Lifetime Distribution Research Articles

Statistical Framework for Modeling Asymmetrical Data with Dual Peaks

Objectives: To create a comprehensive framework that effectively identifies the most suitable model for asymmetrical data based on its unique characteristics. Methods: This study proposed a new model named Gompertz-Gumbel distribution (GGD) based on the results from the framework which utilizes various statistical tools, as well as information criteria. A dip test is used to check the modality of the data. To propose a new model, the finite mixture model concept was employed. The location, scale, shape, and weight parameters of the GGD were estimated using the maximum likelihood estimation method. Findings: The suggested framework exhibits superior performance in developing a suitable model for the asymmetrical data with dual peaks, resulting in the best fit for the data. To validate the effectiveness of the proposed model, it has been compared with various models like Gaussian models and two-component mixture models. The GGD's properties have also been determined. The various shapes of the GGD were also analyzed. Novelty: A novel framework is proposed to identify the appropriate model for the asymmetrical data with dual peaks that outperform the existing models. It shows the significance of the framework. Keywords: Lifetime distributions, Mixture models, Information Criteria, Goodness of fit, Asymmetrical data

Determining the lifetime distribution using fractional moments with maximum entropy

Here we propose a model-free, non-parametric method to solve an ill-posed inverse problem arising in several fields. It consists of determining a probability density of the lifetime, or the probability of survival of an individual, from the knowledge of the fractional moments of its probability distribution. The two problems are related, but they are different because of the natural normalization condition in each case. We provide a maximum entropy based approach to solve both problems. This problem provides a concrete framework to analyze an interesting problem in the theory of exponential models for probability densities. The central issue that comes up concerns the choice of the fractional moments and their number. We find that there are many possible choices that lead to solutions compatible with the data but in all of them, no more than four moments are necessary. The fact that a given data set can be accurately described by different exponential families poses a challenging problem for the model builder when attaching theoretical meaning to the resulting exponential density.

Inference on process capability index Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} for a new lifetime distribution

In various applied disciplines, the modeling of continuous data often requires the use of flexible continuous distributions. Meeting this demand calls for the introduction of new continuous distributions that possess desirable characteristics. This paper introduces a new continuous distribution. Several estimators for estimating the unknown parameters of the new distribution are discussed and their efficiency is assessed through Monte Carlo simulations. Furthermore, the process capability index Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} is examined when the underlying distribution is the proposed distribution. The maximum likelihood estimation of the Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} is also studied. The asymptotic confidence interval is also constructed for Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document}. The simulation results indicate that estimators for both the unknown parameters of the new distribution and the Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} provide reasonable results. Some practical analyses are also performed on both the new distribution and the Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document}. The results of the conducted data analysis indicate that the new distribution yields effective outcomes in modeling lifetime data in the literature. Similarly, the data analyses performed for Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} illustrate that the new distribution can be utilized for process capability indices by quality controllers.

Chitosan Mediated FAPbBr3 Nanocrystal Thin‐Films with High Color Purity and Enhanced Hole Mobility

Composite materials which combine the advantages of both embedded constituents have been a successful strategy for developing novel multi‐functional materials. Here, we demonstrate the synthesis of nanoscale materials of organic‐inorganic hybrid lead halide perovskites (OIH‐LHP) with enhanced optoelectronic properties and photostability by utilizing biomimetic ligand, chitosan. Notably, nanocrystals fabricated with chitosan mediated ligands exhibit an increase in photoluminescence quantum yield by 300% and fluorescence lifetime by 1.5 times. Consequently, the lifetime distribution of the photoluminescence emission decreases to a value as low as 6 ns. More interestingly, even though chitosan is a wide band gap insulating material, its incorporation onto the perovskite NCs enhances the bulk hole mobility by at least an order of magnitude in comparison to the pristine material. With detailed spectroscopic and structural studies, we correlate these enhancements in optoelectronic parameters to the improvement in the crystal quality, phase purity, and minimized poly‐dispersity of the nanocrystals. Development of such composite materials with unprecedented optoelectronic properties and outstanding stability will contribute immensely towards high performance nanocrystal devices.

