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This paper is devoted to the iterative interval estimation for nonlinear discrete-time systems. To reconstruct the system state, a sequence of iterative observers is established based on the iterative disturbance estimation and measured output. By means of the Lipschitz condition and H ∞ technique, sufficient conditions are built by the Lyapunov function method to make observation errors convergent. Resorting to the zonotope-based reachability analysis, the reachable set of nonlinear terms and observation errors are analyzed such that the state interval can be supplied. The presented approach is validated by a simulation comparison. [ABSTRACT FROM AUTHOR]

In this paper, a fault diagnosis method for the basic process of microbial growth in wastewater treatment based on interval estimation technology is proposed. First, a nonlinear microbial growth model is converted into a linear time‐varying system. A time‐varying observer is then designed for the generated system, which takes into account an L∞$$ {L}_{\infty } $$ performance. Furthermore, a zonotope‐based set‐membership estimation algorithm is analyzed to synchronize interval estimation operations. In addition, interval residuals are computed from the generated interval state estimation and fault diagnosis is performed for a wastewater treatment bioprocess with sensor fault signals. Finally, the feasibility of the proposed fault diagnosis strategy for the wastewater treatment bioprocess is illustrated through numerical simulations. [ABSTRACT FROM AUTHOR]

This article presents a study of interval estimation approach based on functional interval observers for mecanum‐wheels omnidirectional automated guided vehicle (MOAGV). In the context of MOAGV, the nonlinear system in discrete time incorporates model uncertainty and unknown bounded disturbances. A functional observer is developed by integrating terminal sliding mode and H∞$$ {H}_{\infty } $$ techniques, aiming to reduce the impact of lumped disturbances/uncertainties. Additionally, a novel observer structure is introduced to increase the degrees of freedom in the design process. Subsequently, the linear function bounds are obtained using the reachability analysis of the estimation error. Finally, the performance of the improved functional interval observer is demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract–The Weibull distribution is the most applied model in reliability field for lifetime analysis. The Weibull location parameter, characterizing the minimum possible life, plays a significant role in engineering applications. In this paper, we consider the interval estimation on the location parameter when the product's lifetime follows the three-parameter Weibull distribution with a known shape parameter. A novel approach based on the relationship between the minimum order statistics, the location parameter, and the sample size is developed to construct confidence intervals for the Weibull location parameter. Thereafter, we compare it with other two interval estimation approaches by the performances of the coverage probability and the average length via simulations and a real application. The results show that the proposed method outperforms the pivot quantity (PQ) method and the bias-corrected and accelerated (Bca) bootstrap method in small and medium samples in terms of coverage probability. [ABSTRACT FROM AUTHOR]

In order to solve the problem of strain modal identification under strain monitoring signals with poor vibration modal information, this paper proposes a strain mode identification method with statistical stability significance. This method removes noise, vehicle-induced effects, and temperature effects from the original dynamic strain signal, retaining only vibration-related components, and obtaining a statistically stable high quality bridge strain power spectrum, thereby identifying high quality strain mode parameters. Furthermore, in order to verify the confidence level of the strain modes obtained by this method, this paper adopts the interval estimation method to estimate the power spectrum, natural frequency, damping ratio, and modal shape after statistical processing. The credibility of strain modes has been estimated by interval estimation. The confidence interval of 95% confidence for each modal parameter is obtained, achieving the confidence-level evaluation of corresponding variable modal parameter identification. In response to practical engineering problems, this paper evaluates the actual bridge data of Tongji Road Bridge in Shanghai, and explains the abnormal phenomena that occurred in the data evaluation based on the measured diseases, verifying the practicality of this method. [ABSTRACT FROM AUTHOR]

