Jacques de Maré

A Robustness Approach to Reliability

Reliability of products is here regarded with respect to failure avoidance rather than probability of failure. To avoid failures, we emphasize variation and suggest some powerful tools for handling failures due to variation. Thus, instead of technical calculation of probabilities from data that usually are too weak for correct results, we emphasize the statistical thinking that puts the designers focus on the critical product functions. Making the design insensitive to unavoidable variation is called robust design and is handled by (i) identification and classification of variation, (ii) design of experiments to find robust solutions, and (iii) statistically based estimations of proper safety margins. Extensions of the classical failure mode and effect analysis (FMEA) are presented. The first extension consists of identifying failure modes caused by variation in the traditional bottom–up FMEA analysis. The second variation mode and effect analysis (VMEA) is a top–down analysis, taking the product characteristics as a starting point and analyzing how sensitive these characteristics are to variation. In cases when there is sufficient detailed information of potential failure causes, the VMEA can be applied in its most advanced mode, the probabilistic VMEA. Variation is then measured as statistical standard deviations, and sensitivities are measured as partial derivatives. This method gives the opportunity to dimension tolerances and safety margins to avoid failures caused by both unavoidable variation and lack of knowledge regarding failure processes.

Random Features of the Fatigue Limit

The classical fatigue limit is often an important characteristic in fatigue design regarding metallic material. The limit is usually obtained from a staircase test in combination with some assumption about the statistical distribution of the limit. This distribution can be of a normal, log-normal or of extreme value type and no particular physical argument gives favor to any specific distribution. This leads to a certain ambiguity in the evaluation of test results which forces the designer to introduce large safety factors. In order to find a physically based statistical distribution for use in staircase tests to determine the fatigue limit we present here a random model for the fatigue limit based on the following assumptions; (i) The square root area model according to Murakami and co-workers is valid, (ii) the randomness in the fatigue limit is induced by the randomness of the maximum defect size, (iii) the random maximum defect size has an extreme value distribution of Gumbel type. This leads to the fatigue limit distribution based on Gumbel (FLG), which is recommended to replace the normal distribution in the evaluation of staircase fatigue tests in case of hard materials. It turns out that the skewness of the resulting distribution depends on the coefficient of variation; with a normal-like non-skewed distribution at the coefficient of variation of five percent.

Variation mode and effect analysis: an application to fatigue life prediction

We 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 around the nominal values with respect to the main influencing variables, while second moment means that only means and variances are taken into account in the statistical procedure. We study the fatigue life of a jet engine component and aim at a safety margin that takes all sources of prediction 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 variations. Other uncertainties are 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 treating also systematic errors as random variables, the whole safety margin problem is put into a common framework of second-order statistics. The final estimated prediction variance of the logarithmic life is obtained by summing the variance contributions of all sources of scatter and other uncertainties, 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.

Tension distribution in multiple V-belt drives

Determination of the tension distribution in a multiple V-belt drive represents a statically indeterminate problem. The analysis can be split into four parts viz: initial tension, torque transmission, tension distribution and statistics. Here a unified theory is presented based on reasonable assumptions. Focus is directed to the maximum belt tension. Simulations have been performed with measured data. Non-linearities caused by gross slip seem to have a minor influence. A simple approximation is presented which sufficiently well fits the simulated results.

Generation of random processes for fatigue testing

In fatigue testing there is a need to generate multivariate random processes meeting certain conditions on distributions, crossing properties and regularity. In this paper it is demonstrated how these conditions can be satisfied. The required process is generated by a random time deformation working on a Gaussian process.

Maintenance for reliability—a case study

The optimal replacement problem for components with stochastic lives has an appealing solution based on the TTT-transform. The issue is revisited for components which are regularly inspected and where statistical uncertainties are taken into account by means of the method of predicted profile likelihood.The ideas are applied on crack growth data on a low pressure nozzle in a jet engine. It turns out that the standard method is not directly applicable and that the effect of uncertainties on the replacement times is not easy to predict.

The behaviour of a non-differentiable stationary Gaussian process after a level crossing☆

A model process is obtained for the behaviour of a non-differentiable but continuous stationary Gaussian process after a level crossing. It is shown that the sampled process conditioned on a crossing of a fixed level in Slepians sense, converges weakly towards the model process, when the sample distance decreases to zero. Further it is noticed that there is no difference between conditioning on a vertical window and on a horizontal window in this case.

An Approach to Multidimensional Equivalent Fatigue Loadings

In the automotive industry, temporal, financial and human constraints require continuous improvements in the design process of new vehicles, by delivering relevant specifications and providing reliability and robustness in design. In order to analyze factors like behaviors of drivers and types of roads and guarantee the reliability of car components, measurements of forces from wheels are stored when the vehicle is tested on tracks and used by customers. The measurements represent the time history of multi-dimensional forces on the four wheels in the longitudinal, vertical and transversal directions. They are applied on structures (suspensions or motoring for instance) during the design life of the vehicles. The context of this paper is the fatigue analysis of multi-input loadings. The study will be focused on random and possibly correlated multi-input processes, representing multidimensional forces. The goal of this paper is to present an approach to generate simple multi-input loadings equivalent to measurements in terms of damage. The simple loadings have to be equivalent for any arbitrary structure, satisfying the reliability requirements imposed by the car manufacturer.© 2005 ASME