Lifetime Distribution Research Articles

Estimation with extended sequential order statistics: A link function approach

AbstractThe model of extended sequential order statistics (ESOS) comprises of two valuable characteristics making the model powerful when modelling multi‐component systems. First, components can be assumed to be heterogeneous and second, component lifetime distributions can change upon failure of other components. This degree of flexibility comes at the cost of a large number of parameters. The exact number depends on the system size and the observation depth and can quickly exceed the number of observations available. Consequently, the model would benefit from a reduction in the dimension of the parameter space to make it more readily applicable to real‐world problems. In this article, we introduce link functions to the ESOS model to reduce the dimension of the parameter space while retaining the flexibility of the model. These functions model the relation between model parameters of a component across levels. By construction the proposed ‘link estimates’ conveniently yield ordered model estimates. We demonstrate how those ordered estimates lead to better results compared to their unordered counterparts, particularly when sample sizes are small.

Lifetime Analysis of Dies Manufactured by Conventional Processes and Reconditioned by Deposition Welding Operation.

The refurbishment of dies by the deposition welding of wear areas is an efficient and economical process. The aim of this study was to conduct a comparative analysis of the lifetimes of different types of dies for the manufacturing of wagon wheels. The analyzed dies were manufactured by conventional processes (Type I) and reconditioned through a deposition welding procedure using a dedicated electrode (Type II). The Anderson-Darling test was conducted to analyze the goodness of fit of the lifetime data specific to the die types. The maximum likelihood estimation method (MLE) with a 95% confidence interval (CI) was applied in order to estimate the lifetime distribution parameters. It was found that the lifetimes of type II dies were longer than those of type I dies. The mean time to failure (MTTF) recorded for reconditioned dies was 426 min, while the mean time to failure of dies manufactured by conventional processes was approximatively 253 min. In addition, an accentuated hazard rate for type I dies compared to type II dies was observed. The results of this analysis emphasized the fact that dies can be restored to their initial operating capacity by successfully using deposition welding procedures that confer a high resistance to operational loads. At the same time, the use of these procedures allows for the sustainable development of resources and waste management.

Tests for homogeneity of distributions of component lifetimes from Type‐II censored system lifetime data with known system structures

AbstractIn system reliability analysis, researchers are interested in evaluating the characteristics of the lifetime distribution of components in a system based on system lifetime data. In collecting system lifetime data, a censoring scheme is often adopted due to time and budget constraints. In this article, we consider the situation where the system lifetime data from two different coherent systems are subjected to Type‐II right‐censoring, and we are interested in testing the homogeneity of component lifetime distributions based on Type‐II censored system lifetime data with known system structures. Based on the Mann‐Whitney test and empirical likelihood ratio tests developed for testing the homogeneity of component lifetime distributions with complete system lifetime data, we propose different non‐parametric test procedures using the permutation of the unobserved censored system lifetimes. We consider a restricted assumption on the censored lifetimes to reduce the permutations required in the computation. The computational approaches to obtain the critical values of the proposed test procedures are provided using the Monte Carlo method. A practical example is used to illustrate the proposed test procedures. Then, the power performance of the proposed test procedures is evaluated and compared through a Monte Carlo simulation study. The simulation results show that the proposed test procedures provide comparable power performance for Type‐II censored system lifetime data in contrast to the complete sample case under different scenarios. Finally, recommendations based on the simulation results and concluding remarks are provided.

Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals

AbstractRecently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal‐Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different causes across different time intervals. The failure count data is common in instances like one‐shot devices where the state of the subjects is inspected at different inspection times rather than the exact failure times. The point estimation of the lifetime distribution in the presence of competing risk has been studied through a divergence‐based robust estimation method called minimum density power divergence estimation (MDPDE) with and without constraint. The optimal value of the tuning parameter has been obtained. The testing of the hypothesis is performed based on a Wald‐type test statistic. The influence function is derived for the point estimator and the test statistic, reflecting the degree of robustness. Another key contribution of this work is determining the optimal inspection times based on predefined objectives. This article presents the determination of multi‐criteria‐based optimal design. Population‐based heuristic algorithm nondominated sorting‐based multiobjective Genetic algorithm is exploited to solve this optimization problem.

Analytical modeling of robustness and stochastic resilience of temporal small-world complex networks

This article explores the impact of online/offline node processes and Byzantine failures on the resilience of small-world network models, considering the lifetime of network nodes. We present novel analytical equations for estimating the expected communication time before user and network isolation, offering a unique perspective on network resilience through the lens of user behavior and involvement. Unlike most analyses focusing on stationary conditions, we employ network renewal processes to model these occurrences in temporal small-world networks where nodes can be online or offline. Our analytical equations, based on node lifetime distributions, shed light on the likelihood of network isolation under these conditions, offering valuable insights for optimizing network design and management. The validation of our analytical models through extensive simulations not only underscores their accuracy but also paves the way for a deeper understanding of temporal network behavior and resilience beyond the small-world paradigm.

