This study proposes a multiresolution wavelet-based framework for improving process monitoring in regression-based quality control systems. The proposed approach integrates the discrete wavelet transform (DWT) with regression control charts by decomposing the fitted-value and residual series into approximation and detail coefficients, thereby enabling the simultaneous monitoring of global process behavior and localized variations. An independent sensitivity analysis compared Daubechies orders db4, db8, db11, db20, and db41 at Decomposition Levels 1 and 2. Among the configurations suitable for the full simulated sample-size range, db11 at Level 1 achieved the highest mean detection probability and was retained for the primary simulation; db41 at Level 1 was retained for the real-data illustration on the basis of a separate development-subset comparison. The performance of the proposed framework was assessed through simulation experiments conducted under different sample sizes, noise levels, and process-shift magnitudes. The evaluation was based on detection probability, false-alarm probability, and conditional average detection delay. The results showed that the wavelet-based charts generally produced narrower control limits, higher detection probabilities, lower false-alarm probabilities, and shorter detection delays than the classical regression control chart, particularly for small process shifts. A real-data application involving the regression modeling of hemoglobin using hematocrit and mean corpuscular volume was also presented. In this application, the wavelet approximation residual chart detected three out-of-control observations, whereas the classical residual chart and the wavelet detail residual chart each detected two. These findings indicate that multiresolution wavelet analysis can enhance the sensitivity of regression-based monitoring schemes and provide a useful statistical framework for detecting global and localized process changes.
We study the limiting behavior of the sum of independent copies of a pseudo-Poisson-type process, also known as the Poisson stochastic index (PSI) process. Under a series scheme satisfying the infinitesimality condition, we prove that the sum of independent PSI processes with random intensity converges, in the sense of finite-dimensional distributions, to a trawl process. To support the theoretical convergence results, we provide a series of Monte Carlo simulations illustrating the behavior of the sum of independent PSI processes. As part of this analysis, we derive an explicit formula for the elements of the slice partition associated with monotonic trawls having an exponential structure of the trawl function. In the special case of PSI processes with nonrandom intensity, we show convergence to a trawl process with an exponential trawl. The connection between PSI processes and trawl processes highlights that the theoretical results obtained can inform the modeling of real-world phenomena, such as irregular event arrivals in communication networks or rare, extreme fluctuations in financial markets. Finally, we investigate structural properties of the trawl process with an exponential trawl, demonstrating that it is generally non-Markovian. We provide examples illustrating how the Markov property of such processes is closely related to the distributional features of the associated Lévy basis bridge.
This paper introduces a new lifetime distribution, called the Maxwell–logistic growth lifetime (MLGL) distribution, obtained by incorporating a logistic-growth hazard structure into the Maxwell-generated family of distributions. In contrast to Maxwell-generated models based on conventional baseline lifetime distributions, the MLGL model incorporates a baseline hazard governed by a logistic-growth ordinary differential equation, providing an interpretable mechanism for dynamically evolving failure risk. The resulting model admits an identifiable three-parameter representation and allows the underlying hazard dynamics to vary according to the logistic-growth parameters. Several distributional and reliability properties are derived. A Monte Carlo simulation study is conducted to examine the finite-sample performance of the estimators. Applications to real lifetime datasets demonstrate that the proposed model provides competitive fits relative to several classical and recently proposed lifetime distributions.
Developing flexible probability distributions capable of capturing complex features observed in lifetime data remains a fundamental challenge in statistical modeling. The limitations of classical probability distributions in adequately modeling varying degrees of skewness, heavy-tailed behavior, and nonmonotonic failure rates have motivated the development of more flexible distributional families based on diverse transformation mechanisms. This paper introduces the alpha power new exponentiated family (APNEF) of distributions, a unified framework that integrates two transformation mechanisms: the new exponentiation transformation and the alpha power transformation. The proposed family extends baseline distributions through multiple shape parameters, enabling flexibility in capturing complex data structures while maintaining computational tractability. We derive key statistical properties of the APNEF, including the quantile function, noncentral and incomplete moments, the Rényi entropy, and the Lorenz and Bonferroni inequality curves. A suite of estimation procedures is developed and assessed via Monte Carlo simulation, evaluating finite-sample performance and consistency and offering guidance on estimator choice. We extend the APNEF to a log-location-scale regression framework to facilitate its application in regression settings. The resulting model falls within the accelerated failure time class, with covariates entering linearly on the log-response scale and a shape parameter determining the form of the error term. The theoretical and empirical effectiveness of the proposed family is demonstrated through applications to lifetime datasets, where the alpha power new Weibull distribution, a member of the APNEF family, consistently outperforms numerous competing models. The findings establish APNEF as a valuable and flexible framework for statistical inference in reliability analysis, survival studies, and other applied domains.
We propose and study the five-parameter beta odd Pareto (BOP) distribution, obtained by applying the beta generator to the odd Pareto baseline. The construction is standard, but it leads to new results on asymptotic tail behavior and identifiability, together with applications to risk management. The density can be positively or negatively skewed, symmetric, unimodal or bathtub-shaped, and the hazard rate can be increasing, upside-down bathtub or bathtub-shaped. We prove every result that admits a closed-form derivation: an exact infinite mixture representation, the boundary behaviour of the density, regular variation of the survival function with tail index α=λβδ and closed integral forms for the quantile function, moments, mean residual life, order statistics and the maximum-likelihood score equations. A Monte Carlo study shows that maximum likelihood recovers risk-relevant functionals (median, high quantiles and value at risk) accurately, while the individual shape parameters remain weakly identified, with undercovering Wald intervals that a Bayesian alternative substantially improves. On automobile insurance claims, BOP outperforms the Pareto distribution and five extensions on likelihood- and distribution-based fit criteria and gives the most accurate value at risk and conditional tail expectation backtests at the 1% level. On a second, independent dataset (Norwegian fire claims, n=4,745), BOP again decisively outperforms its own nested submodels in and out of sample and attains the smallest distribution-based fit statistics of all seven models compared, a robustness check we report in full.
