, stress screening, and quality control measures help reduce early failures.

Random Failure (Useful Life) Phase: This is the longest phase, where the failure rate remains relatively constant. Failures occur randomly due to unforeseen external factors such as environmental conditions, accidental damage, or unpredictable component failures. Regular maintenance, redundancy in design, and robust quality assurance help minimize failures.

Wear-Out Failure Phase: As the product ages, its components degrade due to wear and tear, leading to an increase in the failure rate. Common causes include material fatigue, corrosion, and aging effects in electronic components. Preventive maintenance, component replacement, and design improvements act to extend the product’s lifespan. Applications of the bathtub model are as follows:

• Reliability Prediction: helps manufacturers estimate product lifespan and failure rates.
• Maintenance Planning: guides preventive maintenance schedules to reduce unexpected breakdowns.
• Quality Control: identifies weak points in production and improves manufacturing processes.
• Warranty and Cost Analysis: assists in setting warranty periods and optimizing repair costs.

The bathtub reliability model has a direct impact on product design decisions because it helps engineers anticipate failure rates and optimize durability at every stage of a product’s life cycle.

There are differences between observed, predicted and demonstrated MTBFs.

• Observed—the field failure experienced.
• Predicted—the estimated reliability based on reliability models and predefined conditions.
• Demonstrated—the statistical estimation based on life tests or accelerated reliability testing.

In this work only predicted reliability is undertaken.

3. Experiment, Materials and Methods

3.1. Workbench Phase

The experiment that is used to perform the comparison between the two reliability calculations based on the two mentioned standards has two stages. First, a workbench set-up was made with a converter made only with the two MOSFET transistors, for which a thermal scan was then made in IR with the aim of detecting the temperatures of the SMD-type power transistor capsules with the characteristics in

Table 1. Elected parameters for the converter under study.

Parameters of Convertor	Value
Rated output active power, Po	Max. 0.06 Ω × 25 Amp = 37.5 W
Input voltage, Vin	12 V DC with 5% tolerance
Output voltage, Vout	1.2 V DC ± 50 mV
Switching frequency, fsw	500 khz @ duty cycle = 7.65%
Inductor, L	250 nH/0.75 Ω, flat 1335, superflux
High side (control) MOSFET	IRF 6617, R(DS)on = 6.2 mΩ, Coss = 430 pF, Rth(J-C) = 20 °C/W [16]
Low side (synchro) MOSFET	IRF 6691, R(DS)on = 2.5 mΩ, Coss = 2070 pF Rth(J-C) = 1.4 °C/W [17]
Output capacitor bank, C	MLCC: 4 pcs. × 100 μF [18] HF through hole ceramic: 1 pcs. × 100 nF HF ceramic: 1 pcs. × 100 nF Polymer electrolytic: 2 pcs. × 470 μF [19]
Transient load current step	Current variation between: Idown = 5A, Iup = 25A
Ambient temperature	27 °C

. The table also shows the load level of the converter, the input and output voltages and the switching frequency. The scan results revealed a higher temperature for the low-side MOSFET transistor Q2. The temperatures obtained for the transistors shown in

Table 2. MOSFET technologies, role, type and detected temperature by IR scanning (see also Figure 2).

MOSFET Transistor	Capsule’s Temperature
Q1: High side (control) MOSFET IRF6617	40 °C
Q2: Low side (synchro) MOSFET IRF6691	49 °C

(see Figure 2) are then used in Section 4 to find the thermal stress factor needed to calculate the π_TMOSFET failure rate, which will later be useful in calculating the failure rate for each transistor of power—λ_MOSFET.

The junction temperature of the transistors will be calculated later on the basis of the capsule temperature and the thermal resistance specific to each transistor provided by the catalog.

Reliability prediction results for a MOSFET can have consequences on its parasitic capacitances and overall parameters: Degradation over time—reliability models often consider factors like temperature, voltage stress, and aging effects. These can cause shifts in parasitic capacitances due to changes in oxide thickness or charge trapping. Electrical performance variations—as reliability decreases, key MOSFET parameters such as threshold voltage, transconductance and leakage currents may drift, impacting overall circuit functionality. Failure mechanisms affecting capacitances—factors like hot carrier injection, bias temperature instability, and time-dependent dielectric breakdown can alter capacitances, potentially affecting switching speed and efficiency. Impact on Circuit Design—if reliability prediction results indicate significant degradation risks, designers may need to compensate with different biasing techniques or alternative transistor configurations.