Effects of random meso‐defects on fatigue behavior of welded joints: Damage evolution and lifetime prediction

AbstractRandom meso‐scale defects within welded joints can affect the structural damage process and cause dispersion in the fatigue lifetime of welded joints. In this paper, a meso‐scale stochastic damage approach is used to investigate the effect of random, meso‐scale defects on the fatigue damage lifetime of welded joints under different loads. First, we established an elastic–plastic fatigue damage model considering meso‐defects in the weld metal. Secondly, the fatigue lifetimes for gas tungsten arc welding and gas metal arc welding welded joints were predicted, with most of the predictions within the twofold dispersion factor. Thirdly, the Monte Carlo simulation method was used to investigate the influence of meso‐defect size on the fatigue lifetime dispersion degree, and the fatigue lifetime distribution under different loads was statistically analyzed.

A novel evaluation method of the aging performance of MEMS flow sensor

The development of Micro Electro Mechanical Systems (MEMS) flow sensor towards high level market applications generates various challenges, in particular also on the reliable functionality. With the advancement of reliability engineering technology, aging phenomenon of MEMS devices has been widely concerned. As a result, an aging evaluation method is essential. The accelerated aging testing (AAT) is the most widely used in traditional aging methods. However, its performance is limited by highly economic and time cost. In this paper, a novel aging effect model is proposed, in which a comprehensive approach that integrates AAT, lifetime distribution modeling, and either Finite Element Modeling Simulation (FEMS) or fatigue simulation (FS) as fundamental is explored. However, the difference from the conventional approach was that the AAT results is imported in FS, to confirm fatigue analysis, while FS predictions are instrumental in analyzing degradation or fatigue phenomena and estimation lifetime. In this way, aging performance is illustrated detailed with the lower aging cost and high efficiency. Meanwhile, the results of proposed FS are verified by a thermal cycle (TC) AAT. Specifically, the resistor degradation mechanism, the characteristic parameter degradation is calculated. Moreover, the lifetime evaluation was acquired by the Arrhenius model. Finally, the proposed aging performance evaluation method can be applied to both discrete devices and modules. Compared with the traditional aging method the high aging cost can be eliminated, and the proposed aging evaluation strategy can be used in various temperature conditions.

Ground replenishment strategy optimization of LEO satellite constellations considering performance degradation

This paper optimizes a ground replenishment strategy for large-scale LEO satellite constellations, aiming for ensuring high economic efficiency and performance requirements. Firstly, the uncertainties of influential elements are analyzed and satellite lifetime distributions are estimated to determine satellite operating statuses. Secondly, satellite statuses are used for obtaining real-time constellation status and simulating data package transmission paths. Performance degradation function is then derived by selecting time delay as the key performance. To confront with the performance degradation, an optimization model of ground replenishment strategy is established with the objective of minimizing the overall replenishment cost under the time delay and loading capacity constraints. The model is solved by a Dichotomous-domain algorithm. Finally, a case study of a large-scale STARLINK constellation is adopted to validate the effectiveness of the model and sensitivity analyses are conducted to verify its robustness.

Enhanced positronium lifetime imaging through two-component reconstruction in time-of-flight positron emission tomography

Positronium lifetime imaging (PLI) is a newly demonstrated technique possible with time-of-flight (TOF) positron emission tomography (PET), capable of producing an image reflecting the lifetime of the positron, more precisely ortho-positronium (o-Ps), before annihilation, in addition to the traditional uptake image of the PET tracer. Due to the limited time resolution of TOF-PET systems and the added complexities in physics and statistics, lifetime image reconstruction presents a challenge. Recently, we described a maximum-likelihood approach for PLI by considering only o-Ps. In real-world scenarios, other populations of positrons that exhibit different lifetimes also exist. This paper introduces a novel two-component model aimed at enhancing the accuracy of o-Ps lifetime images. Through simulation studies, we compare this new model with the existing single-component model and demonstrate its superior performance in accurately capturing complex lifetime distributions.

A new extended δ‐shock model with the consideration of shock magnitude

AbstractIn this article, a new ‐shock model that takes into account the magnitude of shocks is introduced and studied from reliability perspective. According to the new model, the system breaks down if either a shock after non‐critical shock occurs in a time length less than or a shock after a critical shock occurs in a time length less than where . The distribution of the system's lifetime is studied for both discrete and continuous intershock time distributions. It is shown that a new model is useful to describe a certain cold standby repairable system.

