An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains

In many applications, the failure rate function may present a bathtub shape curve. In this paper, an expectation maximization algorithm is proposed to construct a suitable continuous-time Markov chain which models the failure time data by the first time reaching the absorbing state. Assume that a system is described by methods of supplementary variables, the device of stage, and so on. Given a data set, the maximum likelihood estimators of the initial distribution and the infinitesimal transition rates of the Markov chain can be obtained by our novel algorithm. Suppose that there are m transient states in the system and that there are n failure time data. The devised algorithm only needs to compute the exponential of m×m upper triangular matrices for O(nm2) times in each iteration. Finally, the algorithm is applied to two real data sets, which indicates the practicality and efficiency of our algorithm

A Poisson-Fault Model for Testing Power Transformers in Service

This paper presents a method for assessing the instant failure rate of a power transformer under different working conditions. The method can be applied to a dataset of a power transformer under periodic inspections and maintenance. We use a Poisson-fault model to describe failures of a power transformer. When investigating a Bayes estimate of the instant failure rate under the model, we find that complexities of a classical method and a Monte Carlo simulation are unacceptable. Through establishing a new filtered estimate of Poisson process observations, we propose a quick algorithm of the Bayes estimate of the instant failure rate. The proposed algorithm is tested by simulation datasets of a power transformer. For these datasets, the proposed estimators of parameters of the model have better performance than other estimators. The simulation results reveal the suggested algorithms are quickest among three candidates

A screened predictive model for esophageal squamous cell carcinoma based on salivary flora data

Esophageal squamous cell carcinoma (ESCC) is a malignant tumor of the digestive system in the esophageal squamous epithelium. Many studies have linked esophageal cancer (EC) to the imbalance of oral microecology. In this work, different machine learning (ML) models including Random Forest (RF), Gaussian mixture model (GMM), K-nearest neighbor (KNN), logistic regression (LR), support vector machine (SVM) and extreme gradient boosting (XGBoost) based on Genetic Algorithm (GA) optimization was developed to predict the relationship between salivary flora and ESCC by combining the relative abundance data of Bacteroides, Firmicutes, Proteobacteria, Fusobacteria and Actinobacteria in the saliva of patients with ESCC and healthy control. The results showed that the XGBoost model without parameter optimization performed best on the entire dataset for ESCC diagnosis by cross-validation (Accuracy = 73.50%). Accuracy and the other evaluation indicators, including Precision, Recall, F1-score and the area under curve (AUC) of the receiver operating characteristic (ROC), revealed XGBoost optimized by the GA (GA-XGBoost) achieved the best outcome on the testing set (Accuracy = 89.88%, Precision = 89.43%, Recall = 90.75%, F1-score = 90.09%, AUC = 0.97). The predictive ability of GA-XGBoost was validated in phylum-level salivary microbiota data from ESCC patients and controls in an external cohort. The results obtained in this validation (Accuracy = 70.60%, Precision = 46.00%, Recall = 90.55%, F1-score = 61.01%) illustrate the reliability of the predictive performance of the model. The feature importance rankings obtained by XGBoost indicate that Bacteroides and Actinobacteria are the two most important factors in predicting ESCC. Based on these results, GA-XGBoost can predict and diagnose ESCC according to the relative abundance of salivary flora, providing an effective tool for the non-invasive prediction of esophageal malignancies

Parameter Estimation of a Multistate Model for an Aging Piece of Equipment under Condition-Based Maintenance

We study a multistate model for an aging piece of equipment under condition-based maintenance and apply an expectation maximization algorithm to obtain maximum likelihood estimates of the model parameters. Because of the monitoring discontinuity, we cannot observe any state's duration. The observation consists of the equipment's state at an inspection or right after a repair. Based on a proper construction of stochastic processes involved in the model, calculation of some probabilities and expectations becomes tractable. Using these probabilities and expectations, we can apply an expectation maximization algorithm to estimate the parameters in the model. We carry out simulation studies to test the accuracy and the efficiency of the algorithm

Insurance claims modulated by a hidden Brownian marked point process

Aimed at better modeling insurance claims in an economic environment driven by business cycles, a new Markov-modulated Poisson process model is proposed, and an algorithm is derived to estimate the hidden Markov process by using the observed information. Our method differs from existing ones in the following ways: the new hidden process can model more efficiently the cyclic state of the economic environment; our theory is based on a variation of the law of large numbers and is easy to understand; the Fourier expansion-based parameter estimation algorithm is flexible and can be more easily implemented than other algorithms. Simulation results not only demonstrate the practicality of our model and algorithm, but also show the efficiency and robustness of the estimation algorithm.Insurance risk models Markov-modulated Poisson processes Brownian motion Reference probability