Accurate statistical modeling of lifetime and reliability data remains a significant challenge in fields such as survival analysis, engineering, and environmental studies, particularly when datasets exhibit varying skewness, heavy tails, and complex hazard rate structures. Classical distributions, including the Burr XII model, often demonstrate limited flexibility in capturing diverse distributional shapes and hazard behaviors observed in real-world data. In this study, a new and flexible distribution, referred to as the Location-Scale Burr XII (LS-Burr XII) distribution, is introduced by adding a location-scale transformation into the classical Burr XII model. The LS-Burr XII distribution captures a wide range of density shapes, including right-skewed, left-skewed, bell-shaped, J-shaped, and reversed J-shaped forms. It also accommodates diverse hazard rate behaviors, including increasing, decreasing, constant, bathtub, unimodal, and modified bathtub shapes. These features extend beyond the capabilities of the classical Burr XII distribution and many of its existing extensions. Several statistical properties of the proposed model are derived, including the quantile function, moments, moment generating function, and order statistics. Parameter estimation is carried out using the maximum likelihood method, and a Monte Carlo simulation study is conducted to assess the performance of the estimators. The practical usefulness of the proposed model is demonstrated using two real-world datasets, including leukemia cancer data from Saudi Arabia and glass fiber strength data obtained from the UK National Physical Laboratory. The performance of the proposed LS-Burr XII distribution is compared with the classical Burr XII model and other existing extensions using standard goodness-of-fit criteria. The results indicate that the proposed model offers greater flexibility and provides a better fit with the observed data. These findings suggest that the LS-Burr XII distribution offers a useful and competitive alternative for modeling complex lifetime data in reliability and biomedical applications.

Estimating lifetime distributions under left-truncated and right-censored (LTRC) data is an important problem in actuarial science because it directly influences premium calculation, reserve valuation, and mortality modeling based on life table data. In insurance practice, delayed entry due to policy enrollment age and incomplete observation due to the end of the study period occur simultaneously, producing observation bias and a complicated likelihood structure. Under this framework, reliable lifetime modeling requires appropriate statistical modeling. Phase-Type (PH) distributions provide a flexible class of lifetime models constructed from absorbing Markov processes and are dense in the class of positive-valued distributions. Their structural flexibility makes them particularly suitable for capturing complex hazard patterns observed in actuarial mortality data. This study applies PH distributions to actuarial life table data under the LTRC framework. In particular, we explicitly formulate and estimate PH distributions using life table data regarded as LTRC observations, which constitutes a novel application in this context. Model parameters are estimated via maximum likelihood. Since increasing the number of phases monotonically improves the likelihood, practical implementation requires careful consideration of model complexity. To address this issue, we employ the Extended Information Criterion (EIC), which incorporates bootstrap-based bias correction of the log-likelihood, to examine phase selection. Furthermore, we compare PH distributions with conventional lifetime distributions using EIC, providing a systematic evaluation of their relative performance under the LTRC setting. The numerical results demonstrate the practical applicability of PH distributions to actuarial lifetime modeling under LTRC data. We observe the trade-off between improved goodness-of-fit and increased model complexity as the number of phases grows, and show that EIC can be used to support practical analysis of model complexity and model comparison in this context.

Modern manufacturing systems are becoming increasingly complex as production lines integrate multiple interconnected processes. In multi-process mechanical manufacturing systems, deviations in upstream operations often propagate downstream, resulting in performance degradation and reliability loss in subsequent machines. To mitigate such degradation, this paper introduces the concept of release-controlled capacity, where each machine’s operational capacity can be dynamically adjusted or released in response to system conditions. Continuous-time Markov chains (CTMCs) capture the stochastic degradation of machines by modeling transitions through discrete performance states, where systems can only move from higher to lower capacity due to wear or failure. Quality–Reliability (Q-R) dependency quantifies how upstream product quality deviations accelerate downstream machine degradation rates, linking product quality to system reliability. These two concepts provide the theoretical foundation for the proposed quality state-space model. A Controlled Capacity Release (CCR) mechanism allows for the dynamic activation of reserved resources to compensate for performance loss. It is driven by a combination of hardware resources and a control system. Unlike traditional "pure-death" models that only account for monotonic degradation, the proposed model incorporates CCR as probabilistic recovery transitions to higher-capacity states, effectively capturing the system's ability to restore performance through automated control or buffer utilization.