In this paper, an interval estimation scheme is developed for delayed switched positive systems (DSPS) with mode-dependent average dwell time switching. A lossless zonotopic estimation approach is proposed for the delayed intersection zonotope with the positive generator matrix. First, considering the existence of asynchronism between the system mode and the correction matrix mode, the mismatched intersection zonotope is constructed for DSPS to verify the consistency between the system model and outputs. Then, by utilizing the introduced radius definitions, the ℓ∞ performance is addressed to optimize the size of delayed intersection zonotopes. Subsequently, we present a joint-design approach of switching signals and the mode-dependent correction matrix by constructing positive generator matrix-based delayed radius functions. Furthermore, guaranteed nonnegative state bounds are derived for the considered DSPS based on the proposed lossless zonotopic estimation criteria. Finally, detailed simulations are conducted to validate the feasibility and superiority of the developed methods. [ABSTRACT FROM AUTHOR]

This paper presents an effort to investigate the estimations of the Weibull distribution using an improved adaptive Type-II progressive censoring scheme. This scheme effectively guarantees that the experimental time will not exceed a pre-fixed time. The point and interval estimations using two classical estimation methods, namely maximum likelihood and maximum product of spacing, are considered to estimate the unknown parameters as well as the reliability and hazard rate functions. The approximate confidence intervals of these quantities are obtained based on the asymptotic normality of the maximum likelihood and maximum product of spacing methods. The Bayesian estimations are also considered using MCMC techniques based on the two classical approaches. An extensive simulation study is implemented to compare the performance of the different methods. Further, we propose the use of various optimality criteria to find the optimal sampling scheme. Finally, one real data set is applied to show how the proposed estimators and the optimality criteria work in real-life scenarios. The numerical outcomes demonstrated that the Bayesian estimates using the likelihood and product of spacing functions performed better than the classical estimates. [ABSTRACT FROM AUTHOR]

The family of neutrosophic distributions has received considerable attention from the scientific community, due to the flexible parametric form of its probability density function, in modeling many physical phenomena with imprecise information. In this study, we consider a generalization of Singh Maddala distribution for handling fuzzy data sets. This study presents a new research endeavor: quantifying the lifespan of manufacturing enterprises using the Neutrosophic Singh Maddala Distribution (NSMD). This work significantly enhances the theoretical foundations by providing novel formulations for the moments and mode of the NSMD distribution. In addition, it expands the study beyond the traditional Maddala model by examining conventional statistical models. For estimating the unknown parameters, the maximum likelihood estimation has been used in neutrosophic framework. Characterizations are obtained in terms of neutrosophic measures. The assessment of model performance, carried out using the goodness of fit criterion, highlights the superiority of NSMD compared to other models. In the application section, a real data on carbon emission is provided for usefulness of the proposed model. [ABSTRACT FROM AUTHOR]

This paper proposes a novel total cost model for the micro‐products' entire life cycle that takes into account the uncertainty of the model parameters. The total cost includes pre-sale manufacturing and post-sale warranty costs. Additionally, different marketing strategies are also given based on the weight of internal and external costs. Furthermore, limited data and unknown effects in experiments may cause large errors in parameter estimates. This could prevent the achievement of reliable designs. To address this, robust optimization and interval estimation are used. This approach reduces the impact of uncertainty on parameter estimates. It ensures optimality and robustness in micro-manufacturing parameters. Example analysis and numerical simulation results show that the proposed method assists companies in selecting the optimal manufacturing parameter level that aligns with their marketing strategies. Besides, considering uncertainty factors can ensure that the optimization results remain guaranteed, even under the worst-case scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we propose an Echinococcosis model with logistic growth. After giving the basic reproductive number R0, we prove that R0 can be used to govern the threshold dynamics of the model: if R0 < 1, the disease will go to extinction, while if R0 > 1, the disease will persist. Based on the data of Echinococcosis in Ürümqi, Xinjiang, China during 2006–2016, we estimate the parameters in the model and calculate that R0 = 1.42 (95% CI [0.767, 4.327]). The results show that Echinococcosis is endemic in Ürümqi, China. In addition, we obtain that MAPE = 3.54% and RMSPE = 3.87%, which indicates that the model has certain reliability and rationality. Furthermore, we carry out the sensitivity analysis of the model parameters to identify the key factors affecting the prevalence of Echinococcosis, and the effective control efforts are suggested focusing on reducing the proportion rate from sheep to dogs and increasing the recovery rate of dogs to curb the prevalence of Echinococcosis in Ürümqi, China. [ABSTRACT FROM AUTHOR]

