ABSTRACT

In the field of industrial applications, the development of reliability technique implies the utilization of models which are able to represent a wide range of physical phenomena, in particular the phenomena that govern component wear.

In excluding the hypothesis of sudden failure caused by applying an excessive stress, a component well adapted to its working environment will be affected by a progressive reduction of its mechanical strength until a certain threshold of failure is reached.

If the utilization of common models (e.g. Weibull, Gamma, Log.Normal…) allows to correctly represent certain observed situations, the reliability forecasting is a rather difficult practice because the stresses often deviate from standard values and are affected by inevitable uncertainty.

It is proposed here to state the origin of a probability model of component wear which takes into account physical mechanism of degradation and random stresses applied to a component. Within the limitations of normal application of the model, the component undergoes an elementary damage corresponding to each discrete stress. Failure appears as soon as the accumulation of the stresses reaches a determined threshold, i.e. additive property well verified in practice.

The elementary damage is a non-linear function of energy applied to the component of each stress. This energy is defined by a multiplicative property, namely the product of amplitude by deviation of each stress.

The occurence of the stresses with respect to time obeys a homogeneous Poisson process. The amplitude and duration distributions are of independant Log-Normal distribution. The distribution of cumulative damage is consequently defined by the sum of a random number of the random elementary damages. Failure is reached when the probable damage exceeds the fixed threshold of strength.

This model, initially developped for the study of reliability forecasting of electrical protection components (e.g. overvoltage and overcurrent limiting devices) is in fact, characterized by a higher generality, because many components (electrical, electro-mechanical or mechanical components) are degraded by the accumulation of stresses which are randomly exerted on them during their life time.

Current presentation of the model leads to some analytical results that allow to delimitate the influence of component parameters (i.e. strength) and its environment (i.e. stresses undergone).

The hypotheses adopted correspond to the previous examples of application and cannot satisfy all possible situations. However, the hypotheses were further extended in order to take into account particular cases without lose the advantages of analytical analysis (i.e. amplitude -duration dependance of stresses, randomness of occurence rate and strength).