The proposed approach is validated through numerical experiments in a multi-stage manufacturing system case study. Results demonstrated that the CCR mechanism significantly slows down the rate of reliability degradation compared to traditional models. Furthermore, experimental results revealed that while higher recovery rates improve system stability, the benefits exhibit a diminishing-return effect due to system coupling and Q-R dependency.

Background: Obstetric fistula is preventable, yet many women face prolonged waits before definitive repair. We sought to identify which care pathway factors are most strongly associated with earlier repair and to provide a practical, interpretable survival tool that distinguishes the majority of repair times from the smaller group with prolonged delays.

Methodology: We analysed 257 women with obstetric fistula, measuring weeks to repair and treating unrepaired cases as right‑censored. We developed and fitted a parametric proportional‑hazards survival model (Lehmann Type II (exponentiated‑survival)) with an intuitive baseline that explicitly separates the majority of cases from the long tail, yielding closed‑form survival, hazard, and quantile functions. Simulations were used to stress‑test small‑sample performance typical of single‑centre cohorts. Covariates in the adjusted model were education, antenatal follow-up, delivery mode, labour duration (<2, 2-4, >4 days), and stature (<150 cm against ≥150 cm). Model adequacy was summarised with AIC/BIC and subgroup survival/hazard profiles.

Results: Two pathway factors were dominant. Formal education (HR = 2.87; 95% CI 1.93-4.26) and antenatal care (HR = 2.57; 1.71-3.88) were each associated with a higher instantaneous probability of repair, i.e., earlier repairs and fewer long waits. In contrast, a caesarean section compared to N/V was associated with a lower repair hazard (HR = 0.51; 0.34-0.79), consistent with more complex cases requiring specialist capacity. Labour duration and short stature were not independently strong after adjustment. Simulations confirmed estimator stability in modest cohorts and illustrated how parameter shifts move probability away from the long-wait tail.

Conclusion: Strengthening education‑linked navigation and antenatal engagement should shift repairs earlier and reduce backlogs, while C/S‑related cases warrant specialist triage and theatre skills to prevent accumulation in the long‑wait tail. Because the model’s parameter values and closed‑form outputs translate directly into time‑to‑percentage‑repaired forecasts, it is well suited for scheduling surgical camps, managing bed turnover, and tracking backlog risk in fistula programmes.

Introduction

Advanced countries have experienced prolonged below-replacement fertility, leading to population aging and, in many cases, decline [1,2]. A key consequence is the contraction of childbearing-age cohorts, raising the question of whether restoring fertility to replacement level can stabilize population size [3].

Methods

This study adopts a theoretical cohort–component projection approach grounded in stable population theory and the concept of population momentum [3,4]. Starting from low-fertility-age structures, projections assume an immediate shift to replacement fertility, constant mortality, and zero migration. Population trajectories are assessed through cohort evolution, focusing on reproductive-age groups and momentum effects [5].

Results

The analysis demonstrates that populations shaped by sustained below-replacement fertility exhibit negative population momentum [3]. While replacement-level fertility slows decline, it does not stabilize population size. The extent of decline depends on past fertility suppression, leading to smaller reproductive cohorts and increased population aging [6].

Conclusions

The findings indicate that fertility restoration alone is insufficient to reverse population decline in advanced low-fertility societies. Age structure and demographic inertia strongly shape outcomes [3,4]. Policies must address long-term aging and structural decline beyond fertility measures [2].

References:

1. Bongaarts, J. Human Population Growth and the Demographic Transition. Philos. Trans. R. Soc. B 2009, 364, 2985–2990.
2. Lutz, W.; Sanderson, W.; Scherbov, S. The Coming Acceleration of Global Population Ageing. Nature 2008, 451, 716–719.
3. Keyfitz, N. On the Momentum of Population Growth. Demography 1971, 8, 71–80.
4. Preston, S.H.; Heuveline, P.; Guillot, M. Demography: Measuring and Modeling Population Processes; Blackwell: Oxford, 2001.
5. Spears, D.; Vyas, S.; Weston, G.; Geruso, M. Long-Term Population Projections: Scenarios of Low or Rebounding Fertility. PLoS ONE 2024, 19, e0298190.
6. Sobotka, T. Post-Transitional Fertility: Childbearing Postponement and Low Fertility. Popul. Dev. Rev. 2017, 43, 641–680.

