Two-parameter Model Research Articles

Advanced inference techniques for two-parameter Topp-Leone models under unified progressively hybrid censoring

In this study, we examine the unified progressive hybrid censoring scheme from Topp-Leone models, and we show that while the maximum likelihood estimates of the model parameters are uniquely exist, they cannot be obtained in a closed form. To obtain these estimates, we utilize two frequentist algorithms—the Expectation-Maximization method and an Expectation-Maximization type method. We also derive confidence intervals for the unknown parameters using both asymptotic distributions of the maximum likelihood estimators and bootstrap approaches. Furthermore, we develop sample-based Bayes estimates for the model parameters under different error loss functions, such as square, LINEX, and entropy loss functions. To approximate the Bayes estimates, we apply importance sampling and Metropolis-Hastings algorithms. We also construct Bayes credible intervals for the estimates. To assess the performance of the proposed methods, we conduct a numerical simulation study. Finally, we analyze a real data set to illustrate the practical application of our proposed methods and their findings. The study highlights the usefulness of hybrid censoring schemes and the applicability of various statistical methods for parameter estimation and inference.

Some Two-Parameter Exponential Discrete Distributions and Their Applications

In this paper we considered discrete two-parameter distribution models with variance functions in the ABM and LM classes with variance functions \(\mu(1+\frac{\mu}{p})^r\) and \(\mu(1-\frac{\mu}{p})^{-r}\) respectively (r = 1, 2, . . .). Four example frequency data sets that have received considerable attention in the literature are employed for comparative studies. We also extend our analyses to count data having co-variates (GLM cases) that exhibit over-dispersion, under-dispersion and excess zeros. Models considered here include the NB, the generalized Poisson (GP), the new logarithmic distribution (NLD), the new geometric discrete Pareto distribution (NGDP), the Poisson- Lindley-beta prime distribution (PLB) as well as the Bell-Tuchard (BTD), the discreteWeibull (DWD) and the Poisson-inverse Gaussian (PIG) distributions. All these models belong to the exponential dispersion models for count data. Several measures of comparison (-log-likelihood, Pearson’s grouped X2, Wald’s goodness-of-fit statistic \(X^2_w\) as well as the root mean square error-RMSE) were employed. Our findings indicate that the ABM and LM classes, when r ≥ 2 do not perform any better than either NB or GP with r = 1, 2 respectively and these classes are not computational flexible.

Optimized Modeling Strategies for the Parametrization of a Two-Parameter Friction Model Through Inverse Modeling of Conical Tube-Upsetting Tests

Friction is a critical influencing factor for a variety of forming processes, as it affects, for example, the required forming force. Complex models for the numerical description of friction often have two or more model parameters but lack appropriate calibration methods since calibration schemes developed for one-parameter models are not applicable. The objective of this work is to develop an evaluation method based on inverse modeling of the conical tube-upsetting test in order to allow for the parametrization of a two-parameter friction model, providing a unique solution for the model parameters. It is based on a comparison of the specimen’s outer contour for several points in time throughout the forming process according to the finite element model of the test. An optimization algorithm minimizes the deviation between the experimental and the simulated contour by adapting the friction model parameters. A two-parameter model is used that considers normal stress as well as relative velocity. First, purely numerical investigations show the necessity of a model adaption due to insufficient data. The modeling scheme is therefore adapted to consider data from two tests with different relative velocities. The results suggest a unique solution for the determination of the friction model parameters for purely numerical studies as well as for experimental conditions, comparing with the evolving contour of the conical tube-upsetting test specimen. Thus, this study presents a promising approach for the calibration of two-parameter friction models.

Numerical Study of Complex Heat Transfer and Aerodynamics in a Tube Furnace with a Flat Fuel Combustion Mode

The object of the study is a tubular furnace for steam reforming of natural gas. The channel walls are formed by a refractory lining and a tubular screen with a known temperature. The chamber volume is filled with a selectively radiating, absorbing and weakly scattering medium of gaseous fuel combustion products. The research method is based on the numerical solution of a system of two-dimensional integro-differential equations of radiative gas dynamics, closed by a two-parameter model of turbulent convection. It is shown that when burners are located on the side walls of the radiation chamber, a significant restructuring of the heat flux distribution occurs. A decrease in the chamber width is accompanied by an increase in both radiant and convective heat fluxes to the tubular screen.