Space charge region recombination in highly efficient silicon solar cells

The recombination rate in the space charge region (SCR) of a silicon-based barrier structure with a long Shockley–Reed–Hall lifetime is calculated theoretically by taking into account the concentration gradient of excess electron-hole pairs in the base region. Effects of the SCR lifetime and applied voltage on the structure ideality factor have been analyzed. The ideality factor is significantly reduced by the concentration gradient of electron-hole pairs. This mechanism provides an increase of the effective lifetime compared to the case when it is insignificant, which is realized at sufficiently low pair concentrations. The theoretical results have been shown to be in agreement with experimental data. A method of finding the experimental recombination rate in SCR in highly efficient silicon solar cells (SCs) has been proposed and implemented. It has been shown that at the high excess carrier concentration exceeding 1015 cm–3 the contribution to the SCR recombination velocity from the initial region of SCR that became neutral is significant. From a comparison of theory with experiment, the SCR lifetime and the ratio of the hole to the electron capture cross sections are determined for a number of silicon SCs. The effect of SCR recombination on the key characteristics of highly efficient silicon SCs, such as photoconversion efficiency and open-circuit voltage, has been evaluated. It has been shown that they depend not only on the charge carrier lifetime in SCR, but also on the ratio of hole to electron capture cross sections σp /σn. When σp /σn < 1, this effect is significantly strengthened, while in the opposite case σp /σn > 1 it is weakened. It has been ascertained that in a number of highly efficient silicon SCs, the distribution of the inverse lifetime in SCR is described by the Gaussian one. The effect described in the paper is also significant for silicon diodes with a thin base, p-i-n structures, and for silicon transistors with p-n junctions. In Appendix 2, the need to take into account the lifetime of non-radiative excitonic Auger recombination with participation of deep impurities in silicon is analyzed in detail. It has been shown, in particular, that considering it enables to reconcile the theoretical and experimental dependences for the effective lifetime in the silicon bulk.

Bayesian Inference for Inverse Power Exponentiated Pareto Distribution Using Progressive Type-II Censoring with Application to Flood-Level Data Analysis

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process’s performance under this ideal scheme.

Fitting various medical and engineering applications using the new lifetime distribution with a mathematical framework

Sustainability considerations play a crucial role in informing the modeling and fitting of medical and engineering data, ensuring the development of robust and environmentally conscious solutions. This paper delves into the investigation of a novel continuous distribution, aiming to provide a thorough understanding of its various fundamental mathematical and statistical properties. The analysis encompasses an exploration of survival functions, hazard rate functions, quantile, skewness, kurtosis, moments, mean time to failure, mean time to repair, insurance pricing principles, availability, and mean residual (past) lifetime functions. The proposed model demonstrates versatility in modeling both asymmetric and symmetric data across various kurtosis shapes. It can effectively handle outlier observations and accommodate different shapes of failure rates, including unimodal, bathtub, increasing, or decreasing patterns. This makes the proposed model suitable for modeling data in diverse fields. The maximum likelihood approach is employed to estimate model parameters using complete and upper recorded values. A simulation study is conducted to evaluate the performance of the estimators under different sample sizes for both complete and upper recorded values. To further demonstrate the flexibility and effectiveness of the new model, two datasets from medical and engineering domains are utilized for validation and testing purposes.

Low-mass Stars: Their Protoplanetary Disk Lifetime Distribution

While most protoplanetary disks lose their gas within less than 10 Myr, individual disk lifetimes vary from <1 Myr to ≫20 Myr, with some disks existing for 40 Myr. Mean disk half-lifetimes hide this diversity; only a so-far nonexisting disk lifetime distribution could capture this fact. The benefit of a disk lifetime distribution would be twofold. First, it would provide a stringent test on disk evolution theories. Second, it could function as an input for planet formation models. Here, we derive such a disk lifetime distribution. We heuristically test different standard distribution forms for their ability to account for the observed disk fractions at certain ages. We here concentrate on the distribution for low-mass stars (spectral types M3.7–M6, M s ≈ 0.1–0.24 M ⊙) because disk lifetimes depend on stellar mass. A Weibull-type distribution (k = 1.78, λ = 9.15) describes the observational data if all stars have a disk at a cluster age t c = 0. However, a better match exists for lower initial disk fractions. For f(t=0) = 0.65, a Weibull distribution (k = 2.34, λ = 11.22) and a Gaussian distribution (σ = 9.52, μ = 9.52) fit the data similarly well. All distributions have in common that they are wide, and most disks are dissipated at ages >5 Myr. The next challenge is to quantitatively link the diversity of disk lifetimes to the diversity in planets.

