Pär Johannesson, Fraunhofer-Chalmers Research Centre for Industrial Mathematics

Variation Mode and Effect Analysis:
A Case Study of an Air Engine Component




Abstract

We will present an application of the probabilistic branch of
Variation Mode and Effect Analysis (VMEA) implemented as a first
order, second moment reliability method.  First order means that the
failure function is approximated to be linear with respect to the main
influencing variables, second moment means that only means and
variances are taken into account in the statistical procedure.

We study the fatigue life of an air engine component and aim at a
safety margin that takes all scatter and uncertainties into account.
Scatter is defined as random variation due to natural causes, such as
non-homogeneous material, geometry variation within tolerances, load
variation in usage, and other uncontrolled variation.  Uncertainty is
defined as unknown systematic errors, such as model errors in the
numerical calculation of fatigue life, statistical errors in estimates
of parameters, and unknown usage profile.

By defining also uncertainties as random variables, the whole safety
margin problem is put into a common framework of second order
statistics, with the Gauss' approximation formula as the main tool.
By using a simple log transformation, the failure function is regarded
as linear enough for a proper estimate of the scatter and uncertainty
contributions based on the first order approximation.

Thus, the final estimated variance of the logarithmic life is obtained
through summing the variance contributions of all sources of scatter
and uncertainty, and it represents the total uncertainty in the life
prediction.  Motivated by the central limit theorem this logarithmic
life random variable may be regarded as normally distributed, which
gives possibilities to calculate relevant safety margins that, in
turn, is transformed back to fatigue life margins for comparisons with
demands.