Novel family of probability generating distributions: Properties and data analysis

Abstract Current probability distributions often fall short when modeling lifespan data with non-monotonic hazard rate shapes, highlighting a gap in probability theory. To address this issue, this study introduces the novel family of probability-generating distributions (NP-G) as a solution to capture complex data patterns better. This research aims to develop and validate the NP-G distributions, which include a two-parameter continuous model based on the Weibull distribution. The study extensively explores the mathematical properties of the NP-G distributions, including series expansions of probability density functions, and evaluates various probabilistic measures such as moments, stress strength, mean deviations, entropy measures, and order statistics. Using the maximum likelihood method for parameter estimation and conducting a numerical simulation analysis, the study assesses the performance of the proposed extended exponentiated Weibull model. The findings demonstrate that this new model offers superior fit and accuracy compared to existing distributions when applied to two referenced datasets. This advancement is significant as it provides a more effective tool for analyzing lifespan data with non-monotonic hazard rates, enhancing both theoretical understanding and practical applications in fields such as reliability engineering and survival analysis.

Reliability analysis of the vehicle door system EDCU based on Weibull distribution

The paper established a two-parameter Weibull distribution model to analyze the failure law of key components of metro vehicles and employed the least squares method to fit the parameters of the Weibull function. The paper provided a detailed introduction of the model's parameter fitting method based on actual historical failure data. Taking the EDCU (Electrical Door Control Unit) as an example, the failure rate, cumulative failure rate, and reliability of EDCU for 3 different vehicle models were calculated, and the calculation results were verified to conform to the Weibull distribution through Q-Q diagrams. The results show that although the designed service life of EDCU of vehicle door system is 15 years, the reliability of the EDCU decreases significantly around 10 years. The EDCU reliability of the three vehicle models declines by 22%, 4.2%, 10.6% and the failure rates are 2.7%, 0.57%, 1.13%. Based on the reliability of EDCU mentioned above, while ensuring the reliability of components, the maintenance methods of components can be optimized to reduce maintenance costs.

Performance Evaluation for Positive Displacement Motors by Combining Fluid-Structure Interaction Simulations and Experiments

Summary The aim of this study is to propose a method for evaluating the performance of positive displacement motors (PDMs) from the perspective of robustness and energy conversion efficiency. Monitoring contact force and leakage is challenging when a steel rotor driven by liquid undergoes planetary motion within the rubber lining of the stator. A 3D model with a nominal diameter of 172 mm is established, along with a flow field of the same outer diameter as the stator. The constitutive parameters are determined according to the two-parameter Mooney-Rivlin model. After merging the overlapping nodes of the rubber lining and steel housing, the degrees of freedom are constrained from the exterior of the stator. Four-step loads are applied in ascending order. The average difference in overall efficiency between the experimental results and the simulation of the same model PDM is 1.58%. The sequential simulations include three sets of nine variables: lead (800 mm, 914.4 mm, 1200 mm), interference fit (0.1 mm, 0.2 mm, 0.3 mm), and rubber hardness (70 HA, 80 HA, 85 HA). Contact force differentials on each sealing band are calculated before and after stable operation. The reliability and stability of the cavities are assessed using the mean and variance of the force differentials. Efficiencies after each load stabilization are calculated to compare performance. For loads other than 200 N·m, the overall efficiency of the PDM with the optimized parameter combination increased by 2.98%, 0.27%, and 2.32%, respectively. Finally, this parameter combination is applied to a curved profile PDM. For loads other than 200 N·m, the overall efficiency increased by 3.22%, 0.89%, and 5.14%. This method, which combines the fluid-structure interaction (FSI) with an analysis of robustness and efficiencies, can be used to analyze the strengths and weaknesses of different parameter PDMs and to assess the performance of different profile motors.

Anchored Chitosan-Functionalized Magnetite Nanoparticles for Crystal Violet Decolorization from Aqueous Samples.