3.2. Simulation PSPICE Phase

In the simulation phase of the experiment, in order to obtain the temperature of the capacitors, a PSPICE simulation of the converter circuit shown in Figure 3 was carried out, in which realistic SPICE models provided by the component manufacturers were used for the capacitors [18,19]. A U12–U15 switch configuration was used in the schematics to simulate a step-type load, thus subjecting the converter to a considerable stress level. All calculations and measurements were made in the continuous conduction mode (CCM) operating condition for the converter. This manner of getting the temperature of the capacitor capsules by simulation can deliver some advantage in removing the sources of some criticisms that are addressed at the IR thermal scanning, which is especially susceptible to re-flexion aluminum capacitor capsules.

Capacitors can be affected by several stress factors that influence their performance and longevity. Here follow some of the most common factors:

• Temperature—high temperatures can accelerate the degradation of the dielectric material inside capacitors, leading to reduced capacitance and potential failure.
• Voltage—Excessive voltage can cause dielectric breakdown, where the insulating material inside the capacitor fails, leading to short circuits.
• Ripple current—High ripple currents can cause internal heating, which can degrade the capacitor over time.
• Charge–discharge cycles—Frequent charging and discharging can wear out the dielectric material, reducing the capacitor’s effectiveness.
• Humidity—Moisture can penetrate non-hermetic capacitors, leading to corrosion and electrical leakage.

The ripple current is defined as an RMS value of the current flowing into and out of the capacitor each time the switch state turns ON and OFF. Further, the current ripple flows through the so-called ESR—the so-called equivalent series resistance within the capacitor—hence it will dissipate power, as given by the well-known formula for power, i.e.,

$$P_{dissipate}=I_{RMS}^2·ESR$$

(5)

Some combinations of n = 1/3 aluminum polymer can-type SMD electrolytic and m = 1/6 MLCC–SMD-type capacitors are considered in [18]. Each capacitor’s current ripple was measured with PSPICE at a maximum load current where the ripple yields the highest value. The results show that, if using more than four ceramic capacitors, the number of electrolytic capacitors does not influence the current ripple.

Among various choices, the optimized and specific calculation refers to an optimal combination of two electrolytic and four ceramic capacitors; one piece of HF ceramic capacitor through hole mounting (THD) was added in parallel for a better behavior at high frequencies. From [20], the simulation of the circuit gives a 2 A intensity of the ripple current. As a result, the temperature change of the GRM32ER60J107ME20 ceramic MLCC capacitors packaged in the SMD 1210 style, results in an ambient temperature T_amb = 27 °C

P_{dissipate by capacitor} = ΔT/R_TH

(6)

where R_TH represents the thermal resistance in °C per watt and ΔT is the allowable temperature rise of the capacitor under test i.e., the temperature difference between capacitor and ambient environment.

$$\begin{array}{ll}{\Delta T}_{MLCC}=R_{thermic-MLCC}·P& =R_{thermic}·I_{RMS}^2·{ESR}_{MLCC}\\ & =157{\displaystyle \frac{°\mathrm{C}}{\mathrm{w}}}·2^2·8\mathrm{m}\mathrm{\Omega }=5.024°\mathrm{C}\end{array}$$

so,

$$MLCC-temperature=T_{amb}+{\Delta T}_{MLCC}isabout32°\mathrm{C}$$

(7)

and the temperature change for the PCF0J472MCL6G aluminum polymer can-type SMD capacitors, packaged in an SMD V-style with a 6 A intensity of the current ripple, results in an ambient temperature T_amb = 27 °C

$$\begin{array}{ll}{\Delta T}_{polyme{r}_{cap}}& =R_{thermic-polymercap}·P\\ & =R_{thermic}‧I_{RMS}^2‧{ESR}_{polyme{r}_{cap}}\\ & =50{\displaystyle \frac{°\mathrm{C}}{\mathrm{w}}}‧6^2‧18\mathrm{m}\mathrm{\Omega }=32.4°\mathrm{C}\end{array}$$

so,

$$Polyme{r}_{cap}-temperature=T_{amb}+{\Delta T}_{polyme{r}_{cap}}isabout59°\mathrm{C}$$

(8)

As with the power transistors in the converter, we will use the temperatures obtained from the simulation to calculate the thermal stress factor necessary for the subsequent calculation of the failure rate of all three types of capacitors in the bank component of the output filter.

