Mihaela Barreau

Bayesian estimation in accelerated life testing

A common problem of high-reliability computing is, on the one hand, the magnitude of total testing time required, particularly in the case of high-reliability components; and, on the other hand, the number of devices under testing. In both cases, the objective is to minimise the costs involved in testing without reducing the quality of the data obtained. One solution is based on Accelerated Life Testing (ALT) techniques which permit decreasing the testing time. Another solution is to incorporate prior beliefs, engineering experience, or previous data into the testing framework. It is in this spirit that the use of a Bayesian approach can, in many cases, significantly reduce the number of devices required. This paper presents a study of the Arrhenius-Exponential model by an evaluation of parameters using Maximum Likelihood (ML) and Bayesian methods. A Monte Carlo simulation is performed to examine the asymptotic behaviour of these different estimators.

Reliability analysis of mechatronic systems using censored data and petri nets: application on an antilock brake system (abs)

Reliability estimation is becoming established as an important issue of the design process of mechatronic systems (i.e. systems involving in their implementation more basic technologies, such as mechanics, electronics and software). We propose to estimate the mechatronic system reliability using stochastic Petri Nets. The failure times are simulated in the Petri Nets model integrating the reliability of the components of the mechatronic system. The reliability is estimated from simulated failure times by using the Maximum Likelihood method. The paper is illustrated by an application example on ABS system. This paper presents the results of a co-operational work, getting together mechanical, electronic, and software engineers. The proposed method allows reliability evaluating both for n mechatronic systems and for their different sub-systems. An application to a vehicle Antilock Brake System (ABS) illustrates this method. We model the mechanical, electronic and embedded software sub-systems, to design, to check and to estimate the reliability of the ABS. Reliability evaluation of mechatronic systems requires the modeling of failure behavior of different components. We propose to evaluate mechatronic systems reliability using censored data. By using the failure times of the system, we compute the values of the parameters for all the components by maximum likelihood estimator with censored times

Bayesian Estimation of Degradation Model Defined by a Wiener Process

The constantly increasing market request of high quality vehicles ask the automotive manufacturers to perform lifetime testing in order to verify the reliability levels of new products. In this paper, we deal with two difficulties in reliability assessment for mechanical parts. On one hand, there is the small number of parts available for testing. On the other hand, there is the problem of wear. In the automotive applications, mechanical components subjected to relative motion of parts have to be designed against wear. In this paper, the Bayesian estimation of Wiener process parameters (usually used to define the degradation process) is studied to improve the estimation accuracy in incorporating the available knowledge on the product. In particular, the finite element results and expert knowledge are considered as “a priori”. For wear prediction by FEM, a model based on Archard law was developed for the brake disc wear.

Reliability assessment of mechatronic systems: operating field data analysis

The reliability analysis of complex mechatronic systems is a very important engineering issue, in order to guarantee their functional behavior. We propose the evaluation of mechatronic systems reliability using censored data for operating field for different technologies, e.g. mechanics, electronics, and software. For ultra reliable system for which we have little data, we use an estimation method, stochastic expectation maximization (SEM), to increase the evaluation accuracy. The SEM method is used to estimate the reliability parameters with better accuracy than with maximization likelihood method.

Dependability analysis of complex mechatronic systems

Abstract The dependability analysis of complex mechatronic systems is a very important engineering issue, in order to guarantee their functional behavior. Most of the critical failures are generated by the interactions between the sub-systems, implemented in different technologies, e.g. mechanics, electronics, and software. Therefore, the analysis of the system as a whole is not enough and it becomes necessary to study all the interactions in order to estimate the systems dependability.

Safety driven optimization approach for automotive systems

In this paper, we propose an approach for system design and architecture optimization driven by safety and cost constraints. It consists of an architecture synthesis and mapping approach that takes into account the safety constraints in the ISO 26262 context. It allows, at one hand, to reach a system preliminary architecture by choosing the best component that reduce the overall cost. On the other hand, it leads to a mapping that respects the safety constraints related to safety levels and to dependent failures. We use exhaustive and genetic algorithm based approaches for the optimization. The use of these two approaches depends on the size of the considered problem. We demonstrate that these approaches can be used efficiently to reach an optimal design.

Bayesian estimation of degradation model defined by a Wiener process - Application on disc brake wear

Abstract The constantly increasing market request of high quality vehicles ask the automotive manufacturers to perform lifetime testing in order to verify the reliability levels of new products. In this paper, we deal with two difficulties in reliability assessment for mechanical parts. On one hand, there is the small number of parts available for testing. On the other hand, there is the problem of wear. In the automotive applications, mechanical components subjected to relative motion of parts have to be designed against wear. In this paper, the Bayesian estimation of Wiener process parameters (usually used to define the degradation process) is studied to improve the estimation accuracy in incorporating the available knowledge on the product. In particular, the finite element results and expert knowledge are considered as “a priori”. For wear prediction by FEM, a model based on Archard law was developed for the brake disc wear.

Bayesian Estimation of Failure Probability in Mechanical Systems Using Monte Carlo Simulation

Abstract This article presents a method allowing to integrate the prior knowledge on mechanical component in the failure probability estimation. The proposed method uses the Bayesian method and the Monte-Carlo results obtained by 3 kinds of simulation : Direct, Importance sampling and Conditional expectation. Different methods of prior distribution definition, which is needed for Bayesian inference, are presented using all available information concerning the studied system (First Order Reliability Method (FORM), First Order Second Moment (FOSM), Reliability handbook, …). Two examples illustrate the method and show its efficiency.

MC/DC Test Case Generation Approaches for Decisions

Modified Condition/Decision Coverage (MC/DC) is a structural coverage criterion that aims to prove that all conditions involved in a Boolean expression (decision) can influence the result of that expression. In the context of aeronautic and automotive, MC/DC is highly recommended and even required for most critical applications structural coverage. However, due to complex decision that are often embedded in those applications, generating a set of MC/DC compliant test cases for any of these decisions is a non trivial and time consuming task for testers. In this paper we present an early work of an approach to automatically generate MC/DC test cases for different kinds of decisions. Thus, we introduce three different techniques to deal with MC/DC test case generation for decisions.

Bayesian Parameter Estimation with Prior Weighting in ALT Model

Abstract This paper provides an overview of the application of Bayesian inference to accelerated life testing (ALT) models for the concrete case of estimation by Maximum of Aposteriori (MAP) method in the case of constant stress levels. It studies the Bayesian inference over the accelerated life model as presented in [9]. It suites, integrates and generalizes the particular cases presented in [12] and [13]. Towards the end, weighting of the prior information according to data is integrated. The paper also illustrates an experimental example.