In this research, 3-(triethoxysilyl)propyl isocyanate (TESPIC) functionalized chitosan was successfully synthesized to fabricate silica-coated magnetite nanoparticles (Fe3O4@SiO2-CS MNPs). The synthesized MNPs were characterized using XRD, FT-IR, SEM, and TEM instruments and were utilized for the decolorization of Crystal Violet cationic dye (CV). The affecting variables controlling CV removal efficiency were investigated using the Taguchi fractional factorial design method (L16 array). Under the optimized removal conditions (adsorbent amount = 0.12 g (4.8 g L-1), pH = 4, ionic strength = 0.05 mol L-1 NaCl, and 30 min stirring), 98.2% of the CV dye was eliminated. The kinetic and equilibrium adsorption isotherms were explained by the pseudo-second-order kinetic (R2 = 0.999) and Freundlich isotherm models, respectively. MATLAB's fmincon function as an efficient solution was applied in order to compare the Redlich-Peterson three-parametric isotherm model with two-parametric models. Moreover, the Fe3O4@SiO2-CS-TESPIC MNPs showed recyclability and reusability for subsequent runs. The findings confirmed that these functional MNPs can be considered as proper adsorbents for the removal of CV dye from the aqueous solutions.

Automatic setting optimization for robotic upper-extremity rehabilitation in patients with stroke using ReoGo-J: a cross-sectional clinical trial

Stroke-induced upper-extremity paralysis affects a substantial portion of the population, necessitating effective rehabilitation strategies. This study aimed to develop an automated program, incorporating the item response theory, for rehabilitation in patients with post-stroke upper-extremity paralysis, focusing on the ReoGo-J device, and to identify suitable robot parameters for robotic rehabilitation. ReoGo-J, a training device for upper-extremity disorders including 71 items, was administered to over 300 patients with varying degrees of post-stroke upper-extremity paralysis. Each item was rated on a three-point scale (0, very difficult; 1, adequate; 2, very easy). The results were analyzed using the graded response model, an extension of the two-parameter logistic model within the framework of the item response theory, to grade the training items based on ability of the patients. The relationship between the predicted ability, an indicator of the predicted ability the paralyzed upper-extremity to perform an item in the item response theory analysis (higher numbers indicate higher ability, lower numbers indicate lower ability), and the items in the Fugl–Meyer assessment (FMA), which indicate the degree of paralysis, was analyzed using Pearson’s correlation coefficient. This study included 312 patients with post-stroke upper-extremity paralysis. The predicted ability (θ) of the tasks included in the original ReoGo-J test for forward reaching, reaching for mouth, rotational reaching, radial reaching (2D), abduction reaching, reaching in eight directions, radial reach (3D), and reaching for head ranged from − 2.0 to − 0.8, − 1.3 to − 0.8, − 1.0 to − 0.1, − 0.7 to 0.3, − 0.2 to 0.4, − 0.4 to 0.6, − 0.1 to 0.6, and 0.5 to 0.6, respectively. Significantly high correlations (r = 0.80) were observed between the predicted ability of all patients and the upper-extremity items of shoulder-elbow-forearm in the FMA. We have introduced an automated program based on item response theory and determined the order of difficulty of the 71 training items in ReoGo-J. The strong correlation between the predicted ability and the shoulder-elbow-forearm items in FMA may be used to ameliorate post-stroke upper-extremity paralysis. Notably, the program allows for estimation of appropriate ReoGo-J tasks, enhancing clinical efficiency.Trial registration: https://www.umin.ac.jp/ctr/index-j.htm (UMIN000040127).

Two-parametric prescan calibration of gradient-induced sampling errors for rosette MRI.

The aim of this study was to develop a simple, robust, and easy-to-use calibration procedure for correcting misalignments in rosette MRI k-space sampling, with the objective of producing images with minimal artifacts. Quick automatic calibration scans were proposed for the beginning of the measurement to collect information on the time course of the rosette acquisition trajectory. A two-parameter model was devised to match the measured time-varying readout gradient delays and approximate the actual rosette sampling trajectory. The proposed calibration approach was implemented, and performance assessment was conducted on both phantoms and human subjects. The fidelity of phantom and in vivo images exhibited significant improvement compared with uncorrected rosette data. The two-parameter calibration approach also demonstrated enhanced precision and reliability, as evidenced by quantitative relaxometry analyses. Adequate correction of data sampling is a crucial step in rosette MRI. The presented experimental results underscore the robustness, ease of implementation, and suitability for routine experimental use of the proposed two-parameter rosette trajectory calibration approach.