4. Reliability Prediction Using the Two Standards: The Methodology Behind It

4.1. Input Data for Calculus with MIL-HDBK-217 Standard

This paper continues the reliability calculus found in [1], which was focused on an output capacitor bank’s failure rate calculation according to MIL-HDBK-217 rev.2 cap.10.1—Capacitors; thus, we use the same schematic for the converter as in [1], where SPICE simulation was used for a multiple-constraint choice of capacitor bank (Figure 3) with the same parameters (Table 1). Part stress analysis prediction will be used further. This method is applicable when most of the design is completed and a detailed part list including part stresses is available. It can also be used during later design phases for reliability trade-offs vs. part selection and stresses.

4.1.1. Reliability Calculation for the MOSFETs

According to subchapter 6.9 (specification MIL-S-19500) from the MIL217 standard, we can calculate the failure rate for FET transistors using the following formula:

λ_{MOSFET-MIL-HDBK-217} = λ_base × π_T × π_Q × π_E

(9)

expressed in [F/10⁶ h] or [FIT].

For MOSFETs λ_base = 0.06, thermal stress factor

$${\mathsf{\pi }}_{\mathrm{T}}=e^{-[1925\times \left({\displaystyle \frac{1}{T_j+273}}-{\displaystyle \frac{1}{298}}\right)]}$$

(10)

where T_j = junction temperature (about 40 °C for _High-MOSFET and about 49 °C for λ_Low-MOSFET); quality factor π_Q = 1, for the Joint Army Navy (JAN) category (i.e., parts at the highest quality level of manufacturing); and environment factor π_E = 1, for ground benign (GB) environment. As a result, we obtain the following:

λ_{High-MOSFET-MIL-HDBK-217} = 0.06 × 1.4 × 1 × 1 = 0.084 [F/10⁶ h] or 84 [FIT]

(11)

λ_{Low-MOSFET-MIL-HDBK-217} = 0.06 × 1.6 × 1 × 1 = 0.096 [F/10⁶ h] or 96 [FIT]

(12)

The environment the device will see is a factor along with the type of packaging technology (ceramic vs. plastic or metal packaging).

4.1.2. Reliability Calculation for Capacitors

We show here the equation for failure rate of either electrolytic or ceramic capacitors stated by the above-mentioned standard:

λ_{capacitor-MIL-HDBK-21 7} = λ_base × π_T × π_Q × π_V × π_SR × π_E × π_C

(13)

Because our investigated DC–DC converter is a synchronous buck converter, with a series structure from a reliability calculation point of view, we apply the parts count approach. Thus, the overall system failure rate can be written as being the sum of all of the components’ failure rate.

$${\lambda }_{\mathrm{system}}={\sum }_{i=1}^N{\lambda }_i$$

(14)

Equation (14) illustrates the total failure rate [19,20], with N = total number and λ_i = the failure rate for the ith component.

The calculus in [1] has the following results for the three types of capacitors used in the converter (in accordance with Table 1):

λ_{polymer electrolytic capacitor-MIL-HDBK-217} = 0.015333864 [F/10⁶ h] or 15.334 [FIT]
(for two pieces in parallel)

(15)

λ_{MLCC capacitor-MIL-HDBK-217} = 0.52585624 [F/10⁶ h] or 525.9 [FIT]
(for four pieces in parallel)

(16)

λ_{ceramic HF capacitor-MIL-HDBK-217} = 0.007666932 [F/10⁶ h] or 7.666 FIT
(for only one piece)

(17)

and for the entire bank:

λ_{capacitor bank -MIL-HDBK-217} = the sum of the above three values
              = 0.548861812 [F/10⁶ h] or 548.9 [FIT]
(2 × polymer + 4 × MLCC + one ceramic HF through hole)

(18)

MTBF_{capacitor bank -MIL-HDBK-217} = 1821952

(19)

4.2. Input Data for Calculus with the SN 29500 Standard

To predict reliability using the SN 29500 standard [5], one must take the following steps:

• Define the system—start by outlining the system, sub-systems, and components. This can be undertaken using a reliability prediction tool that supports SN 29500.
• Gather data—collecting accurate data for each component. This includes environmental conditions, operational profiles, and stress factors.
• Apply failure rates—using the failure rate data provided in the SN 29500 standard. These data are specific to different types of electronic and electromechanical components.
• Calculate failure rates—input the data into the prediction tool. The tool will use the SN 29500 models to calculate the failure rates for each component and the overall system.
• Analyze results—review the calculation of failure rates to identify potential reliability issues and areas for improvement.

The SN 29500 standard, developed by Siemens, is used to estimate the failure rates of electronic components for reliability analysis. The key components of SN 29500 are as follows:

• Failure rate data—this provides expected failure rates for various types of electronic components, such as resistors, capacitors, and integrated circuits.
• Temperature factors—these are adjustments based on the operating temperature of the components.
• Voltage factors—these are adjustments based on the operating voltage.
• Current factors—these are adjustments based on the operating current.
• Stress factors—these are adjustments based on the percentage of time the component is under stress.

These factors help in calculating the failure in time (FIT) rate, which is crucial for assessing the reliability of components in safety-critical applications. SN 29500 failure rate calculation for MOSFETs are valid for the following [21]:

4.2.1. Reference Conditions

• Failure criteria, i.e., complete failures and changes of major parameters leading to failure in the majority of applications.
• Time interval, i.e., the operating interval of time, which needs to be greater than 1000 h.
• Operating voltage, i.e., about 50% of the maximum permissible voltage.
• Junction temperature θj, stated in Table 1, Table 2 and

  Table 3. Elected parameters for capacitors within output filter of converter under study.

  Capacitor Type	Temperature
  PCF0J471MCL6GS—Polymer electrolytic SMD can-type, ESR = 18 mΩ—from Nichicon	59 °C
  GRM32ER60J107ME20—MLCC, SMD-class II (X7R) ESR = 8 mΩ—from Murata	32 °C

  (page 4 from SN 29500-3: expected values for discrete semiconductors—Siemens Norm, Edition 2009-06)
• Description of environment, i.e., the same statement as in IEC 60721, where parts 3-1, 3-2, and 3-3 are valid.
• Operating mode, i.e., continuous duty under constant stress.

The expected values under reference conditions λ_ref, are found in the abovementioned tables from the standard and should be understood in terms of their operation under the above-stated reference conditions. From Table 1—failure rate for transistors from standard—we find that λ_ref (power-MOSFET) = 200 FIT for θj = 125 °C. The conversion from reference condition to operating conditions is as follows:

λ = λref × π_T

(20)

where π_T, is the temperature dependence factor:

π_T = [A‧e(E_a1‧z) + (1-A) × e(E_a2 × z)]/[A‧e(E_a1 × z_ref) +(1-A) × e(E_a2 × zr_ef)]

(21)

where

z = 11,605 × (1/T_Uref − 1/T₂) [1/eV]

(22)

and

z_ref = 11,605 × (1/T_Uref − 1/T₁) [1/eV]

(23)

where T_Uref = θ_Uref + 273 [°K], T₁ = θj,₁ + 273 [°K], T₂ = θj,2 + 273 [°K], and A, E_a1, E_a2, and θUref are constants, as found in a specific table within standard; θj_,1 represents the virtual (equivalent) junction temperature in [°C]; and θj_,2 is the actual junction temperature in [°C] obtained from thermal IR scanning from [y]. For power transistors we have A = 1, E_a1 = 0.4 eV, E_a2 = 0.7 eV, θ_Uref = 40 °C, and θj_,2 = θ_U + Δθ, with θ_U = mean ambient temperature of the component in °C. Additionally, we find Δθ = P × Rth with P = operating power dissipation, Rth = thermal resistance (junction to ambient). For Q1—high MOSFET—we have θj_,2, high MOSFET = 40 °C and from the transistor’s datasheet we have R_(DS)on = 6.2 mΩ, Coss = 430 pF (output MOSFET capacitance), and Rth_(J-C) = 20 °C/W (thermal resistance from junction to case).

