## Reliability test design

Reliability and durability fit together in product validation testing. Often, the product’s life requirement is being able to withstand loading over a specified duration with reliability and confidence requirements, like this:

The part must be free of visible cracks with a reliability greater than 90% with a 90% lower 1-sided confidence bound after being subjected to loading representative of 4,000 service hours.

Durability, life data and reliability analyses can help engineers answer critical questions like how long to test and how many parts to test in order to meet these life requirements. In this article, we discuss the important link between testing to prove durability and testing to demonstrate reliability.

## Creating durability test specifications

Product validation testing is an important step in the design process. The goal of validation or durability tests is to prove that the part is indeed capable of withstanding the loading that it will see in service. These tests are often the last step before approving the part for production. This means the tests are crucial to understanding both the durability and reliability of the product.

Durability tests are often run in the controlled environment of the test lab, and can be specified in a number of ways. Typically, these test specifications are built around the concept of specified excitation or loading over a prescribed duration. The test spec may call for quasi-static loading (i.e., time-independent loading in which inertial effects can be ignored) or dynamic loading (i.e., time-dependent loading in which inertial effects are important). Note that it is important to ensure that the loading in the lab creates the same failure modes as one would expect in the field.

Validation tests need to be correlated to service loading. This correlation can be quantified using the concept of fatigue damage equivalence, in which the loading profile described in the lab test spec is tailored so that the test specimens will accumulate the same fatigue damage as the product sees in service. This fatigue damage correlation allows us to 1) link test time to service life time, so a potential failure in the lab can be correlated to hours or miles in the hands of the customer, and 2) replicate long service lives in a short test duration.

nCode GlyphWorks durability analysis software includes a number of tools to quickly and efficiently reduce complicated service loading into an equivalent damage test spec. For example, consider a product like a lifting implement that is subject to cyclic loading. This loading can be measured in service and used to define the durability test spec.

The measured service loading looks like this:

Notice that it is highly variable in cyclic content. It may be advantageous in terms of both cost and timing to replicate the fatigue damage of this variable amplitude loading in the test lab with a simple cyclic load called a *constant amplitude spec*. The use of the SN curve and fatigue damage analysis allows us to calculate the cyclic range and number of cycles for an equivalent damage test spec. Shown below is an example of this. The fatigue damage incurred during one cycle of service loading (which ranges from -1124N to 1163N) is 1.00E-3, while the fatigue damage from one cycle of reversible constant amplitude (850N) loading is 4.91E-6. Thus, fatigue rules show that 204 constant amplitude cycles (1.00E-3 / 4.91E-6 = 204) are needed to produce the fatigue damage of the measured service loading.

These techniques allow engineers to create a test spec that addresses product durability through fatigue damage equivalence. However, these lab tests should demonstrate both product durability and reliability. Take, for example, this stated durability requirement:

The part must be free of visible cracks with a reliability greater than 90% with a 90% lower 1-sided confidence bound after being subjected to loading representative of 4,000 service hours.

If the world were deterministic, we could ignore reliability and the equivalent damage validation test could be run on a single part. Pass a single part without failure and we could consider the design validated — at least, deterministically. However, variability in material strength, loading, etc. is present all around us, and we need to recognize this in order to meet the stated durability and reliability target.

## Introducing reliability to the durability test

### Weibull and other life distributions

Time-to-failure data can be quantified and modeled using life data analysis concepts. Failure times are analyzed to understand trends in the product’s failure rate behavior. These relationships can be modeled using life distributions, such as exponential, lognormal and Weibull. The lognormal and Weibull distributions are often used for durability failure modes because the shapes of their probability density functions can model failure modes associated with wearout. We will discuss the use of the Weibull distribution in the remainder of this article.

The Weibull distribution is characterized by two important parameters: eta and beta. Eta is called the "characteristic life" and represents time to 63.2% of the population having failed. Beta is the shape parameter, which describes the slope of the probability of failure curve on Weibull probability paper. Different values of beta can have marked effects on the behavior of the distribution. The beta parameter plays a critical role in linking durability and reliability in the validation test.

### Reliability and confidence levels

Reliability is defined as the probability that an item survives to a particular time. For example, 90% reliability at 500 hours implies that if 100 brand new units were put in the field, then 90 of those units would not fail by 500 hours. Confidence level is a measure of possible variability in an estimate due to only taking a sample of a larger population. From a practical perspective, it provides a way of ensuring that a sufficient number of units were tested before computing a reliability value. For example, to demonstrate a 90% reliability at a 90% confidence level requires more specimens (and/or test time, if a distribution is assumed) than demonstrating a 90% reliability at a 60% confidence.

Reliability at specific confidence levels can be demonstrated by testing a number of samples. Consider the case where the reliability target is 90% with a 90% lower 1-sided confidence level at 100 hours. We could test 22 parts and if every part survived 100 hours, then we would have demonstrated the reliability requirement. However, this sample size may be prohibitively large. We could consider decreasing the sample size, but the tradeoff is that a reduced sample size would require a longer test time. Alternatively, the test time of 100 hours might be too long. We could consider decreasing test time, but the tradeoff is that more parts would need to be tested.

ReliaSoft Weibull++ software can help answer these questions:

- How many samples should we test?
- How long should we test?
- How are reliability targets at specific confidence levels related to the number of samples and test duration?

## Reliability test design in ReliaSoft Weibull++

We will now use a Test Design folio in Weibull++ to answer these questions.

In this example, let us assume that the durability test spec has been established using fatigue damage equivalence, and that 10 hours in the test lab is equivalent to the product’s target service life. We will also assume that the product’s failure rate behavior is well characterized by a Weibull distribution with a beta value of 3.15.

If the reliability requirement is 90% reliability and 90% confidence at 1 life, Weibull++ tells us that we need to test 22 samples to 1 life with 0 failures:

##### Test spec 1: Demonstrate R90C90 @ 1 life by testing 22 samples to 1 life

This number of samples may not be acceptable in terms of cost or timing. One way to address this concern is to run longer with fewer samples. For example, if we can run 2 lives (20 hours) on each sample without failure, the number of samples drops drastically:

##### Test spec 2: Demonstrate R90C90 @ 1 life by testing 3 samples to 2 lives

This illustrates that we can demonstrate the same value of reliability at a specific confidence level with fewer test specimens by running durability tests longer. We have a tradeoff between the number of samples to test, duration of test and demonstrated reliability and confidence level. This is particularly useful if it is difficult to obtain a large number of test articles.

The key parameter needed to quantify this balance is the Weibull shape parameter beta. Beta must be used anytime the test duration and reliable life times are different, as it quantifies the benefit to demonstrated reliability that is gained by testing longer. Mathematically this can be expressed for a zero failure test as:

where:

- n
_{units}is the number of specimens on test - t
_{test}is the test duration - R
_{required}is the reliability target - t
_{required}is the time associated with the reliability target - CL is the confidence level associated with the reliability target
- β is the Weibull shape parameter

## Conclusion

Reliability and durability fit together in product validation testing. Durability can be addressed by creating fatigue damage equivalent test specifications that correlate to service loading. Fatigue analysis techniques in GlyphWorks can be used to shorten the duration of a test by creating a loading profile with equivalent fatigue damage to a service loading history. Reliability can be addressed by testing multiple samples. The Test Design folio in Weibull++ can be used to assess the tradeoff between the number of samples to test, duration of test and the demonstrated reliability and confidence.