Load transfer model for vertically loaded non-circular piles

The load-transfer (LT) method, involving a series of ‘t-z’ springs to represent pile shaft-soil interaction and a ‘q-z’ spring to represent pile tip-soil interaction, is widely used to model the load–displacement behaviour of vertically loaded piles. While a plethora of LT models have been proposed for piles with circular cross sections, they are not directly applicable to non-circular (NC) cross sections. Therefore, there is a lack of tailored solutions for rectangular, H-shaped and X-shaped piles even though they are common in geotechnical practice. The aim of this paper is to develop a general theoretical framework for the construction of LT curves for NC piles. This framework allows NC piles with any cross section to be considered. The LT curves for NC piles are formulated using a two-parameter hyperbolic model which requires input of (a) the initial elastic LT stiffness and (b) the unit ultimate shaft friction. The elastic stiffness for vertically loaded NC piles with arbitrary cross sections is described using a rigorous semi-analytical (SA) solution involving variational principles. A nonlinear numerical solution for the pile governing equation with the incorporated t-z and q-z curves is achieved using the Runge-Kutta (RK) method. The proposed LT curves are used to construct the pile governing equation and a numerical solution using the Runge-Kutta (RK) method is proposed to predict the responses of NC piles in drained sand. The proposed theoretical LT predictions of pile response are validated through comparisons to elastic–plastic finite element calculations.

The entropy-transformed Gompertz distribution: Distributional insights and cross-disciplinary utilizations

A novel two-parameter continuous model titled the entropy-transformed Gompertz (ETGPZ) distribution has been developed via the entropy transform. A new framework has been investigated and found to meet the criteria of the probability function. By significantly improving the functional shape and having the ability to model the most likely form of the hazard rate function, this new modification has increased the adaptability of the typical distribution. Some of its core characteristics, such as its statistical and computational features, are clearly presented. A thorough simulation analysis has been done to examine the final behavior of maximum likelihood estimators while estimating model parameters. We assess the performance and practical applicability of the ETGPZ distribution using eight real datasets from engineering and biomedical fields. The results demonstrate that the ETGPZ outperforms the baseline Gompertz (GPZ) distribution, highlighting its superiority and broader potential for various applications.

Transit-guided radiation therapy: a novel patient monitoring approach

Background and purposeTransit-Guided Radiation Therapy (TGRT) is a novel technique that uses the transit portal images (TPIs) acquired with Electronic Portal Image Devices (EPID) to quantify patient position errors during the treatment. It has been validated using anthropomorphic phantoms but a validation in a clinical setting was lacking. A pilot clinical study is presented to confirm our previous results. Materials and methodsA prospective study was conducted between June and December 2022 with patients who received whole-brain or breast radiotherapy treatments. The selected treatments were composed of radiation fields using skin-flash, where the body contour projected a sharp edge on the EPID which has been used as a surrogate of the true patient position. Daily imaging procedures were applied as scheduled before running the one- and two-parameter model (1PM and 2PM) of the TGRT formalism on the acquired TPIs to independently estimate the patient position errors. Results43 patients and 1015 TPIs have been assessed. The 2PM showed a better correlation with the true position errors (R2 = 0.76 vs. 0.73), a lower detection threshold (0.77 mm vs. 1.24 mm), and a lower overcorrection risk above the detection threshold (7.0 % vs. 11.1 %) than the 1PM. Overall, the 2PM would have significantly reduced the true position errors by a factor of 0.58 (0.49 – 1.27) (p < 0.0001). ConclusionThe TGRT technique has confirmed the ability to reduce the position errors in a clinical setting, demonstrating the potential to enhance the patient position monitoring without increasing treatment time or patient dose.

A unified EM framework for estimation and inference of normal ogive item response models.

Normal ogive (NO) models have contributed substantially to the advancement of item response theory (IRT) and have become popular educational and psychological measurement models. However, estimating NO models remains computationally challenging. The purpose of this paper is to propose an efficient and reliable computational method for fitting NO models. Specifically, we introduce a novel and unified expectation-maximization (EM) algorithm for estimating NO models, including two-parameter, three-parameter, and four-parameter NO models. A key improvement in our EM algorithm lies in augmenting the NO model to be a complete data model within the exponential family, thereby substantially streamlining the implementation of the EM iteration and avoiding the numerical optimization computation in the M-step. Additionally, we propose a two-step expectation procedure for implementing the E-step, which reduces the dimensionality of the integration and effectively enables numerical integration. Moreover, we develop a computing procedure for estimating the standard errors (SEs) of the estimated parameters. Simulation results demonstrate the superior performance of our algorithm in terms of its recovery accuracy, robustness, and computational efficiency. To further validate our methods, we apply them to real data from the Programme for International Student Assessment (PISA). The results affirm the reliability of the parameter estimates obtained using our method.