Hence, in order to calculate the failure rate value, we find the following:

P_{Conduction-Loss} = R_(DS)on × (I_Load)² = (6.2 mΩ) × (5.43 A)² = 182.80638 mW

(24)

P_{Switching-Loss} = f_SW·Coss × (Vin)² = 250 kHz × 430 pF × (12 V)² = 15.48 mW

(25)

P_Total-Loss = P_{Conduction-Loss} + P_{Switsching-Loss}/2 = 190.54 mW

(26)

T_case= 40 °C, T_junction = T_capsule+ Rth_(J-C) × P_Total-Loss = 40 °C + 20 °C/W × 0.19054 W = 60.6 °C

(27)

For Q2—low MOSFET—we have θj_,2, low MOSFET = 49 °C, and from the transistor’s datasheet we have R_(DS)on = 2.5 mΩ, Coss = 2070 pF (output MOSFET capacitance), and Rth_(J-C) = 1.4 °C/W (thermal resistance from junction to case).

Hence, in order to calculate the failure rate value we find the following:

P_{Conduction-Loss} = R_(DS)on × (I_Load)² = (2.5 mΩ) × (5.43 A)² = 73.71 mW

(28)

P_{Switching-Loss} = fSW·Coss·(Vin)² = 250 kHz × 2070 pF × (12)² = 74.52 mW

(29)

P_Total-Loss = P_{Conduction-Loss} + P_{Switsching-Loss} / 2 = 110.97 mW

(30)

T_case = 49 °C, T_junction = T_capsule+ Rth_{(J-C) ·} P_Total-Loss = 49 °C + 75.121 = 124.12 °C

(31)

π_T-HighMOSFET = 0.092, so λ_HighMOSFET = λref × π_T-HighMOSFET = 200 × 0.092 = 18.4 [FIT]

(32)

π_T-LowMOSFET = 0.15, so λ_LowMOSFET = λref × π_T-LowMOSFET = 200 × 0.15 = 30 [FIT]

(33)

4.2.2. Operating Stress Conditions

Operating stress conditions are typical in industrial environments that are similar to IEC 60654-1 class C, i.e., sheltered locations which have an average temperature of 40 °C over long periods of time. The value θ1 = 40 °C from the standard table indicates 25 °C from ambient temperature plus the internal self-heating due to ripple current through capacitor. The value θ2 is the actual capacitor’s temperature obtained from the SPICE simulation [18,19], shown in Table 2.

Taking account of Section 3 and after extracting the data from the SN 29500 standard’s tables we found the following [1]:

• For polymer capacitor we have the following: C2 = 1.9; C3 = 3; U_max = 6.3 V; U_ref/U_max = 0.8; U = 1.2 V; U/U_max = 0.19048; A = 0.4; E_a1= 0.14; E_a2 = 0; θ_Uref = 40 °C; θ1 = 40 °C; θ2 = 28 °C (see Table 2 within the SN 29500 standard); T_Uref = 313 [°K]; T1 = 313 [°K]; T2 = 301 [°K]; zref = −3632327.923 [1/eV]; and z = −1.478139959 [1/eV], with the following results: λ_{ref-polymer electrolytic} = 3; π_U = 2.735932892; π_T = 0.542388224; π_Q = 2.
• For MLCC capacitor we have the following: C2 = 1; C3 = 4; U_max = 6.3 V; U_ref/U_max = 0.5; U = 1.2 V; U/U_max = 0.19048; A = 1; E_a1 = 0.35; E_a2 = 0; θ_Uref = 40 °C; θ1 = 40 °C; θ2 = 32 °C (see Table 2 within the SN 29500 standard); T_Uref = 298 [°K]; T1 = 313 [°K]; T2 = 305 [°K]; z_ref = −362327.923 [1/eV]; and z = −1.478139959 [1/eV], with the following results: λ_ref-MLCC = 2; π_U = 3.71; π_T = 0.712242068; π_Q = 2;
• For ceramic through hole HF capacitor we have the following: C2 = 1; C3 = 4; U_max = 25 V; U = 1.2 V; U_ref/U_max = 0.5; U/U_max = 0.048; A = 0.4; E_a1= 0.14; E_a2 = 0; θ_Uref = 40 °C; θ1 = 40 °C; θ2 = 32 °C (see Table 2 within the SN 29500 standard); T_Uref = 313 °K; T1 = 313 °K; T2 = 301 [°K]; z_ref = −3632327.923 [1/eV]; and z = −1.478139959 [1/eV], with the following results: λ_{ref-ceramic cap HF} = 3; π_U = 2.735932892; π_T = 0.542388224; π_Q = 2.