One of the lifetime distributions is the Iwueze distribution, which is constructed by combining the exponential and gamma distributions. In this paper, confidence intervals (CIs) are proposed for the parameter of the Iwueze distribution using the likelihood-based, Wald-type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap methods. We evaluated the performance of the proposed CI methods through Monte Carlo simulation in terms of their coverage probability (CP) and average length (AL) in various scenarios. Furthermore, we had also derived the explicit formula for the Wald-type CI, which is straightforward for computation. The simulation results showed that the likelihood-based and Wald-type CIs returned satisfactory results according to coverage probabilities, even for the setting of small sample sizes. On the other hand, both the bootstrap-t and BCa bootstrap CIs yield CPs lower than the nominal confidence level when sample sizes are small. However, as the sample sizes increase, the CP of all CIs tend to approach the nominal confidence level. The parameter values also have a minor influence on the CP of all CIs when the sample size is fixed. Moreover, the AL of all CIs decreases as the sample size increases. The Wald-type and likelihood-based CIs have very similar ALs for all parameter values. In general, the bootstrap-t CI tends to yield the shortest interval. The effectiveness of all CIs was demonstrated by applying them to medical and engineering data, yielding results consistent with those of the simulation study. [ABSTRACT FROM AUTHOR]

State of health (SOH) estimation of lithium-ion (Li-ion) batteries is of great importance for battery use, maintenance, management, and economic evaluation. However, the current SOH estimation methods for Li-ion batteries are mainly targeted at specific charging strategies by using deterministic estimation models, which cannot reflect uncertain information such as randomness and fuzziness in the battery degradation process. To this end, a method for estimating the SOH interval of Li-ion batteries applicable to different charging strategies is proposed, which extracts multiple feature parameters from the cyclic charging and discharging data of batteries with different charging strategies, and automatically selects the optimal combination of feature parameters for a specific charging strategy by using the cross-validation method. In addition, considering the limited number of cycles in the whole life cycle of Li-ion batteries as a small sample, support vector quantile regression (SVQR), which integrates the advantages of support vector regression and quantile regression, is proposed for the estimation of SOH interval of lithium-ion batteries. Li-ion battery charge/discharge cycle data with deep discharge degree is selected as the training set for offline training of the SVQR model, and the trained model is used for online estimation of the SOH of Li-ion batteries of different charging strategies. The proposed method is validated using three datasets with different charging strategies. The experimental results show that the proposed method is applicable to different charging strategies and the estimation results are better than those of quantile regression, quantile regression neural network and Gaussian process regression.

Abstract.This article primarily considers the statistical inference of the scale parameter, shape parameter, and reliability of the generalized logistic distribution in both censored and uncensored cases. For the progressively Type-II censored and complete samples, the frequentist method is utilized to construct asymptotic confidence intervals, and the Bayesian inference method is employed for constructing the point estimators as well as posterior credible intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Furthermore, the non parametric generalized fiducial method is introduced to estimate the survival function. Simulation results demonstrate that the generalized fiducial method consistently outperforms other methods in terms of mean square error, average length, and empirical coverage. Finally, two real datasets are used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

This article proposes a two‐step interval estimation method for continuous‐time linear time‐invariant systems with unknown but bounded disturbances and measurement noise. In the first step, H∞$$ {H}_{\infty } $$ method is used to design a robust reduced‐order observer that attenuates the impact of the system uncertainties on the estimation error. In the second step, a non‐conservative interval prediction of the estimation error is achieved by applying a symmetric set‐integration approach. The resulting tight set‐valued state estimation is obtained by combining the point estimation from the reduced‐order observer with the predicted estimation error set provided by the set‐integration method. Compared to the conventional methods, the proposed method is built on less‐restrictive design conditions, that allow one to deal with a large range of applications. On the other hand, numerical simulations show that the proposed method offers more precise interval estimation compared to an optimal reduced‐order interval observer selected from recent literature. [ABSTRACT FROM AUTHOR]

