RESUMEN
Control charts have been used to monitor product manufacturing processes for decades. The exponential distribution is commonly used to fit data in research related to healthcare and product lifetime. This study proposes an exponentially weighted moving average control chart with a variable sampling interval scheme to monitor the exponential process, denoted as a VSIEWMA-exp chart. The performance measures are investigated using the Markov chain method. In addition, an algorithm to obtain the optimal parameters of the model is proposed. We compared the proposed control chart with other competitors, and the results showed that our proposed method outperformed other competitors. Finally, an illustrative example with the data concerning urinary tract infections is presented.
RESUMEN
Measurement errors are inevitable in practice, but they are not considered in the existing process performance index. Therefore, we propose an estimation method of process performance index for the two-parameter exponential distribution with measurement errors to fill this gap. In this paper, the relationship between the unobservable actual value and measurement value is considered as full error model, and the maximum likelihood estimation method is considered to obtain the unknown parameters. In addition, we also use the Bootstrap method to construct confidence intervals of process performance index. The performance of the proposed estimation is investigated in terms of bias, mean square error (MSE) and average interval length. Simulation results show that the proposed estimator outperforms other estimators. Finally, an example of the mileage data of the military personnel carrier is given to illustrate the implementation of the proposed estimation method.
RESUMEN
When the binary response variable contains an excess of zero counts, the data are imbalanced. Imbalanced data cause trouble for binary classification. To simplify the numerical computation to obtain the maximum likelihood estimators of the zero-inflated Bernoulli (ZIBer) model parameters with imbalanced data, an expectation-maximization (EM) algorithm is proposed to derive the maximum likelihood estimates of the model parameters. The logistic regression model links the Bernoulli probabilities with the covariates in the ZIBer model, and the prediction performance among the ZIBer model, LightGBM, and artificial neural network (ANN) procedures is compared by Monte Carlo simulation. The results show that no method can dominate the other methods regarding predictive performance under the imbalanced data. The LightGBM and ZIBer models are more competitive than the ANN model for zero-inflated-imbalanced data sets.