A new family of lifetime distributions with different directions of hazard rate

A new family of lifetime distributions with different directions of hazard rate

Marshall-Olkin Bilal distribution with associated minification process and acceptance sampling plans

In this paper, a new two parameters lifetime distribution, called Marshall-Olkin Bilal distribution is introduced and the structural properties are discussed. The proposed model results from the Marshall and Olkin class of distributions with the baseline model as Bilal distribution. We examined the statistical aspects like moments, quantile function, order statistics and entropy. The hazard function can model increasing and upside-down bathtub shaped data sets. The model parameter estimation is carried out by maximum likelihood estimation and a simulation study is performed. The flexibility of the proposed model is evaluated by two real data sets, compared with the competing models. Its application in time series is studied by the associated autoregressive minification process and the auto-correlation structure is derived. The acceptance sampling plans formulated for the proposed model and the characteristic results are illustrated.

An Integrated Predictive Maintenance and Operations Scheduling Framework for Power Systems Under Failure Uncertainty

Maintenance planning plays a key role in power system operations under uncertainty as it helps providers and operators ensure a reliable and secure power grid. This paper studies a short-term condition-based integrated maintenance planning with operations scheduling problem while considering the possible unexpected failure of generators as well as transmission lines. We formulate this problem as a two-stage stochastic mixed-integer program with failure scenarios sampled from the sensor-driven remaining lifetime distributions of the individual system elements whereas a joint chance constraint consisting of Poisson Binomial random variables is introduced to account for failure risks. Because of its intractability, we develop a cutting-plane method to obtain an exact reformulation of the joint chance constraint by proposing a separation subroutine and deriving stronger cuts as part of this procedure. We also derive a second-order cone programming-based safe approximation of this constraint to solve large-scale instances. Furthermore, we propose a decomposition algorithm implemented in parallel fashion for solving the resulting stochastic program, which exploits the features of the integer L-shaped method and the special structure of the maintenance and operations scheduling problem to derive valid and stronger sets of optimality cuts. We further present preprocessing steps over transmission line flow constraints to identify redundancies. To illustrate the computational performance and efficiency of our algorithm compared with more conventional maintenance approaches, we design a computational study focusing on a weekly plan with daily maintenance and hourly operational decisions involving detailed unit commitment subproblems. Our computational results on various IEEE instances demonstrate the computational efficiency of the proposed approach with reliable and cost-effective maintenance and operational schedules. History: Accepted by Andrea Lodi, Area Editor for Design &amp; Analysis of Algorithms—Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.0154 .

Kinetics of RNA-LNP delivery and protein expression

Lipid nanoparticles (LNPs) employing ionizable lipids are the most advanced technology for delivery of RNA, most notably mRNA, to cells. LNPs represent well-defined core–shell particles with efficient nucleic acid encapsulation, low immunogenicity and enhanced efficacy. While much is known about the structure and activity of LNPs, less attention is given to the timing of LNP uptake, cytosolic transfer and protein expression. However, LNP kinetics is a key factor determining delivery efficiency. Hence quantitative insight into the multi-cascaded pathway of LNPs is of interest to elucidate the mechanism of delivery. Here, we review experiments as well as theoretical modeling of the timing of LNP uptake, mRNA-release and protein expression. We describe LNP delivery as a sequence of stochastic transfer processes and review a mathematical model of subsequent protein translation from mRNA. We compile probabilities and numbers obtained from time resolved microscopy. Specifically, live-cell imaging on single cell arrays (LISCA) allows for high-throughput acquisition of thousands of individual GFP reporter expression time courses. The traces yield the distribution of mRNA life-times, expression rates and expression onset. Correlation analysis reveals an inverse dependence of gene expression efficiency and transfection onset-times. Finally, we discuss why timing of mRNA release is critical in the context of codelivery of multiple nucleic acid species as in the case of mRNA co-expression or CRISPR/Cas gene editing.

Standby redundancy allocation for series and parallel systems

. The allocation of redundant components to a system is an efficient technique to improve its lifetime. In this article, we study the problem of two standby redundancy allocations for series and parallel systems, consisting of n-component (n≥2), in the sense of various stochastic orderings. It is assumed that components and redundancies follow a general lifetime distribution. For the case of allocating two redundancies to a series (parallel) system, we show that allocating the relatively stronger redundancy to the weaker component and the weaker redundancy to the stronger components can result in a system lifetime that is longer (shorter) in terms of the usual stochastic order. Moreover, various results associated with the hazard rate and reversed hazard rate orders are established. The outcomes of various papers are strengthened and generalized through our results. In addition, some applications are provided to illustrate our findings.