This paper studies a secure iterative interval estimation approach for cyber-physical systems subject to stealthy deception attacks. Under the hypothesis that the system is accessed by a stealthy attack, an iteration scheme integrating the T-N-L observer framework is employed to reconstruct the system state. With the help of a structure separation method, a sufficient condition in terms of linear matrix inequality is provided to obtain convergent observation errors under deception attacks. Resorting to the reachability analysis, a secure state interval is built by means of the analyzed attack bounds and the observation error interval. Simulation studies verify the effectiveness of the proposed method for attack and attack-free cases. [ABSTRACT FROM AUTHOR]

Estimation of forging load in a closed-die forging process is important for process planners and designers. Physics-based models of the process require very high computational time as well as accurate input data. This work estimates the forging load by extracting the information from similar products in the shop floor. Accuracy of the estimate is optimized by means of a Kalman filter. A novel feature of this work is that instead of one deterministic estimate, three estimates, viz. lower, upper and most likely, are obtained. For demonstrating the efficacy of the proposed methodology, finite element method simulations using ABAQUS are used in lieu of real shop floor data. Six different products each having eight models are considered. Forging is supposed to be carried out with as well as without lubrication. In different cases, Kalman filtered most-likely estimate came very close to actual (FEM simulated) forging load and in no case deviation was more than 9%. The estimation error keeps on reducing with availability of data in an exponential manner. In an ideal case of no fluctuation in the measured actual (FEM simulated) forging load, error reduced from 30 to 5 kN after 7 data; further 13 data reduced the error to 1.7 kN. The interval of estimation (i.e. the difference between upper and lower estimates) also keeps on reducing with the availability of more data. For example, for an axisymmetric product, availability of 6 more data reduced the range of estimation from 62 to 25 kN. This establishes the efficacy of Kalman filter. In the proposed procedure the data is stored in an open source relational database management system, the MySQL, which can be retrieved easily. In Industry 4.0, shop floor data is easily available. Hence, the proposed method can be applied readily in real production shops. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme. These elements (X1, Y1), (X2, Y2), ⋯, (Xk, Yk) follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution. The system is regarded as operating only if at least s out of k (1 ≤ s ≤ k) strength variables exceed the random stress. The multicomponent reliability of the system is given by Rs,k=P(at least s of the (Z1, ⋯, Zk) exceed T) where Zi = min(Xi, Yi), i = 1, ⋯, k. The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms. The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known. The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k. The reliability estimators are compared by using the estimated risks through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

CBA is a sports event that allows fans to enjoy themselves and players to give full play, and traditional Chinese cultural values have a profound influence on it. This paper takes the 100 sets of historical rating data of the fourteen teams in CBA league as the basic basis, firstly, we simply deal with the 100 sets of historical rating data and use Excel function formula to find out the mean, extreme deviation and variance of each team, then we carry out SAS normal test, and we find that except for the very few data with large deviation, the historical rating data satisfy the normal distribution. Through the outlier algorithm to screen the values, compare the confidence intervals as well as carry out hypothesis testing, to objectively and scientifically explore the probability of each team winning the championship in the CBA league. Compare the probability of winning the championship of these fourteen teams and predict the top four teams in the CBA league to ensure that the prediction results are as reasonable as possible. With the help of hierarchical analysis to qualitatively analyze the level of each team, and then through cluster analysis to compare these data, and combined with the trend of the development of the world's basketball movement, the use of multiple regression and SPSS to analyze the level of the team's factors, in-depth thinking about the league, a more reasonable to give a more scientific to improve the probability of the team's winning the championship, and to promote better development of the basketball movement. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Shanghai Jiao Tong University (1006-2467) is the property of Journal of Shanghai Jiao Tong University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, a new process capability index is proposed. The new index is quantile-based, can be used in normal and non-normal measurements, and is a general form of the conventional Cpm. The new index is investigated by relying on the Weibull distribution, which holds significant importance in quality control and reliability studies. Point estimation for the index is discussed with parametric and non-parametric approaches. Moreover, several estimators based on methods such as Bayesian and bootstrap are suggested for interval estimation. A Monte Carlo simulation study is conducted to evaluate the performance of methodologies in both on-target and off-target processes. In addition, numerical examples are provided to evaluate two real-world problems where the measurements follow both the Weibull and normal distributions. The usability of the index is particularly evident when evaluating the ball size data in the first real data analysis, where the classical Cpm index is not used.

