Optimal choice among a class of nonparametric estimators of the jump rate for piecewise-deterministic Markov processes

A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times. We focus on the nonparametric estimation problem of the jump rate for such a stochastic model observed within a long time interval under an ergodicity condition. We introduce an uncountable class (indexed by the deterministic flow) of recursive kernel estimates of the jump rate and we establish their strong pointwise consistency as well as their asymptotic normality. We propose to choose among this class the estimator with the minimal variance, which is unfortunately unknown and thus remains to be estimated. We also discuss the choice of the bandwidth parameters by cross-validation methods.Comment: 36 pages, 18 figure

SemiMarkov: An R Package for Parametric Estimation in Multi-State Semi-Markov Models

Multi-state models provide a relevant tool for studying the observations of a continuoustime process at arbitrary times. Markov models are often considered even if semi-Markov are better adapted in various situations. Such models are still not frequently applied mainly due to lack of available software. We have developed the R package SemiMarkov to fit homogeneous semi-Markov models to longitudinal data. The package performs maximum likelihood estimation in a parametric framework where the distributions of the sojourn times can be chosen between exponential, Weibull or exponentiated Weibull. The package computes and displays the hazard rates of sojourn times and the hazard rates of the semi-Markov process. The effects of covariates can be studied with a Cox proportional hazards model for the sojourn times distributions. The number of covariates and the distribution of sojourn times can be specified for each possible transition providing a great flexibility in a model’s definition. This article presents parametric semi-Markov models and gives a detailed description of the package together with an application to asthma control

Optimal test case selection for multi-component software system

The omnipresence of software has forced upon the industry to produce efficient software in a short time. These requirements can be met by code reusability and software testing. Code reusability is achieved by developing software as components/modules rather than a single block. Software coding teams are becoming large to satiate the need of massive requirements. Large teams could work easily if software is developed in a modular fashion. It would be pointless to have software that would crash often. Testing makes the software more reliable. Modularity and reliability is the need of the day. Testing is usually carried out using test cases that target a class of software faults or a specific module. Usage of different test cases has an idiosyncratic effect on the reliability of the software system. Proposed research develops a model to determine the optimal test case policy selection that considers a modular software system with specific test cases in a stipulated testing time. The proposed model, models the failure behavior of each component using a conditional NHPP (Non-homogeneous Poisson process) and the interactions of the components by a CTMC (continuous time Markov chain). The initial number of bugs and the bug detection rate are known distributions. Dynamic programming is used as a tool in determining the optimal test case policy. The complete model is simulated using Matlab. The Markov decision process is computationally intensive but the implementation of the algorithm is meticulously optimized to eliminate repeat calculations. This has saved roughly 25-40% in processing time for different variations of the problem

Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields

This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners

Detecting Turning Points with Many Predictors through Hidden Markov Models

This paper explores the American business cycle with the Hidden Markov Model (HMM) as a monitoring tool using monthly data. It exhibits ten US time series which offer reliable information to detect recessions in real time. It also proposes and assesses the performances of different and complementary “recession models” based on Markovian processes, discusses the most efficient and easiest way of encompassing information through these models and draws three main conclusions: simple HMM are decisive to monitor the business cycle and some series are proved highly reliable; more sophisticated models such as the Dynamic Factor with Markov Switching (DFMS) model or Stock and Watson’s Experimental Recession Index seem not to be more powerful than simple (univariate or pseudo-multivariate) Hidden Markov Models, which remain far more parsimonious; combining information in temporal space seems to work marginally better than in probability space for high frequency data. We conclude about leading and “real time detection” properties related to HMM and give some hints for further research.Business Cycle, Markov Switching, Dynamic Factor, Coincident Indicators

Supporting group maintenance through prognostics-enhanced dynamic dependability prediction

Condition-based maintenance strategies adapt maintenance planning through the integration of online condition monitoring of assets. The accuracy and cost-effectiveness of these strategies can be improved by integrating prognostics predictions and grouping maintenance actions respectively. In complex industrial systems, however, effective condition-based maintenance is intricate. Such systems are comprised of repairable assets which can fail in different ways, with various effects, and typically governed by dynamics which include time-dependent and conditional events. In this context, system reliability prediction is complex and effective maintenance planning is virtually impossible prior to system deployment and hard even in the case of condition-based maintenance. Addressing these issues, this paper presents an online system maintenance method that takes into account the system dynamics. The method employs an online predictive diagnosis algorithm to distinguish between critical and non-critical assets. A prognostics-updated method for predicting the system health is then employed to yield well-informed, more accurate, condition-based suggestions for the maintenance of critical assets and for the group-based reactive repair of non-critical assets. The cost-effectiveness of the approach is discussed in a case study from the power industry

Remaining useful life estimation in heterogeneous fleets working under variable operating conditions

The availability of condition monitoring data for large fleets of similar equipment motivates the development of data-driven prognostic approaches that capitalize on the information contained in such data to estimate equipment Remaining Useful Life (RUL). A main difficulty is that the fleet of equipment typically experiences different operating conditions, which influence both the condition monitoring data and the degradation processes that physically determine the RUL. We propose an approach for RUL estimation from heterogeneous fleet data based on three phases: firstly, the degradation levels (states) of an homogeneous discrete-time finite-state semi-markov model are identified by resorting to an unsupervised ensemble clustering approach. Then, the parameters of the discrete Weibull distributions describing the transitions among the states and their uncertainties are inferred by resorting to the Maximum Likelihood Estimation (MLE) method and to the Fisher Information Matrix (FIM), respectively. Finally, the inferred degradation model is used to estimate the RUL of fleet equipment by direct Monte Carlo (MC) simulation. The proposed approach is applied to two case studies regarding heterogeneous fleets of aluminium electrolytic capacitors and turbofan engines. Results show the effectiveness of the proposed approach in predicting the RUL and its superiority compared to a fuzzy similarity-based approach of literature