Modified age-based replacement

The maintenance policy age-based replacement (ABR) is widely specified in OEM instructions. The practical application of ABR raises concerns about ensuring consistent adherence to prescribed replacement schedules for extended periods. ABR lacks periodicity, resulting in scheduling asynchrony with designated time slots, while alternative policies such as block replacement (BR) provide periodicity at the expense of efficiency. Additionally, scepticism about ABR is based on its simplicity and restrictive assumptions, which include ideal replacements and the one-component system assumption. The task of estimating component lifetime distributions and defining critical parameters such as cost of failure presents significant challenges. We study “modified age-based replacement” (MABR) in response to the limitation of aperiodicity, so that preventive replacements exhibit quasi-periodic behavior. We quantify the cost-inefficiency of MABR compared to ABR, thus informing the practical implications of introducing periodicity into the ABR policy and highlighting the need to incorporate real-world constraints, such as time slots for maintenance actions. The findings indicate that MABR and a special case are reasonably efficient provided the slot-interval is not too large. This is a useful insight for practical application of ABR type policies for scheduling preventive maintenance.

Annealing effects on the structural, positron annihilation parameters, and electrical properties of Fe2O3- PbO2-TeO2 glasses

This study focuses on the transformation of selected glasses consisting of 20Fe2O3–xPbO2–(80–x)TeO2 (where x = 5, 10, 15, 20, and 25 mol%) with varying concentrations of PbO2, into nanomaterials through annealing at a temperature close to the crystallization temperature (Tc). The physical and chemical properties of the resulting samples were investigated. The chemical structure was analyzed using Fourier Transform Infrared spectroscopy (FTIR), which revealed no significant chemical changes except for an increase in the concentration of PbO2. X-ray diffraction (XRD) was used to study the crystal structure. Improvements were seen with increasing PbO2 concentrations, and these improvements were further increased after the sample was annealed. Furthermore, positron annihilation lifetime (PAL) spectroscopy was used to study the microstructure, more precisely the size of vacancy-type defects. A correlation was established between the PAL and the properties of the samples. The size of the vacancy-type defects was confirmed by calculating the distribution of the long lifetime deduced from the PAL. In this work, the overall influence of PbO2 concentration and thermal treatment on the chemical and crystalline structures, electrical conductivity, and microstructure of the studied nanomaterials is highlighted. The results provide valuable insights into the relationship between the PAL and the properties of the samples and provide potential opportunities to tailor their properties for different applications.

A new estimation approach based on phi‐divergence measures for one‐shot device accelerated life testing

AbstractOne‐shot device testing data are used only once and they get destroyed when tested. As these products usually have large mean times to failure under normal operating conditions, accelerated life tests are commonly used to infer their lifetime distribution. While much work has been done to determine the maximum likelihood estimates (MLEs) of model parameters for one‐shot device accelerated life testing, the efficiency of these methods may not be guaranteed for small to moderate sample sizes. In this paper, we develop new estimators and confidence intervals based on phi‐divergences, we show that they outperform the conventional MLE under different lifetime distributions and present an example to illustrate all the inferential methods developed here.

A new three-parameter lifetime distribution for environmental data analysis: the Harris extended modified Lindley distribution

A new three-parameter lifetime distribution for environmental data analysis: the Harris extended modified Lindley distribution

On the Statistical Properties of the Remkan Distribution

The Remkan distribution is a two-parameter lifetime distribution that has been introduced into the literature to meet the ever-growing demand for the development of new lifetime distributions to meet the goodness of fit demand of complex datasets. The mathematical properties of the Remkan distribution have been derived in the literature. This study therefore aims to derive important statistical properties including the mode, quantile function, order statistics, entropy, stochastic ordering, average absolute deviation, and mid-point and Reliability indices such as the survivorship or existence measurement function, risk measurement function, and average residual measurement lifetime function.

A Discrete Odd Lindley Half-Logistic Distribution with Applications

In the reality, the most of lifetime data is discrete in nature, despite it is known that this data is continuous. As a consequence, the tendency to convert the continuous lifetime distributions to its discrete counterpart has raised. The nature of the most lifetime data in real life is discrete, thus, many of researchers interested to convert. This article aims to introduce a new one-parameter discrete distribution, namely Discrete Odd Lindley Half-Logistic (DOLiHL) distribution. The DOLiHL distribution is derived by discretizing the analogue continuous distribution, using a survival discretization technique. An intensive study of this distribution is provided, including characteristic functions and statistical properties. Moreover, the unknown parameter is estimated using different methods of estimation namely, the maximum likelihood method, method of moments, least squares method and Cramer-von Mises minimum distance estimation method. A simulation study is conducted to examine the distribution’s behavior and compare between the estimation methods at different sample sizes. To evaluate the efficiency of this distribution against other competitive distributions, an implementation on real data in different fields is performed. In conclude, the DOLiHL distribution has assured its efficiency of fitting in lifetime and count data from various fields in real life.