JUROJIN – Statistics for Fatigue Testing and Reliability Analysis

Our statistics program JUROJIN supports the planning and evaluation of durability tests. Methodology and program structure are based on projects and practical application cases with car and commercial vehicle industry.  A number of vehicle manufacturers and suppliers are using Jurojin to solve typical tasks quickly and efficiently.

Test plans can be prepared that ensure maximum information yield despite small sample sizes. Often, conducted tests do not conform to the initial plan but include deviations, for example, unplanned premature shut-downs. In such cases, to compensate, JUROJIN adaptively generates extended test plans. The software was greatly expanded in the context of bilateral industry projects.

When verifying the design life of vehicle components several questions arise:

  • How many prototypes need to be tested? At what test duration?
  • Either many short or few long tests?
  • How to analyse the test results?
  • Required statistical confidence level?
  • Are different suppliers producing the same quality?
  • Is it possible to expand a components homologation to a modified version?
  • etc.


To deal with those problems it makes sense to deploy some advanced mathematical statistics. Next to established methods like Maximum Likelihood, probability papers and success runs, new methods for bootstrap-small-sample-corrections, the consideration of all knowledge from censored samples and adapted analysis of variance are useful.

Statistical package JUROJIN

The implementation of these advanced algorithms has produced the software package JUROJIN. Leading guidelines have been:

  1. Mathematical benchmark: optimalconsideration of all information coming from the sample. Elaborate techniques help lowering the sampling efforts.
  2. Easy operability: inhibition threshold is lowered by guided handling of tidied up user intercaes. In addition results becomre more traceable.
  3. Modifiability: professional users define templates for the less experienced users.

Scope of the software package JUROJIN:

  • Design of technical survival data and fatigue life experiments
  • Data analysis with selected algorithms
  • Graphical data reduction
  • Consideration of samll sample sizes
  • Usage of all information coming from censored data
  • Calculation of continuative experiments in case of refused homologation
  • Analysis of variance

Adaptive Design of Test Schedules

Classical test designs following the success-run paradigm, need a specific number of parts to reach a given life time without failure. To reduce the number of required components the testing time should exceed the design life by a factor called life time ratio. This leads to an increased risk of not getting the reliability approved, even if the components come from a population with good quality. Testing subsequent components as reaction on that will increase the consumer’s risk. In this case, poor component populations will pass the test with increased probability.

Jurojin quantifies this risk and assists in the selection of a suitable strategy:

  • Add few components with the same testing time
  • Add more components with decreased testing time
  • Reactivate some of the components without failure

JUROJIN - Additional Modules

Efficient Woehler Models

Woehler fatigue tests
© Photo ITWM

Woehler fatigue tests

For cyclic loads with medium to high amplitudes, the relationship between load amplitude and fatigue strength (S-N-curve) is often observed to be linear in a double-logarithmic diagram. For lower amplitudes, a nearly horizontal curve is typical. In this range loads may theoretically be applied “infinitely often” (more than 10**6 repetitions). Traditionally, regression in load direction is performed based on the information [component fails/component is durable] to identify the infinite strength regime.

The fact that the fatigue strength for components that do fail is not considered leads to information loss – high-cycle fatigue and infinite life behavior are evaluated using separate tests. Driven by industrial cooperation projects we developed a new stochastic model that allows joint identification of high-cycle fatigue and infinite life or very-high-cycle fatigue behavior. Random variables describe the transition region and the scattering of the fatigue life.

Reliable Warranty Data Evaluation

Missing data situation for warranty data
© Photo ITWM

Missing data situation for warranty data

In addition to evaluating components under development, JUROJIN also supports the analysis of warranty data for parts already in production. The available input data for such an analysis only refers to failed components and provides no information on the fatigue life of intact components. Forecasting on this basis typically would be too pessimistic. Also, as soon as the first components are no longer covered by the warranty period, defects are no longer fully reported to the manufacturer. In this situation, the forecasts would become too optimistic.

In projects with industrial partners this incompleteness (missing data) has been modelled and a corrected likelihood-function developed. Combined with a usage model of the intact units, JUROJIN now applies Monte-Carlo simulation to calculate statistically complete data as a basis for extrapolation. Reliable failure forecasts for future time points are thus possible even in the early phases of the warranty period.