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Optimal and economic design of multiple deferred state repetitive group sampling plan for assuring mean life under a family of lifetime distributions

In this paper, a designing methodology of the multiple deferred (dependent) state repetitive group sampling plan is developed to ensure the mean lifetime of the products under the truncated life test, which follows a family of different lifetime distributions. An approach of two points on the operating characteristic curve is followed to obtain the optimal plan parameters with the known shape parameter values for various mean life ratios under different lifetime models. The proposed sampling plan is illustrated with a numerical example. The application of the proposed sampling plan is explained with a real-life example based on Burr XII distribution. Comparison is made among the performances of the proposed sampling plan using the different lifetime distributions; these performances are also compared with a single sampling plan using Burr XII distribution based on mean life assurance. Finally, an economic design of the proposed sampling plan is discussed, along with some cost models to minimize the total cost.

A New Extended Exponentiated Lomax (EEtLx) Distribution for Life Data

This paper proposes a new life distribution with both unbounded and bounded support. The proposed Extended Exponentiated Lomax (EEtLx) distribution is derived from the New Extended Exponentiated-G (NEET-G) family of Elgarhy, Haq, Gozel, and Nasir (2017). The maximum likelihood estimation method is used to estimate parameters of the proposed distribution and derive the relevant properties. The model is applied to patient relief times (minutes) after receiving a particular analgesic using different selection criteria (Log likelihood, Akaike Information Criteria (AIC), and Bayesian Information Criteria (BIC)). Resulting distributions are compared to well-established lifetime distributions in literature. The total time on test (TTT) plot is also used to determine whether the hazard rate function for this data increases or decreases, which subsequently reveals a decreasing trend. The proposed distribution remains the best fit compared to competing distributions. It is recommended that this distribution can be applied, not only in medical science, but also in reliability science, engineering, and economics fields.

Bivariate Lomax Distribution Based on Clayton Copula: Estimation and Prediction

Lomax distribution has been studied by many statisticians due to its important role in reliability modeling and lifetime testing. The bivariate Lomax distribution is an important lifetime distribution in survival analysis. In this article, a bivariate Lomax distribution is constructed based on Clayton copula. The joint probability density function and the joint cumulative distribution function are derived in closed forms. Some properties of this bivariate distribution are discussed. The maximum likelihood and Bayes estimators for the unknown parameters are derived. Also, the maximum likelihood and Bayesian two-sample prediction for the future observations are obtained. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, one real data set under the proposed distribution is considered to illustrate its flexibility and applicability for real-life applications.

Improving the Performance of a Parallel-Series System Based on Lindley Distribution

In this paper, a parallel-series system is improved. All components assume independent and identically distributed. The Lindley distribution with three parameters is assumed to be a lifetime distribution for the components. Four methods are used to improve the performance of the parallel-series system. The γ-fractiles and equivalence factors are derived. Finally, numerical results are discussed.

A Statistical Model of Hazard Rate Change Caused by a Random Shock

In the framework of statistical reliability analysis, we propose a model describing the change of reliability of a technical component after certain event, as for instance a shock, or the failure and maintenance. Two kinds of failure rate changes are considered, namely a shift of virtual age of analyzed component and the acceleration of its subjective time. The objective is to estimate both the baseline lifetime probability distribution and the magnitude of these changes. The estimation procedure is based on the maximum likelihood method, both parametric and nonparametric distributions of lifetime are considered. Further, a graphical method of the goodness-of-fit test is proposed. The method is then checked on artificial examples, finally a real data problem is solved.

A novel lifetime analysis of repairable systems via Daubechies wavelets

AbstractIt is well-known that minimally repaired systems are characterized by non-homogeneous Poisson processes. When the underlying lifetime distribution function or its associated intensity function is completely known, the statistical inference of the cumulative number of failures/repairs is made through some standard techniques. On the other hand, when the parametric form of the lifetime distribution or the intensity function is not known, non-parametric inference techniques such as non-parametric maximum likelihood estimate (NPMLE) and kernel-based estimates are employed. Since these techniques are based on the underlying lifetime data, the resulting estimates of the cumulative number of failures/repairs with respect to the system operation time are discontinuous and troublesome in assessing the reliability measures such as reliability function and mean time to failure, etc. In this paper, we propose a novel lifetime analysis of the repairable systems via Daubechies wavelets. More specifically, we generalize the seminal Daubechies wavelet estimate by Kuhl and Bhairgond (Winter Simul Conf Proc 1:562–571, 2000) by combining the ideas on NPMLE and KMBs. In both simulation experiments and real data analyses, we investigate applicability of our Daubechies wavelet-based approaches and compare them with the conventional non-parametric methods.