Patient feasibility as a novel approach for integrating IRT and LCA statistical models into patient-centric qualitative data-a pilot study.

Clinical research increasingly recognizes the role and value of patient-centric data incorporation in trial design, aiming for more relevant, feasible, and engaging studies for participating patients. Despite recognition, research on analytical models regarding qualitative patient data analysis has been insufficient. This pilot study aims to explore and demonstrate the analytical framework of the "patient feasibility" concept-a novel approach for integrating patient-centric data into clinical trial design using psychometric latent class analysis (LCA) and interval response theory (IRT) models. A qualitative survey was designed to capture the diverse experiences and attitudes of patients in an oncological indication. Results were subjected to content analysis and categorization as a preparatory phase of the study. The analytical phase further employed LCA and hybrid IRT models to discern distinct patient subgroups and characteristics related to patient feasibility. LCA identified three latent classes each with distinct characteristics pertaining to a latent trait defined as patient feasibility. Covariate analyses further highlighted subgroup behaviors. In addition, IRT analyses using the two-parameter logistic model, generalized partial credit model, and nominal response model highlighted further distinct characteristics of the studied group. The results provided insights into perceived treatment challenges, logistic challenges, and limiting factors regarding the standard of care therapy and clinical trial attitudes.

Electroplasticity constitutive modeling of aluminum alloys based on dislocation density evolution

Electrical current can effectively improve the plasticity of metallic materials. The tensile deformation behavior of Al alloys under the pulsed electrical current assisted quasi-static unidirectional tension (EAT) has been investigated. Materials under the EAT exhibits periodic electro-softening and strain-hardening behaviors, i.e., a ratchet shape mechanical response. However, establishing a constitutive model to accurately predict the ratchet shape mechanical behavior, especially during the EAT interval, and accurately predicting the strain-hardening behavior of materials are critical issues that need to be solved urgently. In this study, based on the Taylor polycrystalline model, thermal activation theory and dislocation density evolution theory, a two-parameter dislocation density electroplasticity constitutive model with forward and reverse dislocation density evolution was developed to describe the periodic coupling effect of the electro-thermal-mechanical fields during EAT. The tensile deformation behaviors of AA 6061-T6 and AA 7075-T6 under the effect of a pulsed electrical current were quantitatively predicted using the proposed constitutive model. The results show that the correlation coefficient between the predicted and experimental results of the constitutive model can reach 0.84–0.99, implying that the proposed constitutive model can accurately predict the complex electroplasticity behavior of Al alloys during EAT.

Time-dependent mechanical behavior analysis using Weibull models of cellulose hollow fiber membranes produced by green solvent

The mechanical behavior of sustainable (“green”), bio-based cellulose hollow fiber membranes (hereafter, hollow fiber) produced using green solvent, which is potential for desalination and solvent-resistant nanofiltration, can be evaluated either in dry or water-conditioned (wet) states. However, the effect of conditioning time on the mechanical behavior of hollow fibers has not been conclusive. In this work, an extensive evaluation involving an experimental campaign and rigorous application of statistical models for cellulose hollow fibers produced using green solvent (1-ethyl-3-methylimidazolium diethyl phosphate or [EMIM][DEP]) via a dry-jet spinning technique is reported. First, we evaluated the microstructures and separation performance (water permeation, solute rejection) of hollow fibers made of different cellulose concentrations (10–15 wt%) in both pristine and conditioned states. Then, the strength, stiffness, and ductility of hollow fiber samples of different gauge lengths (25 and 50 mm) were measured by a standard tensile test device. Here, the effect of conditioning time on mechanical properties was evaluated after the hollow fiber samples were water-immersed at different times (from 30 s to 2 months). The strength distribution of conditioned hollow fibers was modeled and analyzed using two-parameter and three-parameter Weibull models. Our results showed that the cellulose content of 15 wt% in the hollow fibers produced a denser microstructure, providing the lowest molecular weight cut-off (MWCO). The cellulose content and gauge length slightly modified the mechanical properties of hollow fibers when they were evaluated in pristine, dry conditions. The mechanical properties of hollow fibers were drastically reduced after 10 min of water immersion, beyond which their properties were stabilized. Weibull modeling of mechanical reliability showed that two- or three-parameter Weibull could estimate the failure probability of hollow fibers quite well. Nonetheless, the three-parameter Weibull is better than the two-parameter one in terms of accuracy in determining the threshold strength located at the “lower-end tail.” Our analysis provides a rigorous demonstration of Weibull modeling in evaluating the time-dependent mechanical behavior of ductile, cellulose-based hollow fiber membranes, which is essential to support the design and development of future hollow fiber membranes in desalination industries.