In view of the drawback of traditional deterministic prediction that it cannot provide uncertainty information, this study proposed a prediction model that integrates point estimation and interval estimation, and innovatively applied it to the field of food safety risk pre-warning. In the point estimation, wavelet packet decomposition (WPD) was used to decompose the weekly risk level sequence and the autoregressive integrated moving average (ARIMA) model was used for prediction. In the interval estimation, the generalized autoregressive conditional heteroskedastic (GARCH) model was used to predict the residual. The WPD-ARIMA-GARCH model established in this study was applied to the safety risk prediction of soy sauce and pot-roast meat products from a certain region. The results showed that the safety risk of soy sauce and pot-roast meat products from this region was relatively high at the end of March and July in 2019, which was consistent with the actual situation. Meanwhile, in the risk prediction of soy sauce and pot-roast meat products from 10 different regions, the mean square error, mean absolute error, and mean absolute percentage error of the model were 1.626, 0.806, and 20.824, respectively, and the prediction interval normalized average and coverage width-based criterion values at the 90% confidence interval were both 0.024, which could cover all true values. Therefore, the model has high prediction accuracy and low error, is useful for risk control for the quality and safety of soy sauce and pot-roast meat products, and provide technical support for daily food safety supervision.

This paper presents an approach for design a continuous-time interval observer for linear parameter varying (LPV) systems in the presence of disturbances that are considered unknown but bounded. The proposed observer is used for the design of a sensor fault detection scheme using the input to state stability (ISS) approach through a Lyapunov quadratic function. The conditions of stability and positivity are presented by a set of linear matrix inequalities (LMIs). The performance of the proposed method is shown in simulation using a case study based on a single-link flexible joint robotic system.

The limitations of Cohen’s κ are reviewed and an alternative G-index is recommended for assessing nominal-scale agreement. Maximum likelihood estimates, standard errors, and confidence intervals for a two-rater G-index are derived for one-group and two-group designs. A new G-index of agreement for multirater designs is proposed. Statistical inference methods for some important special cases of the multirater design also are derived. G-index meta-analysis methods are proposed and can be used to combine and compare agreement across two or more populations. Closed-form sample-size formulas to achieve desired confidence interval precision are proposed for two-rater and multirater designs. R functions are given for all results.

Of interest in this paper is the development of a model that uses fixed, then inverse sampling of binary data that is subject to false-positive misclassification in an effort to estimate a proportion. From this model, both the proportion of success and false-positive misclassification rate may be estimated. Also, three first-order likelihood-based confidence intervals for the proportion of success are mathematically derived and studied via a Monte Carlo simulation. The simulation results indicate that the likelihood ratio interval is generally preferable over the Wald and score interval. Lastly, the model is applied to two different real-world medical data sets. [ABSTRACT FROM AUTHOR]

Copyright of Shipin Kexue/ Food Science is the property of Food Science Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent years, several probability distributions have been introduced in the literature to analyze the data exhibiting an upside-down bathtub–shaped failure rate; an inverse Pareto distribution (IPD) is an appropriate choice among them. For stress–strength reliability models, estimation of parameters is an interesting area of research. In this article, we estimate the stress–strength reliability parameter R = P (X > Y) (where X and Y are strength and stress variables, respectively) of the IPD, whereby we focus on the problem of fixed-accuracy confidence interval estimation of R. It is established that the proposed interval estimation problem cannot be solved with the help of any fixed sample technique. As a result, we propose a two-stage sequential sampling strategy (which reduces the sample size significantly) to solve the given estimation problem. We obtain the expressions of several exact operating characteristics associated with our two-stage sampling technique. We also establish that the proposed two-stage procedure enjoys interesting first-order asymptotic properties. The detailed simulation analyses support our theoretical findings, and two real data sets based on insurance claims reinforce the practical utility of the proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new sampling design extending the well-known ranked set sampling, which we named dual-rank ranked set sampling. Unlike the original ranked set sampling scheme, dual-rank ranked set sampling is based on two ranking sets stages, as the double ranked set sampling design. Dual-rank ranked set sampling differs from double ranked set sampling, however, since it requires only $ n^2 $ n 2 initially selected units to draw a sample of size n, whereas double ranked set sampling is based on $ n^3 $ n 3 units to provide a sample of similar size. We verified that the dual-rank ranked set sampling sample estimator of the population mean is an unbiased estimator for the corresponding population parameter when the underlying distribution is symmetric. A simulation study was carried out to evaluate the efficiency of dual-rank ranked set sampling. The simulation results pointed out that dual-rank ranked set sampling estimation is more efficient than simple random sampling and ranked set sampling, and it is a cost-effective alternative to double ranked set sampling estimation. The problem of interval estimation for dual-rank ranked set sampling was also addressed. An application based on fish ageing data is finally presented. [ABSTRACT FROM AUTHOR]