Reliability inference based on inverted exponentiated Rayleigh lifetime distribution under unified hybrid censored scheme

In this study, we investigated the Inverted Exponentiated Rayleigh Distribution (IERD), a significant and efficient continuous lifetime distribution commonly applied in lifespan research. Our focus was on estimating unknown parameters for a two-parameter inverted exponentiated Rayleigh distribution using unified hybrid censored data. We considered both maximum likelihood and Bayesian estimation approaches. Specifically, we employed the Gibbs within Metropolis–Hastings samplers method to develop approximate Bayes estimators utilizing informative and non-informative priors, along with symmetric and asymmetric loss functions. In addition, we utilized Markov chain Monte Carlo (MCMC) samples to derive maximum posterior density credible intervals. Simulation experiments were conducted to assess the efficacy of the proposed methodologies, and actual data analysis was performed to validate the proposed estimators.

Electrical Properties of FeGa0,4In1,6Se4 on Alternating Current

The temperature and frequency dependences of the dielectric constant and electrical conductivity of FeGa0,4In1,6Se4 crystals on alternating current have been studied. In the FeGa0,4In1,6Se4 crystal, normal dispersion occurs in the frequency range 2·102104 Hz, and the lifetime distribution of defects obeys the law n(τ) ~ τ−1.75. With increasing temperature, the reason for an increase in the value of the real part of the dielectric constant is an increase in the concentration of defects. The experimentally observed monotonic decrease in the imaginary part of the dielectric constant depending on frequency indicates the presence of relaxation dispersion in the FeGa0.4In1.6Se4 crystal. It has been established that in the temperature range 294,5 ÷ 343 K at frequencies 2∙102 ÷ 106 Hz for electrical conductivity the law σ ~ f S (0.1 ≤ S ≤ 1.0) is satisfied. It was shown that the conductivity in those crystals is characterized by a band-hopping mechanism. Activation energies were determined from the dependencies.

Analysis of a new extension version of the exponential model using improved adaptive progressive censored data and its applications

This article covers the issue of evaluating the two shape parameters and reliability metrics of a novel Kumaraswamy-exponential lifetime distribution, whose density exhibits a left-skewed, right-skewed, or symmetric shape, through a type-II improved adaptive progressively censored sample. Both conventional and Bayesian viewpoints are used to evaluate the various parameters, which include point and interval estimations. While the estimation of one of the shape parameters requires a numerical solution, the other shape parameter estimation can be carried out in closed form by the classical method. Besides, the likelihood method’s asymptotic traits are employed to provide interval estimations for all parameters. Leveraging the Markov chain Monte Carlo process, the symmetric squared loss function and independent gamma priors are taken into account for calculating Bayes points and the highest posterior density interval estimations. To illustrate the accuracy, compare estimation methods, and show the applicability of the various suggested methods, a simulation examination and a pair of applications are looked at. In the end, four accuracy indicators are taken into consideration to figure out the best progressive censoring pattern. The numerical results indicate that when collecting samples using the suggested censored procedure, it is advisable to use the Bayesian estimation approach for evaluating the Kumaraswamy-exponential distribution.

A NEW flexible exponent power family of distributions with biomedical data analysis

Probability distributions are widely utilized in applied sciences, especially in the field of biomedical science. Biomedical data typically exhibit positive skewness, necessitating the use of flexible, skewed distributions to effectively model such phenomena. In this study, we introduce a novel approach to characterize new lifetime distributions, known as the New Flexible Exponent Power (NFEP) Family of distributions. This involves the addition of a new parameter to existing distributions. A specific sub-model within the proposed class, known as the New Flexible Exponent Power Weibull (NFEP-Wei), is derived to illustrate the concept of flexibility. We employ the well-established Maximum Likelihood Estimation (MLE) method to estimate the unknown parameters in this family of distributions. A simulation study is conducted to assess the behavior of the estimators in various scenarios. To gauge the flexibility and effectiveness of the NFEP-Wei distribution, we compare it with the AP-Wei (alpha power Weibull), MO-Wei (Marshal Olkin Weibull), classical Wei (Weibull), NEP-Wei (new exponent power Weibull), FRLog-Wei (flexible reduced logarithmic Weibull), and Kum-Wei (Kumaraswamy Weibull) distributions by analyzing four distinct biomedical datasets. The results demonstrate that the NFEP-Wei distribution outperforms the compared distributions.