5. Results

Once we have undertaken the calculations, we obtain the following:

λ_{polymer electrolytic capacitor-SN 29500} = 0.004451813 [F/10⁶ h] or 4.451 [FIT] (one piece)

(34)

λ_{MLCC capacitor-SN 29500} = 0.005285 [F/10⁶ h] or 5.285 [FIT] (one piece)

(35)

λ_{ceramic HF capacitor-SN 29500} = 0.00389908 [F/10⁶ h] or 3.899 [FIT] (one piece)

(36)

For the entire capacitor bank we obtain the following:

λ_{capacitor bank-SN 29500} = 0.06788410532 [F/10⁶ h] or 67.9 [FIT]
(2 × polymer + 4 × MLCC + one ceramic HF through hole)

(37)

MTBF_{capacitor bank-SN 29500} = 14,730,989 h

(38)

These data are grouped within

Table 4. Calculated values of failure rate and MTBF for the converter under study.

Component or Device	λMIL-217 [FIT]	πT MIL-217	πT SN 29500	λSN 29500 [FIT]	MTBFMIL-217 [h]	MTBFSN 29500 [h]
2 × polymer electrolytic SMD PCF0J471MCL6GS—Polymer electrolytic SMD can-type	15.334	NA	0.542388224	11.23
4 × MLCC SMD GRM32ER60J107ME20—MLCC, SMD-class II (X7R)	525.89	NA	0.712242068	85.5
1 × ceramic through hole HF	7.666	NA	0.542388224	7.85
Entire capacitor bank (2 × polymer)‖(4 × MLCC)‖ (1 × ceramic through hole HF)					1,821,952 h	9,562,057 h
High side (control) MOSFET IRF6617	84	2	0.092	18.4
Low side (synchro) MOSFET IRF6691	96	4.9	0.15	30
Entire converter Capacitor bank + MOSFETs					1,371,949 h	6,536,802 h

.

A diagram comparison of the two failure rates for the entire capacitor bank is shown in Figure 4. We find a significant difference between the two standard’s calculation results. A lesser difference is obtained by calculus with the SN 29500 standard and for the very same schematic and capacitors. The same observation for the entire converter’s MTBF is true and the results can be seen in Figure 5.

Figure 6 and Figure 7 show, via pie diagram, the failure rate distribution for every part of the converter and for both calculations upon the used standard.

The SN 29500 Standard, developed by Siemens, is often considered superior to other reliability standards for several reasons, as follows:

• Comprehensive data, because SN 29500 provides extensive failure rate data for a wide range of electronic and electromechanical components. These data are regularly updated to reflect the latest industry findings and technological advancements.
• Sophisticated models are used, where the standard includes detailed and sophisticated calculation models that are particularly effective for components used in harsh environments. These models help in accurately predicting the reliability of components under various stress conditions.
• Ease of use, where, despite its sophistication, the SN 29500 standard maintains simplicity in the required model parameters, making it accessible for engineers to use without extensive additional training.
• Industry acceptance, due to the SN 29500 standard being widely accepted and used in various industries, particularly in automotive and industrial applications, in turn due to its reliability and accuracy in predicting component failures.
• Focus on harsh environments, because the standard is specifically designed to address the reliability of components in harsh environments, which is crucial for industries where components are exposed to extreme conditions.

