IEEE Power Electronics Magazine Compendium - March 2018 - 108

Operation Improvement
Reliability Metrics
* Reliability
* Life Cycle
* Margin
* Weakness
* Cost
* Wear Out
* ......

Mission
Profiles
Reliability Tools
?
Converter
Designs

Design Improvement

FIG 1 An advanced approach for the reliability prediction of a
power electronics system.

Reliability Versus Time
R = 0.99

R = 0.9

0.8
0.7
0.6
0.5

5,000

4,500

4,000

3,500

3,000

2,500

2,003 Hours
2,000

1,500

1,000 1,277 Hours

0

The widely used term mean time to failure (MTTF)
represents the average time that a group of samples fails.
It is generally used in some reliability standards and handbooks for military and aerospace applications. The MTTF
can be deduced from the reliability function F(t) by (2). It is
worth mentioning that the MTTF is an oversimplified term,
which is independent of time and loses the whole picture
of the reliability performance, such as failure distribution
and hazard rate. Therefore, benchmarking the systems or
components by using MTTF is discouraged if the reliability
function or CDF curve can be generated [1]-[3].

#

R (t) dt.

(2)

0

Time (Hours)
FIG 2 An example of reliability and percentile lifetime of a
type of 1,100-V/40-µF film capacitors under 85 °C and 85% RH
with a 5% capacitance drop as the end-of-life criteria [3]. R(t):
reliability with time; F(t): unreliability.

Accordingly, a comprehensive reliability description
includes five important aspects: definition of failure criteria, stress condition, reliability numbers (%), confidence
level (%), and the time of interest. A reliability number can
vary by adjusting any one of the other four aspects.
Understanding the metrics used in reliability engineering
is a fundamental step for the assessment of reliability performance and to be able to set the modeling targets. In the
following, several important concepts and definitions are
first clarified.

Reliability, Failure Rates, Mean Time to Failure, and Lifetime
To quantify reliability from a reliability engineering perspective, a time-varying variable R(t) as a percentage is used and
represents the percentage of a group of samples that can
properly function at a certain time t. From the point view of
individual sample, R(t) can be also represented as the prob-

108

(1)

3

0.4
0.3
0.2
0.1
0

t-c b
F (t) = 1 - exp ;- a h k E .

MTTF =

500

Reliability, R (t ) = 1-F (t )

1.0
0.9

ability of one sample that can function at a certain time.
Similarly, the unreliability F(t) can be defined as percentage
of a group of samples (or probability of one sample) that fail
at a certain time t.
F(t) can simply be calculated from 1 - R (t) . The plot of
F(t) against time t is also referred to as the cumulative distribution function (CDF) curve, which in most cases can
be fitted by an analytical function with three parameters
c, b, and h developed by Walloddi Weibull in 1951 [4], as
shown in (1)

IEEE PowEr ElEctronIcs MagazInE

z	 December 2016

To better quantify the lifetime of the system or component, percentile lifetime Bx is more suitable and recommended for use. It is the time when a group of samples has
a certain percentage of failure. For example, a B10 lifetime
corresponds to the time at which 10% of the samples in a
group have failed or the time at which a testing sample has
10% probability of failure. The percentile lifetime can easily be solved from the reliability function or CDF curve,
and the time-varying characteristic of failure is still kept.
Figure 2 describes the relationship between the reliability
and percentile life based on an example of film capacitors. The B1 lifetime (R = 0.99) and B10 lifetime (R = 0.9) in
the example are 1,277 and 2,003 hours, respectively.
The failure rate m (t) [also called hazard rate h(t)] is
another important reliability metric widely used in reliability
engineering. It describes the frequency with which a system
or component fails. It can be expressed in failures per unit of
time by deducting the reliability function R(t) as
1 d 61 - R (t)@
m (t) = R (t)
.
dt

(3)

A typical failure rate curve against the time in the life
cycle of a power electronics product is plotted in Figure 3. It
is composed of three reliability functions and is known as
the bathtub curve [2]. By examining the fitting parameters
b in the reliability functions, three types of failures that are
dominant at different stages of the life cycle can be identified. The first part is dominated by early failures caused
by infant mortality, with a decreasing failure rate (where



Table of Contents for the Digital Edition of IEEE Power Electronics Magazine Compendium - March 2018

Contents
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