A cold standby system with two non-identical units with different failure rates is analyzed. The main emphasis is placed on how correlation between repair and failure times affects reliability measures. It involves examining the process of repair and replacement when a substandard unit experiences a failure. Assuming that the first unit remains operational during the repair or replacement process of the substandard unit, the system is considered to have failed when both units are in failure mode simultaneously. Various reliability measures and statistical distributions are used to assess the effectiveness of the system. An exponential distribution of the failure time, a general distribution of the time taken for repairs and Bivariate Exponentials are used for correlation. The time it takes for the entire system to fail when both units are in failure mode (MTSF), the proportion of time during which the system is operational (Availability), how often repair workers are needed to address failures, the duration in which repair workers are occupied (Busy Period Analysis), and the financial implications of the system's operation (Profit) are calculated using a Semi-Markov procedure and the Regenerative point method. The main focus is on understanding the reliability and effectiveness of a system with two non-similar units, emphasizing the correlation between repair and failure times. The analysis of this correlation can provide valuable insights into system performance and maintenance strategies. Graphs using MATLAB are prepared to present and interpret findings.

Flood Frequency Analysis (FFA) is a key statistical tool used to estimate the magnitude and probability of flood events associated with different return periods. Traditionally, FFA relies on the Annual Maximum Series (AMS), which considers only the largest flood event recorded each year. However, in regions that experience multiple flood events annually, such as Attanagalu Oya in Sri Lanka, the AMS approach may fail to capture important secondary or tertiary floods. To overcome this limitation, the present study applies the Partial Duration Series (PDS) method, which includes all flood events exceeding a predefined threshold and therefore provides a more comprehensive representation of flood characteristics. A threshold range between 3.5 m and 5.0 m, with increments of 0.1 m, was systematically evaluated to identify the most suitable level for event extraction. To ensure statistical independence among flood events, a declustering technique was applied to remove dependent peaks. Five probability distributions, Gumbel, Generalized Extreme Value (GEV), Lognormal, Weibull, and Generalized Pareto Distribution (GPD), were fitted to the PDS dataset. Parameter estimation was performed using established techniques, including the Method of Moments, Maximum Likelihood Estimation, and L-moments, depending on the specific distribution. Model performance was assessed using Nash–Sutcliffe Efficiency (NSE), Percent Bias (PBIAS), Root Mean Square Error (RMSE), and the RSR index. Results indicated that the GEV distribution provided the best overall performance (NSE = 0.9714, PBIAS = 0.1101, RMSE = 0.0252, and RSR = 0.1691), highlighting its suitability for design flood estimation and risk assessment in the study area. The Gumbel and Weibull models showed acceptable performance. The findings emphasize the importance of improved threshold selection and parameter estimation methods, as well as the potential integration of multivariate approaches to better capture flood dynamics and support effective hydrological planning and disaster risk management.

Introduction
Flexible lifetime distributions play a central role in both the theoretical development and practical application of survival and reliability analysis. Emerging experimental lifetime data in engineering and biological sciences often display skewness, heavy tails, and non-monotonic hazard rates that classical lifetime distributions fail to capture. Motivated by these limitations, this study introduces a new four-parameter lifetime distribution called the Transmuted Exponential–Weibull–Exponential (TE-W-E) distribution that extends the existing Weibull–exponential distribution. The TE-W-E is proposed to enhance the flexibility of the Weibull–exponential distribution for positive data.

Method
The TE-W-E distribution is constructed using the transmuted exponential-G generator to the Weibull–exponential distribution. The flexibility of the Weibull–exponential distribution was increased by inducing scale and transmuted parameters. Comprehensive derivations of its mathematical and statistical properties are presented. Expressions for the probability density, cumulative distribution, ordinary and central moments, moment generating, survival, and hazard functions were analytically derived. Model parameters were estimated using the maximum likelihood method, and the observed Fisher information matrix was derived to establish the asymptotic inference. Monte Carlo simulations were conducted to evaluate estimator performance under different sample sizes in terms of bias, variance, and mean squared error.

