Reliability Requirements and Specifications
One of the most essential aspects of a
reliability program is defining the reliability goals that a product needs
to achieve. This article will explain the proper ways to describe a
reliability goal and also highlight some of the ways reliability
requirements are commonly defined improperly.
Designs are usually based on specifications. Reliability requirements are
typically part of a technical specifications document. They can be
requirements that a company sets for its product and its own engineers or
what it reports as its reliability to its customers. They can also be
requirements set for suppliers or subcontractors. However, reliability can
be difficult to specify. It is easy to use "qualitative" language such as,
"our product needs to exceed customer expectations" or "our product should
be more reliable than its competition." Joseph Juran, a famous quality
pioneer, said, "If you don't measure it, you don't manage it." If an
organization does not specify reliability goals numerically, it loses
control over managing its products' reliability improvements.
What are the essential elements of a
reliability requirement?
There are many facets to a reliability requirement statement.
Measurable:
Reliability metrics are best stated as probability statements that are
measurable by test or analysis during the product development time frame.
Customer usage and operating environment:
The demonstrated reliability goal has to take into account the customer
usage and operating environment. The combined customer usage and
operating environment conditions must be adequately defined in product
requirements. Many types of stresses or customer behaviors can be combined
to describe the usage and operating environment. The descriptions can be
done in many ways. For instance:

Using constant values. For
example: Usage temperature is 25^{o
}C. This could be an average value or, preferably, a high stress
value that accommodates most customers and applications.

Using limits. For example: Usage
temperature is between 15^{o
}C and 40^{o }C.

Using distributions. For example:
Usage temperature follows a normal distribution with mean of 35^{o }
C and standard deviation of 5^{o
}C.

Using timedependent profiles. For
example: Usage temperature starts at 70^{o }C at t = 0,
increases linearly to 35^{o }C within 3 hours, remains at that
level for 10 hours, then increases exponentially to 50^{o }C
within 2 hours and remains at that level for 20 hours. A mathematical
model (function) can be used to describe such profiles.
Time:
Time could mean hours, years, cycles, mileage, shots, actuations, trips,
etc. It is whatever is associated with the aging of the product. For
example, saying that the reliability should be 90% would be incomplete
without specifying the time window. The correct way would be to say that,
for example, the reliability should be 90% at 10,000 cycles.
Failure definition:
The requirements should include a clear definition of product failure. The
failure can be a complete failure or degradation of the product. For
example: part completely breaks, part cracks, crack length exceeds 10 mm,
part starts shaking, etc. The definition is incorporated into tests and
should be used consistently throughout the analysis.
Confidence:
A reliability requirement statement should be specified with a
confidence level, which allows for consideration of the variability of data
being compared to the specification.
Understanding Reliability Requirements
Assuming that customer usage and operating environment conditions and
what is meant by a product "failure" have already been defined, let us
examine the probability and life element of a reliability specification. We
will look at some common examples of reliability requirements and understand
what they mean. We will use an automotive product for illustration.
Requirement Example 1:
Mean Life (MTTF) = 10,000
miles
The Mean Life (or MeanTimeToFailure [MTTF]) as a sole metric is flawed
and misleading. It is the expected value of the random variable (mean of the
probability distribution). Historically, the use of MTTF for reliability
dates back to the time of wide use of the exponential distribution in the
early days of quantitative reliability analysis. The exponential
distribution was used because of its mathematical (computational)
simplicity. The exponential distribution has just one parameter, the MTTF
(or its reciprocal, the "failure rate," which is constant, thus the reason
for its simplicity). Few products and components actually have a constant
failure rate (i.e. no wearout, degradation, fatigue, infant
mortality, etc.).
The MTTF might be one of the most
misunderstood metrics among reliability engineering professionals. Some
interpret it as "no failure by 10,000 miles," which is wrong! Some interpret
it as "by 10,000 miles, 50% of the product's population (50^{th}
percentile) will fail." The "mean," however, is not the same as the
"median," so this is only true in cases where the product failure
distribution is a symmetrical distribution, such as the normal distribution.
If the product follows a nonsymmetrical distribution (such as Weibull,
lognormal and exponential), which is usually the case in reliability
analysis situations, then the mean does not necessarily describe the 50^{th}
percentile, but could be the 20^{th} percentile, 70^{th}, 90^{th},
etc., depending on the distribution type and the estimated parameters of
that distribution. In the case of the exponential distribution, the
percentile that matches the mean life is actually the 63.2%! If the
intention of using the mean life as a metric is to describe the time by
which 50% of the product's population will fail, then the appropriate metric
to use would be the B50 life.
Let us use the following example for
illustration. A company tested 8 units of a product manufactured by two
different suppliers. The failure results are shown next.
Supplier 1 (miles) 
Supplier 2 (miles) 
866, 2243, 3871, 5798, 8209, 11363, 16044,
24889 
5985, 7593, 8702, 9627, 10501, 11390,
12416, 13857 
The two different data sets were modeled
using a Weibull distribution and rank regression based on X (RRX). The MTTFs
calculated based on the two different distributions are:

MTTF_{1} = 9999.6 miles

MTTF_{2} = 9999.4 miles
These MTTFs are almost the same. So, based on this type of reliability
metric, the two suppliers' reliability can be considered to be equal.
Now, let us look at the reliability plots
for the two suppliers' failure distributions.
After examining the above plot, does the
conclusion that the two suppliers' reliability is almost the same still hold
true? Even though the two suppliers' MTTFs are almost the same, the above
plot indicates that their reliabilities are significantly different. For
example, Supplier 1's reliability at 10,000 miles is 36.79%, whereas
Supplier 2's reliability at 10,000 miles is 50.92%. This is a considerable
difference in reliability.
In this example, because the Weibull
distribution is not a symmetrical distribution, the MTTFs do not correspond
to the 50^{th}
percentile of failures. The actual percentiles can be calculated using the
reliability function. The percentile, P, of units that would fail by t =
MTTF is:
The 50^{th} percentile of failures can
be computed using the B50 metric.

B50_{1} = 6,930 miles

B50_{2} = 10,066 miles
Attempting to use a single number to describe
an entire lifetime distribution can be misleading and may lead to poor
business decisions.
Requirement Example 2: MTBF =
10,000 miles.
Unfortunately, the term MTBF (MeanTimeBetweenFailures) has often been
used in place of MTTF (MeanTimeToFailures). Many reliability textbooks
and standards erroneously intermix these terms. MTTF and MTBF are the same
only in the case of a constant failure rate (exponential distribution
assumption). MTBF should be used when dealing with repairable systems,
whereas MTTF should be used when looking for the mean of the first
timetofailure (i.e. nonrepairable systems).
Requirement Example 3:
Failure rate = 0.0001 failures per mile.
The use of failure rate as a reliability requirement implies an
exponential distribution, since this is the only distribution commonly used
for reliability (life data) analysis that has a constant failure rate. For
the exponential distribution, MTTF = 1/Failure Rate = 1/0.0001 = 10,000
miles. Thus, this reliability requirement is equivalent to Example 1. Most
distributions used for life data analysis have a failure rate that varies
with time. In these cases, MTTF is not equal to 1/Failure Rate.
Consequently, the only way that using a failure rate for a reliability
requirement would make sense for distributions other than the exponential
distribution would be if a time were also specified.
Requirement Example 4: B10
life = 10,000 miles.
BX refers to the time by which X% of the units in a population will have
failed. This metric has its roots in the ball and roller bearing
industry. It then found its way to other industries and is now just a
statistical metric that is widely used. This reliability requirement means
that 10% of the population will fail by 10,000 miles. Or, in other words,
the reliability of the product is 90% at 10,000 miles. This metric is a good
metric because it does not make the exponential distribution assumption and
also because it states clearly the percentile of failures by a certain time
value.
Requirement Example 5: 90%
Reliability at 10,000 miles.
This is equivalent to the previous example.