The Poisson distribution may not fit the data in several real-life circumstances. In this case the zero-truncated Poisson-Lindley (ZTPL) distribution has been proposed as a statistical model for counting data that do not include zero values. The index of dispersion (IOD) is a valuable tool for evaluating the suitability of the distribution in modelling observed count data. Nevertheless, the examination of the non-parametric bootstrap method for estimating confidence intervals (CIs) of the IOD of the ZTPL distribution has not been conducted. The study of the non-parametric bootstrap CI for the IOD can provide a more nuanced and informative understanding of data variability. This is crucial for various applications including comparisons between groups, risk assessment, decision-making, and ensuring the robustness of statistical conclusions. This study aims to investigate the performance of non-parametric bootstrap CIs derived from percentile, simple, and biascorrected bootstrapping methods. Coverage probability and average length are evaluated using Monte Carlo simulation. The simulation results demonstrate that achieving the designated confidence level using non-parametric bootstrap CIs is unattainable for small sample sizes, irrespective of the other parameters. In addition, the performance of the nonparametric bootstrap CIs does not differ significantly when the sample size is large. The biascorrected bootstrap CI demonstrates superior performance compared to other methods, even when dealing with limited sample sizes. Using two numerical examples, non-parametric bootstrap methods are utilised to calculate the CI for the IOD of a ZTPL distribution. The results match those of the simulation study. [ABSTRACT FROM AUTHOR]

In this paper, the unit Garima distribution is introduced. It is used for analysing proportional data. Some statistical properties of the proposed distribution are investigated, including survival and hazard functions, order statistics, quantile function, and stress-strength reliability measures. A new family of continuous distributions, called the unit Garima-generated family of distributions, is also provided. It used the unit Garima distribution as the main generator. Some sub-models of the unit Garima-generated family of distributions are provided, such as the unit Garima-beta, unit Garima-Weibull, and unit Garima-normal distributions. The method of maximum likelihood is used to estimate the model parameters. A Monte Carlo simulation is used to illustrate the performance of the percentile confidence interval construction for each parameter of the proposed distributions. Finally, the developed distributions are applied to eight real data sets. [ABSTRACT FROM AUTHOR]

This article focuses on the interval estimation of the generalized Rayleigh distribution with scale and shape parameters. The generalized fiducial method is used to construct the fiducial point estimators as well as the fiducial confidence intervals, and then their performance is compared with other methods such as the maximum likelihood estimation, Bayesian estimation and parametric bootstrap method. Monte Carlo simulation studies are carried out to examine the efficiency of the methods in terms of the mean square error, coverage probability and average length. Finally, two real data sets are presented to demonstrate the applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This article focuses on the interval estimation of the generalized Rayleigh distribution with scale and shape parameters. The generalized fiducial method is used to construct the fiducial point estimators as well as the fiducial confidence intervals, and then their performance is compared with other methods such as the maximum likelihood estimation, Bayesian estimation and parametric bootstrap method. Monte Carlo simulation studies are carried out to examine the efficiency of the methods in terms of the mean square error, coverage probability and average length. Finally, two real data sets are presented to demonstrate the applicability of the proposed method.

