# SKF – Statistical Modelling of Mechanical Bearing Life Testing #SWI2015

The goal is to model and optimize bearing life testing time under constraints. The constraints are from various kinds:

• Number of available test machines (each machine has 2 test positions): $$K$$
• Number of life tests to be run: $$N$$
• Statistical distribution assumed for individual bearing life: Weibull ($$L_{10}$$,$$\beta$$)
• Assessed precision: the expected maximum ratio between confidence bounds on life parameters

The parameters that need to be optimized are:

• The number of samples/machines per each test (can differ from one test to another)
• The order of the tests
• The individual test strategy (censoring, replacement…)
• Bias correction method for the maximum likelihood Estimation used for the confidence bounds calculation (when deviating from the type II censoring scheme)

In order to assess the last point, Monte Carlo simulations are needed, where random test data following specific test scenarios should be generated. The impact on the final result of the bias due to the generated test data should be quantified as well as a feasible strategy to minimize this effect.