These features make SN 29500 a preferred choice for reliability predictions, especially in industries where precision and up-to-date data are critical. It is useful to note that, for example, in Figure 5, MTBF does not mean that a single unit will last 746 years—it represents the average time between failures in a large population of identical components. If a system has an MTBF of 746 years, it means that in a large sample, failures will statistically occur at a rate of one failure per 746 years of cumulative operation.

6. Discussion

The root cause of the difference between the two standards may be the values for stress factors within the Mil-HDBK-217 standard’s tables, which were stated for the capacitor’s technology at that time. As an example, the basic failure rate values, λ_base, for ceramic capacitors described as “Capacitor, Chip, Multiple Layer, Fixed, Ceramic Dielectric, Established reliability” in table “10.1 Capacitors” is equal to 0.020 and for polymer capacitors described as “Capacitor, Fixed Electrolytic (DC, Aluminum, Dry Electrolyte, Polarized)” is equal to 0.00012. Here, the discussion requires the following (without any intention of criticizing the widely accepted and used standard mentioned above):

• Firstly, λ_base = 0.020 for MLCC makes the final result of the failure rate calculation much larger when compared with SN 29500’s calculation result (548.9 FIT vs. 67.9 FIT).
• Secondly, λ_base = 0.020 for MLCC vs. λ_base = 0.00012 for polymer capacitors seems to be reversed regarding today’s technology for the two types of capacitors (nowadays MLCC capacitors are characterized by a longer useful life than polymer capacitors [17,18])
• The environment that the device will be utilized in is a factor, along with the type of packaging technology.
• Industrial electronics reliability calculations obtained using Siemens SN 29500 are specific mostly for Europe, while MIL-217 is a USA standard.

Despite SN 29500 considering environmental factors, this reliability standard may place more emphasis on conditions typical of industrial and commercial settings, while the MIL-217 standard takes into account a variety of environmental factors such as temperature, humidity, and vibration, which are critical in military and aerospace applications. SN 29500 assumes a general industrial environment, which might limit its applicability in more extreme conditions. This standard is maintained and updated by Siemens, with the latest issues ranging from 2004 to 2011, while MIL-217 has not been updated since 1995.

Environmental factors play a crucial role in reliability estimation, and different prediction standards account for them in varying ways. Environmental differences can impact reliability predictions by showing variability in failure rates. Some standards, like MIL-HDBK-217, use environmental multipliers to adjust failure rates based on conditions such as temperature, humidity, and vibration. Other standards, such as SN 29500, incorporate environmental stress factors differently, often focusing on specifically industrial (automotive) conditions. Typical industrial and commercial settings are expressed by the average and moderate conditions found in most industrial and commercial applications, by the range of environmental factors determining the average and moderate conditions that can be encountered in various applications, and extreme conditions (which can be encountered in certain applications, such as military ones or those that require performance in extreme environmental conditions). All these parameters for the above mentioned field situations are synthesized in

Table 5. Typical SN 29500 industrial and commercial settings, environment factor range and MIL 217 more extreme conditions.

Parameter	Temperature [°C]	Humidity [%]	Vibration [g]	Pressure [bar]	Radiation [W/m2]
Typical industrial and commercial settings—SN 29500	20–40	40–60	0.1–1.0	1.0–5.0	1.0–10.0
Environmental factors range—SN 29500	0–70	20–80	0.01–10	0.5–10	0.1–100
Extreme conditions—MIL HDBK 217F	−40–80	10–90	1.0–100	1.0–5.0	10–1000

below.

SN 29500 provides typical industrial and commercial settings that are more moderate than the extreme conditions in MIL HDBK 217F. The range of environmental factors in SN 29500 is wider than that in MIL HDBK 217F, which makes SN 29500 more flexible and adaptable to various environmental conditions. MIL HDBK 217F provides extreme conditions that are more severe than those in SN 29500, which makes MIL HDBK 217F more suitable for applications that require performance in extreme environmental conditions.

