Weakest link

The weakest component defines the durability. In statistics, this behavior is called weakest link behavior or principle of the weakest link.

Fatigue Testing and Reliability

Design and evaluation of fatigue tests

For commercial vehicles reliability demonstration is required for a large number of vehicle variants. Classical Success Run designs claim a certain number of specimens to survive a multiple of the actual design life. Small sample sizes increase the probability that even populations of good quality will not pass the test. Reacting to that with additional tests will now increase the probability that samples from poor populations pass the test.

We quantify this risks and assist in selecting suitable strategies:

  • Adding few components with same testing time?
  • More components with shorter testing time?
  • Reactivate suspended components?

The results are more efficient designed testing plans and savings in terms of specimens to be tested.

Efficient Woehler models

Woehler fatigue tests
© Photo ITWM

Woehler fatigue tests

Determining components fatigue life and endurance limits involves two separate testing series, each on different load horizons. The reason is a linear relationship (in double logarithmic scale) of load against cycles which inflects to an almost horizontal line. Below this endurance limit all loads can theoretically be tolerated infinitely often. The regression for fatigue life is done in load direction, the one for endurance limit in life time direction.

Motivated by challenges from industry, a new stochastic Wohler model has been developed at Fraunhofer ITWM. Both areas are interpreted in load direction, were the endurance limit is a special case of VHCF (very high cycle fatigue). Random variables regulate the inflection points location and variance. Now, all information can be considered a simultaneous estimation of both parameter sets, including an automated selection of the optimal model complexity.

Dimensioning against variable loads

Typical reliability estimations and reliability demonstrations are based on a given load scenario. This derived reference load represents a very ambitious customer, e.g. the 99% customer. The reliability of the component surviving this scenario is not connected in any way to the reliability when used by customers with varying loads. It can be shown that there is no conservative test scenario to limit this reliability.

To obtain resilient estimations for the reliability at the customers a dimensioning against variable loads is needed. However, the uncertainties of modelling load and strength with statistical distributions have to be taken into account. This can be done by combining statistical and empirical methods. Large and untransparent safety factors may then be replaced by products of statistically justified factors and a considerably decreased remaining safety factor.

Analysis of warranty data

Missing data situation for warranty data
© Photo ITWM

Missing data situation for warranty data

As soon as first claims of soled components come in, estimations of the total forthcoming claims are needed. Typically claim data are incomplete, as they involve failed components only, but not the intact ones. Especially when dealing with small lot sizes in commercial vehicle industry this missing data situation hinders the forecast. Therefore, on one hand, all early results would be way too pessimistic.

On the other hand, later forecasts might be too optimistic: As soon as some components leave the guaranteed period, not all failures are trustworthy reported to the manufacturer.

In several industrial projects both missing data situations were modelled and a corrected likelihood function was derived. Together with a usage model of intact units a Monte Carlo simulation yields complete data sets, giving a solid basis for forecast. Now, reliable forecasts of future points in time are possible even in early phases of sampling.