In this paper, we provide an optimization design for a step‐stress accelerated life test (ALT) with two stress variables when the lifespan of test units is assumed to follow the inverse Weibull (IW) distribution. We first utilize progressive type‐I censoring and accelerated life testing to shorten the time and reduce cost of testing and then adopt a cumulative exposure (CE) model to look at the impact of varying stress levels. A log‐linear relationship between the scale parameter of the IW distribution and stress has been postulated. We obtain the maximum likelihood estimators and Bayes estimators of the unknown model parameters. Under normal operating conditions, we design an optimal test plan via minimizing the asymptotic variance (AV) of the percentile life. We carry out simulation studies to illustrate the performance and optimality of the proposed model. Finally, a real‐life data is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, a reduced-order interval observer (R-IO) design technique is developed for continuous-time descriptor linear-parameter-varying systems with unknown-but-bounded uncertainties. First, by introducing an intermediate variable, the R-IO design amounts to estimating the linear functional of the system states. Then, with a parameter-dependent Luenberger-like structure, the R-IO existence condition is eventually formulated into a set of differential-algebraic equations, not involving any linear transformation process. Further, a parametric solution to such an R-IO is derived through solving the equation set, which clearly shows the design degrees of freedom. Finally, the correctness of the proposed results is verified by a numerical system and an electrical circuit system. [ABSTRACT FROM AUTHOR]

Copyright of Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales is the property of Academia Colombiana de Ciencias Exactas, Fisicas y Naturales and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to achieve accurate and reliable prediction of the dissolved oxygen in ponds and mitigate aquaculture risks, we propose a predictive model based on Feature Construction (FC) pretreatment and Temporal Convolutional Network (TCN) coupled with Bidirectional Gate Recurrent Unit (BiGRU). By constructing statistical features, environmental factor features and seasonal features from the samples, deep-level correlations between variables are explored. Then, the structural feature sequences are processed using multiple layers of convolution and dimensionality reduction through TCN, while preserving the global temporal characteristics and removing redundant information. By integrating BiGRU to model the reduced features, accurate prediction of dissolved oxygen levels is achieved. Furthermore, the Sand Cat Swarm Optimization (SCSO) algorithm is employed to optimize the non-parametric Kernel Density Estimation (KDE) for estimating the distribution range of dissolved oxygen prediction errors. The experimental results indicate that the proposed model achieves superior performance compared to other comparative models, with respective values of 0.027 5 for Mean Squared Error (MSE), 0.143 2 for Mean Absolute Error (MAE), 0.165 8 for Root Mean Squared Error (RMSE), and 0.94 for the Coefficient of Determination (R²). Meanwhile, the interval estimation effectively covers the fluctuation range of dissolved oxygen, thereby quantifying the uncertainty in the prediction process. In the short-term prediction of dissolved oxygen levels in ponds, this model demonstrates notable accuracy and robustness. It is instructive for water quality monitoring in aquaculture and the enhancement of farming efficiency. [ABSTRACT FROM AUTHOR]

High maintenance costs and safety risks due to lithium-ion battery degeneration have significantly and seriously restricted the application potential of batteries. Thus, this paper proposes an efficient calculation approach for state of health (SOH) estimation in lithium-ion batteries that can be implemented in battery management system (BMS) hardware. First, from the variables of the charge profile, only the complete voltage data is taken as the input to represent the complete aging characteristics of the batteries while limiting the computational complexity. Then, this paper combines the light gradient boosting machine (LightGBM) and weighted quantile regression (WQR) methods to learn a nonlinear mapping between the measurable characteristics and the SOH. A confidence interval is applied to quantify the uncertainty of the SOH estimate, and the model is called LightGBM-WQR. Finally, two public datasets are employed to verify the proposed approach. The proposed LightGBM-WQR model achieves high accuracy in its SOH estimation, and the average absolute error (MAE) of all cells is limited to 1.57%. In addition, the average computation time of the model is less than 0.8 ms for ten runs. This work shows that the model is effective and rapid in its SOH estimation. The SOH estimation model has also been tested on the edge computing module as a possible innovation to replace the BMS bearer computing function, which provides tentative solutions for online practical applications such as energy storage systems and electric vehicles. [ABSTRACT FROM AUTHOR]

