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Application Note 001
MSK Reliability Prediction
By Bob Abel, MS Kennedy Corp.; Revised 9/19/2013
Introduction
Reliability prediction has many uses within the field of reliability engineering. Reliability
predictions are used to evaluate design feasibility, compare design alternatives, identify
potential failure areas, trade-off system design factors, and track the impact of design
changes on component, system, and mission reliability.
MS Kennedy uses the MIL-HDBK-217F Notice 2 prediction model, and Windchill
Prediction (formerly Relex) software to generate our reliability prediction reports. It is not
uncommon in the industry for empirical data to be used in the attempt to gain more accurate
predictions, but in accordance with the stated purpose of MIL-HDBK-217 to provide a
common basis for reliability prediction, MS Kennedy does not modify the base failure rates
with empirical data from our vendors.
Methodology Comparison
This analysis compares the results of two methodologies used to calculate component failure
rates. The first method is the MIL-HDBK-217 method, where base failure rates are imported
from the software, and are not specific to the device. Failure rates are only specific to the
technology type and complexity, e.g. semiconductor – transistor, or integrated circuit –
linear <100 transistors, etc. The second method uses vendor supplied life testing data, ChiSquared probability distribution, and the temperature acceleration factor to predict the
component failure rates. For this analysis, a hybrid linear regulator device consisting of two
die level components, a linear regulator controller IC and a BJT pass element, was used to
simplify the process.
λ =
χ2[CL, (2r+2)]
2
1
x
(1)
n x t x AF
(2)
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The method used by the pass element vendor, is based on a web page calculator model that
modifies the device hours (nt) to compensate for temperature acceleration (AF), and then
uses equation 3 to calculate λ from there.
(3)
Regardless of how the component failure rates were calculated, the hybrid failure rates were
calculated based on the following formula from MIL-HDBK-217:
λP = [ΣNCλC](1 + .2πE) πF πQ πL Failures/106 hrs
Given from MIL-HDBK-217:
NC = Number of each particular component
λC = Failure rate of each particular component in failures/106 hrs
πE = Environmental Factor = SF, SC - Space Flight, Commercial = 0.5
πF = Circuit Function Factor = Power = 21
πQ = Quality Factor = MIL-PRF-38534 Class K = 0.25
πL = Learning Factor or years in production = ≥ 2 = 1.0
Values are MSK assumptions for our standard voltage regulator product MTBF reports.
Method I - MIL-HDBK-217 / Windchill Prediction method with Defined Stress Levels
MSK Method
Operating parameters were entered into the Windchill Prediction model to emulate 50% of
max. thermal stress:
Pass element power dissipation = 12.5°C / Rθj-c = 4.334W
(12.5°C = 0.5 X the Δ between the max. transistor die temperature of 150°C and the max.
hybrid case temperature of 125°C)
Windchill - MIL-HDBK-217 model pass element component λ = 3.43 X 10-10
IC Controller – Power dissipation = 206mW
(Base on a conservative minimum VBE and drive resistance value, the specified minimum
pass element β at a 50% derated current level, and an input voltage of 3.234V)
Windchill - MIL-HDBK-217 model IC controller λ = 1.47 X 10-8
λP = [1(3.43 X 10-10) + 1(1.47 X 10-8)](1 + .2(0.50))( 21)( 0.25)(1.0)
= 8.69 X 10-8 Failures/hr
MTBF(hrs) = 1/λP = 1.15 X 107 hrs
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Method II – Chi-Square Method
Life testing for both the controller IC, and the pass element, was performed by the
manufacturers with zero failures. In such cases, you define a confidence level between 0 and
100, and then compute the lower bound chi-square value using two degrees of freedom.
λ =
χ2[CL, (2r+2)]
2
x
1
n x t x AF
χ2[CL, (2r+2)] = The Chi-Squared value at the confidence level CL, and with 2 degrees of
freedom. This value can be calculated or can be obtained from a table.
n = the number of devices that were tested
t = the test time
AF = the temperature acceleration factor based on the Arrhenius equation – see bellow
Note: Manufacturers sometimes specify device hours, which can be used to replace the nt
product.
T2
T1
Ea =
K =
AF =
T1 =
T2 =
Activation energy = 1
Boltzman Constant = 8.617E-05 eV/K
The temperature acceleration factor
Ambient Temperature = 328.15°K (55°C)
Stress Temperature = 398.15°K (125°C)
Confidence
Level
IC Controller λ
Pass Element λ
Hybrid MTBF
0.5
1.47E-09
6.56E-10
81,434,103
0.6
1.95E-09
8.68E-10
61,454,592
0.8
3.40E-09
1.52E-09
35,165,995
0.9
4.86E-09
2.18E-09
24,595,008
0.95
6.33E-09
2.84E-09
18,889,823
Matches Controller IC vendor’s prediction
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Relex Exponential Distribution Alternative for Worse Case
A Chi-square (χ2) distribution with two degrees of freedom is equivalent to the exponential
distribution with a mean of 2. Therefore, after simplifications, the confidence limit for λ is
given by:
λ100(1-α) =
-ln(α)
nT
α = 1 – the desired confidence interval
n = the number of devices that were tested
T = the test time
This calculation does not take the temperature acceleration factor into consideration, but it is
a simple method to predict failure rates at the stress temperature of the life testing lot. When
Ta = Ts in the AF equation (2), then the acceleration factor becomes equal to 1 making the
two methods equivalent.
Ref: Relex
This method was included for information purposes, and was not used in the analysis
because it would yield the same result as the method use by the pass element vendor –
method II
Data Summary
In order to predict component failure rate based on empirical data, assumptions must be
made to make the predictions. These assumptions include activation energy, confidence
level, and operating die temperature. Even if these assumptions are valid and clearly stated,
it makes the task of comparing the data from different methods difficult because it is highly
unlikely that the failure rates for all components in the system were calculated base on the
same assumptions.
The data below shows the results of the two methods, but does not include variances that
would be caused by die temperature or activation energy. There is no confidence level
associated with the MIL-HDBK-217 component failure rate prediction due to the
complexity of the information sourcing.
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MTBF
217 Method
Unaltered
Confidence
Level
MTBF
Chi-Squared
11,511,013
0.5
0.6
0.8
0.9
0.95
0.99
0.999
81,434,103
61,454,592
35,165,995
24,595,008
18,889,823
12,410,265
8,195,232
As you can see from the data, there is a large variance in the result based on the method and
confidence level chosen. The unaltered MIL-HDBK-217 method is more conservative than
the Chi-Squared method utilizing vendor data up to confidence levels exceeding 99%.
Conclusions
Using vendor supplied data, and the underlying assumptions, introduces a lot of variability
that can make reliability prediction and decision making difficult. Reliability predictions
can be a useful tool only if the assumptions made by the preparer are well defined and
understood by the user. There are many variables that can affect the results that may not be
intuitive to everyone using the information.
Using a prediction model like MIL-HDBK-217, including the integral base failure rates,
minimizes the ambiguity involved, and makes the reliability prediction easier to understand
and reduces the need for assumptions.
The main goal of reliability prediction per MIL-HDBK-217 and MIL-STD-756B, is to
provide a relative measure of reliability to aid in design decision making. Extreme caution
should be used in optimizing component failure rates or making any inferences on field
reliability from these predictions.
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