Predictive maintenance for the heated hold-up tank

We present a numerical method to compute an optimal maintenance date for the test case of the heated hold-up tank. The system consists of a tank containing a fluid whose level is controlled by three components: two inlet pumps and one outlet valve. A thermal power source heats up the fluid. The failure rates of the components depends on the temperature, the position of the three components monitors the liquid level in the tank and the liquid level determines the temperature. Therefore, this system can be modeled by a hybrid process where the discrete (components) and continuous (level, temperature) parts interact in a closed loop. We model the system by a piecewise deterministic Markov process, propose and implement a numerical method to compute the optimal maintenance date to repair the components before the total failure of the system.Comment: arXiv admin note: text overlap with arXiv:1101.174

Full vs. no information best choice game with finite horizon

Let us consider two companies A and B. Both of them are interested in buying a set of some goods. The company A is a big corporation and it knows the actual value of the good on the market and is able to observe the previous values of them. The company B has no information about the actual value of the good but it can compare the actual position of the good on the market with the previous position of the good offered. Both of the players want to choose the very best object overall. The recall is not allowed. The number of the objects is fixed and finite. One can think about these two types of buyers a business customer vs. an individual customer. The mathematical model of the competition between them is presented and the solution is defined and constructed.Comment: Submitted to: Stochastic Operations Research in Business and Industry (eds. by Tadashi Dohi, Katsunori Ano and Shoji Kasahara), World Scientific Publishe

Sequential change-point detection when unknown parameters are present in the pre-change distribution

In the sequential change-point detection literature, most research specifies a required frequency of false alarms at a given pre-change distribution $f_{\theta}$ and tries to minimize the detection delay for every possible post-change distribution $g_{\lambda}$. In this paper, motivated by a number of practical examples, we first consider the reverse question by specifying a required detection delay at a given post-change distribution and trying to minimize the frequency of false alarms for every possible pre-change distribution $f_{\theta}$. We present asymptotically optimal procedures for one-parameter exponential families. Next, we develop a general theory for change-point problems when both the pre-change distribution $f_{\theta}$ and the post-change distribution $g_{\lambda}$ involve unknown parameters. We also apply our approach to the special case of detecting shifts in the mean of independent normal observations.Comment: Published at http://dx.doi.org/10.1214/009053605000000859 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bayesian subset simulation

We consider the problem of estimating a probability of failure $\alpha$, defined as the volume of the excursion set of a function $f:\mathbb{X} \subseteq \mathbb{R}^{d} \to \mathbb{R}$ above a given threshold, under a given probability measure on $\mathbb{X}$. In this article, we combine the popular subset simulation algorithm (Au and Beck, Probab. Eng. Mech. 2001) and our sequential Bayesian approach for the estimation of a probability of failure (Bect, Ginsbourger, Li, Picheny and Vazquez, Stat. Comput. 2012). This makes it possible to estimate $\alpha$ when the number of evaluations of $f$ is very limited and $\alpha$ is very small. The resulting algorithm is called Bayesian subset simulation (BSS). A key idea, as in the subset simulation algorithm, is to estimate the probabilities of a sequence of excursion sets of $f$ above intermediate thresholds, using a sequential Monte Carlo (SMC) approach. A Gaussian process prior on $f$ is used to define the sequence of densities targeted by the SMC algorithm, and drive the selection of evaluation points of $f$ to estimate the intermediate probabilities. Adaptive procedures are proposed to determine the intermediate thresholds and the number of evaluations to be carried out at each stage of the algorithm. Numerical experiments illustrate that BSS achieves significant savings in the number of function evaluations with respect to other Monte Carlo approaches

Extrinsic Jensen-Shannon Divergence: Applications to Variable-Length Coding

This paper considers the problem of variable-length coding over a discrete memoryless channel (DMC) with noiseless feedback. The paper provides a stochastic control view of the problem whose solution is analyzed via a newly proposed symmetrized divergence, termed extrinsic Jensen-Shannon (EJS) divergence. It is shown that strictly positive lower bounds on EJS divergence provide non-asymptotic upper bounds on the expected code length. The paper presents strictly positive lower bounds on EJS divergence, and hence non-asymptotic upper bounds on the expected code length, for the following two coding schemes: variable-length posterior matching and MaxEJS coding scheme which is based on a greedy maximization of the EJS divergence. As an asymptotic corollary of the main results, this paper also provides a rate-reliability test. Variable-length coding schemes that satisfy the condition(s) of the test for parameters $R$ and $E$, are guaranteed to achieve rate $R$ and error exponent $E$. The results are specialized for posterior matching and MaxEJS to obtain deterministic one-phase coding schemes achieving capacity and optimal error exponent. For the special case of symmetric binary-input channels, simpler deterministic schemes of optimal performance are proposed and analyzed.Comment: 17 pages (two-column), 4 figures, to appear in IEEE Transactions on Information Theor