This paper is an attempt to study the Xgamma–Weibull distribution using an adaptive progressive type-II censoring plan. This scheme effectively ensures that the experimental time does not exceed a predetermined time limit. Using two classical estimation methods—namely, maximum likelihood and maximum product of spacing—both point and interval estimations for the unknown model parameters, as well as some parameters of life—namely, reliability and hazard rate functions—were obtained. The asymptotic normality of both classical methods was used to determine the approximate confidence intervals for the various parameters. Based on the two conventional methodologies, Bayesian estimations were also investigated using the MCMC technique under the squared error loss function. In addition, the credible intervals of the different parameters were also obtained. To compare the performance of the various approaches, a thorough simulation study was carried out. Furthermore, we propose using several optimality criteria to select the best sampling technique. Finally, two real-world datasets were used to demonstrate how the suggested estimators and optimality criteria operate in real-world circumstances. [ABSTRACT FROM AUTHOR]

Generalized logistic distribution, as the generalized form of the symmetric logistic distribution, plays an important role in reliability analysis. This article focuses on the statistical inference for the stress–strength parameter R = P (Y < X) of the generalized logistic distribution with the same and different scale parameters. Firstly, we use the frequentist method to construct asymptotic confidence intervals, and adopt the generalized inference method for constructing the generalized point estimators as well as the generalized confidence intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Simulation results demonstrate that the generalized fiducial method outperforms other methods in terms of the mean square error, average length, and empirical coverage. Finally, three real datasets are used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Using the augmented Dickey-Fuller test to verify the existence of a unit root in an autoregressive process often requires the correctly specified intercept, since the test statistics can be distinctive under different model specifications and lead to contradictory results at times. In this article, we develop a unified inference that not only unifies the specifications of the intercept but also accommodates different degrees of persistence of the underlying process and heteroscedastic errors. A simulation study shows that the resulting unified unit root test exhibits excellent size control and reasonably good power. In an empirical application, we implement the proposed test to re-examine the presence of unit roots within eleven widely used variables in stock return predictability. [ABSTRACT FROM AUTHOR]

This paper concerns state and fault simultaneous interval estimations for discrete-time linear systems with unknown but bounded uncertainties. Unlike most existing works on interval estimation, the system considered in this work is subject to actuator and sensor faults, while bounded uncertainties exist in both components. Thus, the method developed in this paper can be used for more general conditions. First, the considered system is reformulated as a descriptor one through the augmented vector method. An important lemma for descriptor systems is given in a more accurate description and proven in a very simple way. Then, by using the reachability analysis technique, a new proportional-integral observer-based interval estimation method is proposed. The H∞ technique reduces the influences of time-varying actuator faults and uncertainties. To build the zonotope of bounded uncertainties in the residual system, an equivalent description is introduced. Finally, a numerical example and an industrial system are simulated to demonstrate the efficacy and applicability of the developed method. [ABSTRACT FROM AUTHOR]

In a number of real-world situations, one encounters count data with over-dispersion such that the typical Poisson distribution does not suit the data. In the current situation, it is appropriate to employ a combination of mixed Poisson and Poisson-Sujatha (PS) distributions. The PS distribution has been investigated for count data, which is of primary interest to a number of disciplines, including biology, medicine, demography, and agriculture. However, no research has been conducted regarding generating bootstrap confidence intervals for its parameter. The coverage probabilities and average lengths of bootstrap confidence intervals derived from the percentile, basic, and biasedcorrected and accelerated bootstrap methods were compared using Monte Carlo simulation. The results indicated that it was impossible to achieve the nominal confidence level using bootstrap confidence intervals for tiny sample sizes, regardless of the other settings. Furthermore, when the sample size was large, there was not much of a difference in the performance of the several bootstrap confidence intervals. The biascorrected and accelerated bootstrap confidence interval demonstrated superior performance compared to the other methods in all of the cases examined. Moreover, the effectiveness of the bootstrap confidence intervals was proven through their application to agricultural data sets. The calculations offer significant evidence in favor of the suggested bootstrap confidence intervals. [ABSTRACT FROM AUTHOR]