Additionally, there are differences in environmental assumptions—standards may assume different baseline environments. MIL-HDBK-217 defines multiple operational environments (e.g., ground fixed, airborne, naval sheltered), each one with distinct reliability models. Other standards use conversion matrices to adjust predictions when the operating environment changes. Nevertheless, there is the problem of the adaptability of the prediction figures. Some standards allow for custom environmental adjustments, while others rely on predefined conditions. If a product is moved to a harsher environment than initially predicted, reliability estimates may need recalibration using environmental conversion matrices.

A comparative analysis [22] between Siemens SN 29500, Telcordia SR-332, and MIL-HDBK-217F has demonstrated that SN 29500 provides more realistic estimates of the reliability of modern electronic components. In particular, it was observed that MIL-HDBK-217F can overestimate the failure rate, while SN 29500 better reflects the actual reliability of current commercial components.

We can justify with field data the statement that SN 29500 is more appropriate than MIL-HDBK-217F. This can be achieved using the data shown in Figure 8, which is an excerpt from [22], which in turn shows the failure rates for different prediction standards determined for a batch of 1400 components on five printed circuit boards. Additionally, we can follow the data in

Table 6. Failure rates for the two standards investigated (extracted from Figure 8), the ratio between them, and the resulting ratio within our work.

	Temperature
Failure Rate λ in [F/106 h] According to Prediction Standard	0 °C	10 °C	20 °C	30 °C	40 °C
MIL-HDBK-217F (1995)	8	9.6	12	15.6	20.3
SN 29500 (2008)	1.8	2	2.6	3.5	4.9
FR_Mil217/FR_SN 29500 ratio obtained according to Figure 8	4.444444	4.8	4.615385	4.457143	4.142857
FR_Mil217/FR_SN 29500 ratio obtained within our work	7.2889 × 10−7 [FIT]/1.5298 × 10−7 [FIT] = 4.76461

, which compare the ratio of failure rates for the two standards in question with the ratio found in the investigation carried out in this paper.

The yellow points correspond to the failure rate values for the MIL standard, and the orange ones to the SN 29500 standard. In Table 6 below, these values, plus the failure rate ratios for the two standards in question, are grouped and are also compared with the ratio value obtained in this work.

The ratio between the failure rates for the five red boxex within Figure 8 (coresponding for the five values of temperatures mentioned in Tabe 6) are depicted in the Figure 9 below.

Therefore, it is observed that the ratio between λ_{MIL-HDBK-217F} over λ_{SN 29500} obtained in this investigation (4.76461) is consistent with the field data (between 4.14285 and 4.8) obtained in [22].

7. Conclusions

This paper provides a comparison calculation using two reliability standards: one used worldwide (also the very first to appear on the reliability prediction market) and a newer one that takes account of the newer capacitor’s technology, like polymer and MLCC. A consistent difference appears between the results of the two calculations. According to the calculation using the newer standard, a better MTBF is revealed. These two reliability standards provide a common basis for reliability prediction, based on analysis of the best available data at the time of issue.

As we already know, prediction reliability comparison contributes significantly to various fields by providing insights into the accuracy and dependability of different predictive models. This investigation provides the following key contributions:

• It helps to evaluate the performance of different predictive models by comparing their reliability.
• By comparing the reliability of various design options, engineers can make better-informed decisions regarding which components and configurations to adopt. This assists in choosing the most robust and reliable design.
• Identifying the most reliable components early in the design process can reduce costs associated with failures and maintenance. This leads to more efficient use of resources and budget.

The insights gained from comparing reliability prediction standards can often be applied to different product categories, especially if they share similar operational conditions, materials, or failure mechanisms. Comparison can be useful beyond the original product category that takes account of failure pattern recognition, comparing standards helps identify recurring failure modes, which can be useful for industries dealing with durability concerns, such as automotive or aerospace. Additionally, by optimizing maintenance strategies via the study of reliability data across multiple standards and industries, companies can refine maintenance schedules for various types of equipment. In addition, comparison can improve risk assessment; if one standard is found to provide more realistic predictions, companies can use that insight when evaluating reliability for unrelated products.