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The aim of this article is double: propose a methodology for a probabilistic prognosis, and examine how the prognosis result impacts the maintenance process. First, the prognosis problem is mathematically defined: it consists in computing the distribution of the remaining useful life of the system conditionally to on-line available information. Considering online information allows to provide a specific prognosis for each system according to its life. Second, a global methodology is proposed when the state of the system and its degradations are modeled using a Markov process. This method is basically a two-step technique. On one hand, it requires the computation of the conditional law of the system regarding the available observations. On the other hand, it involves the computation of the reliability of the system. Some reliability computation techniques are proposed when the Markov process is a piecewise deterministic Markov process. The method is illustrated on an aeronautic example: a pneumatic valve within the bleed air system, used to provide regulated air (pressure, temperature) in the cabin. Eventually, the prognosis result is used to help maintenance optimization on an illustrative example. It highlights that the prognosis mainly improves the maintenance decision if the on-line available information is accurate enough.

This article presents prognosis implementation from an industrial perspective. From the description of a use-case (available information, data, expertise, objective, expected performance indicators, etc.), an engineer should be able to select easily, among the large variety of prognosis methods, the ones that are compatible with his objectives and means. Many classifications of prognosis methods have already been published but they focus more on the techniques that are involved (physical model, statistical model, data-based model, ...) than on the necessary inputs to build/learn the model and/or run it and the expected outputs. This paper presents the different strategies of maintenance and the place of prognostics in these strategies. The life cycle of a prognosis function is described, which helps to define relevant, yet certainly not complete, characteristics of prognosis problems and methods. Depending on the maintenance strategy, the prognosis function will not be used at the same step and with different objectives. Two different steps of use are defined when using the prognosis function: evaluation of the current state and prediction of the prognosis output. This paper gives also some elements of classification that will help an engineer choose the appropriate class of methods to use to solve a prognosis problem.The paper also illustrates on one example the fact that, depending on the information at hand, the prognosis method chosen is different.

This paper proposes a way to determine the quality and the amount of available information on a prognosis. For this purpose, a generic probabilistic model of the evolution of dynamic systems, called Piecewise Deterministic Markov Process (PDMP) is proposed and described. Prognosis consists in the computation of the Remaining Useful Life (RUL) of a system, which is defined thereafter for repairable systems. The way information plays a role into RUL is described as well. Then a criterion is proposed to calculate the impact of information on the use of RUL, especially for systems design. The methodology is illustrated with a BLEED system, simplified to allow analytical results. It details the calculation process and highlights where results are most influenced by the information. For future research, this methodology could be applied on more complex models and/or with other criterion, especially to see the interaction with simulation. INDUSTRIAL CONTEXTMaintenance optimization in aeronautic is a major issue because it is at the crossroad of both economical and ecological considerations. Unscheduled maintenance induces a significant cost to airlines and may lead to unnecessary replacements of pieces of equipment. In order to avoid it, prognosis emerges as a key research theme. Prognosis could be considered at different levels: for systems (aircraft), sub-systems (e.g. air system) or components. At systems level, the focus is on functional properties, regardless of the physical degradation of the system. A deterministic degradation model can be reached at component level.The expected outcome of prognosis is often the same for industrial applications. To organize the maintenance, the needed information is the remaining time before the item fails, or is irremediably damaged. This period of time is termed "Remaining Useful Life (RUL)". It represents the time before an item reaches an undesirable state.The estimation of this quantity depends on the information in our possession. This information can concern the item, its past, its current state, its degradation process as well as the future conditions it will evolve in. More information leads to a more accurate prognosis. Moreover, an accurate prognosis yields to a bigger reduction of the maintenance costs. However, each piece of information has a cost.The prognosis approach in industry then implies a tradeoff between the information costs and the maintenance costs.A key issue is the impact of more information on the calculation of the RUL. Understanding this impact will help to decide which investment should be done.Prognosis in industry is then an important research topic which raises many questions: how to find a suitable model for each level (system, subsystem, and component), how to define properly the RUL and how to quantify the impact of information on the prognosis? SYSTEM MODELLINGThe underlying idea behind prognosis is straightforward: the ability to predict the future state of an item before its actual failure will allow the planning of appropriate maintenance ...