The time of interest is 10,000 miles.
This could be design life, warranty period or whatever operation/usage
time is of interest to you and your customers.

The probability that the product will not
fail before 10,000 miles is 90%. Or, there is a probability that 10%
will fail by 10,000 miles.
Although the above two examples (4 and 5)
are good metrics, they lack a specification of how much confidence is to be
had in estimating whether the product meets these reliability goals.
Requirement Example 6: 90%
Reliability at 10,000 miles with 50% confidence.
Same as above (Example 5) with the following addition:
This corresponds to the regression line that goes through the data in a
regression plot obtained when a distribution (such as a Weibull) model
is fitted to timestofailure. The line is at 50% confidence. In other
words, this means that there is a 50% chance that your estimated value
of reliability is greater than the true reliability value and there is a
50% chance that it is lower. Using a lower 50% confidence on reliability
is equivalent to not mentioning the confidence level at all!
Let us use the following example to illustrate calculating this reliability
requirement.
Design A Failure Data
(miles) 
Design B Failure Data
(miles) 
11532, 14908, 16692, 21674, 23832,
25142, 26430, 26605, 27245, 29038, 32816, 37475, 40101, 55969,
56798, 61507, 65141, 73399, 73609, 75953 
18009, 22557
28255, 39164 
The two designs are modeled with a Weibull
distribution and using rank regression on X as the parameter estimation
method. The following figure shows the probability plot for the two designs.
The above plot shows that at 10,000 miles,
the demonstrated reliability of Design B
(96.81%) is superior to Design A's demonstrated reliability
(95.93%) at the 50% confidence (along the probability line). Both designs
meet the reliability requirement; however, the demonstrated reliability of B
is better.
Requirement Example 7: 90%
Reliability for 10,000 miles with 90% confidence.
Same as above (Example 6) with the exception that here, more confidence
is required in the reliability estimate. This statement means that the 90%
lower confidence estimate on reliability at 10,000 miles should be 90%.
If we show the above probability plot with
the 90% onesided confidence bounds, obtained using the Fisher matrix
confidence bounds method, we get the following:
The above plot shows that at 10,000 miles,
the 90% lower bound on reliability is 79.27% for Design B and 90.41% for
Design A. Unlike in the previous example, here, the demonstrated reliability
of A is better than that of B and only A is demonstrated to meet the
reliability requirement. The way this reliability requirement is stated is
better then the requirement of the previous example. In this example, the
requirement is able to uncover the sample size issue and its effect on
reliability analysis.
Requirement Example 8: 90%
Reliability for 10,000 miles with 90% confidence for a 98^{th}
percentile customer.
Same as above (Example 7) with the following addition:

The 98^{th }percentile is a point on the usage stress curve. This
describes the stress severity level for which the reliability is
estimated. It means that 98% of the customers who use the product, or
98% of the range of environmental conditions applied to the product,
will experience the 90% reliability.
To be able to estimate reliability at the 98^{th}
percentile of the stress level, units would have to be tested at that stress
level or, using accelerated testing methods, the units could be tested at
different stress levels and the reliability could be projected to the 98^{th}
percentile of the stress.
Conclusion
As demonstrated in this article, it is important to understand what a
reliability requirement actually means in terms of product performance and
to select the metric that will accurately reflect the expectations of the
designers and endusers. The MTTF, MTBF and failure rate metrics are
commonly misunderstood and very often improperly applied. Whereas, the BX
life or the reliability at a given time are more appropriate metrics because
they can be calculated for any of the statistical distributions commonly
used to analyze product lifetime data and they describe specific, measurable
expectations. Such metrics can be improved by specifying a confidence level
to account for variability within the data and by clearly defining the
anticipated userstress level for which the estimates are made. Therefore,
demonstrating that a product meets a reliability specification such as "90%
Reliability for 10,000 miles with 90% confidence for a 98^{th}
percentile user" provides the greatest likelihood that actual performance
will match the estimates.