Results
The TE-W-E distribution is highly flexible, capable of modelling increasing, decreasing, and bathtub-shaped hazard rate functions. Simulation findings confirmed the consistency and efficiency of the maximum likelihood estimator. Application to two real datasets was demonstrated. The parameter estimates were obtained using the optim function in R software. The proposed TE-W-E model was compared with some well-established competing models: Weibull, Weibull–Exponential, and Weibull–Gamma. It outperforms the models based on likelihood and goodness-of-fit criteria: AIC, BIC, and CAIC. The new parameters contributed to the tail thickness and asymmetry.

Conclusion
The TE-W-E distribution is a robust model for lifetime data. Its flexibility and strong empirical performance make it a valuable contribution to survival and reliability analysis.

Effective control of invasive plant species involves allocating limited management resources across space and time in a manner consistent with underlying population dynamics and operational constraints. This study presents a discrete-time, spatially explicit mathematical model describing the expansion of Chinese privet (Ligustrum spp.), incorporating key biological processes such as seed dispersal, vegetative root propagation, and heterogeneous environmental suitability across a landscape grid. Model parameters governing growth and dispersal are calibrated using published ecological studies and field data compiled by collaborators. The ecological dynamics are coupled with a constrained multi-period optimization framework formulated as a mixed-integer linear programming (MILP) problem that determines when and where control actions should be implemented to minimize long-term reinfestation risk with finite budgets and treatment capacity. To address the multi-period decision structure, the optimization is implemented using a rolling-horizon solution approach, allowing sequential allocation decisions while updating the system state over time. The decision model explicitly accounts for treatment thresholds, spatial prioritization rules, and logistical limitations, enabling the evaluation of realistic management strategies over successive time steps. Simulation results demonstrate that temporally coordinated interventions and targeted spatial prioritization substantially reduce invasion intensity compared to uniform or short-term control policies. In particular, early intervention in high-connectivity cells yields disproportionate long-term benefits by suppressing secondary spread pathways. The proposed integrated modeling approach provides a quantitative decision-support tool for comparing alternative intervention scenarios, assessing trade-offs between cost and effectiveness, and identifying robust management policies under uncertainty. Overall, the framework supports evidence-based, cost-aware planning for invasive species control programs and can be adapted to other spatially spreading invasive organisms.

Introduction
Latent Transition Analysis (LTA) is widely used to model longitudinal changes in unobserved categorical states. However, applied researchers frequently encounter missing data, and there is limited guidance on how different missing data mechanisms, and analytic techniques used to address them, affect the recovery of latent classes and transition parameters. This study evaluates the performance of common methods used to handle missing data within an LTA framework under varying conditions.

Methods
We conduct a Monte Carlo simulation examining a two-class LTA model with binary indicators. Simulation conditions vary sample size, number of time points, number of indicators, missing data mechanism (MCAR vs. MAR), and missing data rate. Class membership follows a time-homogeneous transition matrix, and indicators follow class-specific emission probabilities with measurement invariance across time. Missingness is introduced randomly under MCAR and based on prior observations under MAR. Models are estimated using Full Information Maximum Likelihood (FIML), Multiple Imputation (MI), and weighting-based approaches.

Results
Results indicate that model performance depends strongly on the missingness mechanism and missing data rate. Parameter recovery was more accurate under MCAR than MAR missingness. FIML demonstrated stable performance across most scenarios. MI and weighting methods produced comparable results but were more sensitive to simulation parameters. Larger sample sizes and more indicators substantially improved latent class recovery and reduced bias in emission and transition parameter estimates across methods.

Conclusions
These findings highlight that no single missing data analytic technique is universally optimal. Method choice should be based on the characteristics of data and missingness. The results demonstrate how study design features—such as sample size and number of indicators—interact with the missingness mechanism and rate to influence latent class recovery and transition parameter estimation. Together, these findings highlight the importance of selecting the most appropriate analytic approach when applying LTA to longitudinal data with missingness.