Modified PVDF/PMMA/SiO2 composite nanofibrous membrane in airborne filtration: Transparency, mechanical properties and filtration performance

A comprehensive study on four modified Polyvinylidene Fluoride (PVDF) nanofibrous membrane was conducted to fabricate transparent air filters for the first time when adding Polymethyl methacrylate (PMMA) and SiO2. The modified PVDF nanofibrous membrane properties were extensively characterized using scanning electron microscopy, infrared analysis, crystallinity, and investigated the optical transparency, mechanical properties, and filtration performance. The enhancement of PMMA is greater than the weaken of SiO2 with the PVDF/PMMA/SiO2 membrane average transparency of 70.48 %. The PVDF membrane mechanical strength enhanced by SiO2 and weakened by PMMA is visualized by a Weibull two-parameter distribution model. The PVDF/PMMA/SiO2 membrane filtration efficiency is 94.12–96.39 %, and the impressive quality factor (Qf) of 0.074 Pa⁻1 is superior to other three modified membranes in filtration performance while maintaining the sufficient ultimate tensile strength (UTS) of 20.41±0.28 MPa.

Analytical method of incorporating failure probability to predict the fatigue life of ultra-high-performance concrete (UHPC)

This study predicted the fatigue life (N) of UHPC incorporated with different volume fractions (Vf = 0.0%, 0.5%, 1.0%, 1.5% and 2.0%) of steel fiber under flexural cyclic loading at various stress levels (S). The Weibull distribution, a two-parameter model, was utilized to estimate the distribution of fatigue life in UHPC. Subsequently, three methods were employed to calculate the parameters: the graphical method, the method of moments, and the method of maximum likelihood. The averaged values of these parameters were then obtained to enhance the accuracy of the estimation. The results are presented in the form of S-N diagrams, which depict the quantitative relationship between stress (S) and fatigue life (N). This relationship was determined using the Wohler equation, the modified Wohler equation, and the power equation. By employing these equations, the flexural fatigue strength of UHPC can be accurately predicted. Subsequently, the fatigue failure probability (Pf) was incorporated to enhance the reliability of the S-N quantitative relation. The fatigue testing results were presented in the form of S-N-Pf curves, which comprehensively reflect the relationship between stress, fatigue life, and failure probability. Furthermore, the mathematical relation of the S-N-Pf curves was derived to predict the fatigue life of UHPC with a given failure probability, providing a more comprehensive and accurate assessment of its fatigue behavior.

A meta-analysis of factors influencing the inactivation of Shiga toxin-producing Escherichia coli O157:H7 in leafy greens.

Recent advancements in modeling suggest that microbial inactivation in leafy greens follows a nonlinear pattern, rather than the simple first-order kinetics. In this study, we evaluated 17 inactivation models commonly used to describe microbial decline and established the conditions that govern microbial survival on leafy greens. Through a systematic review of 65 articles, we extracted 530 datasets to model the fate of Shiga toxin-producing Escherichia coli O157:H7 on leafy greens. Various factor analysis methods were employed to evaluate the impact of identified conditions on survival metrics. A two-parameter model (jm2) provided the best fit to most of both natural and antimicrobial-induced persistence datasets, whereas the one-parameter exponential model provided the best fit to less than 20% of the datasets. The jm2 model (adjusted R2=.89) also outperformed the exponential model (adjusted R2=.58) in fitting the pooled microbial survival data. In the context of survival metrics, the model averaging approach generated higher values than the exponential model for >4 log reduction times (LRTs), suggesting that the exponential model may be overpredicting inactivation at later time points. The random forest technique revealed that temperature and inoculum size were common factors determining inactivation in both natural and antimicrobial-induced die-offs.. The findings show the limitations of relying on the first-order survival metric of 1 LRT and considering nonlinear inactivation in produce safety decision-making.