Lifetime Distribution Research Articles

Development of a new exponential generalized family of distribution with its properties and application

In the field of reliability analysis, the selection of an appropriate lifespan model is critical. With a multitude of lifetime distributions accessible, the hunt for a more suited distribution remains essential. In this paper, we offer a unique class of distributions derived from the notion of exponential generalization, improved with changes to boost flexibility. Our suggested distribution incorporates multiple hazard rate profiles, giving enhanced flexibility. Analytical characteristics including the rth moment, moment generating function, quantile function, distribution of order statistics, and Rényi entropy are obtained. Employing maximum likelihood estimation, we estimate the unknown parameters. Through simulation tests and analysis of real-world datasets, we exhibit the model's usefulness compared to five existing lifespan distributions, emphasising the better performance of the GAYUF distribution. This research underlines the GAYUF distribution as a better model in the field of lifespan analysis

Extreme Values and Reliability Measures of Continuous Erlang Mixtures

This study delves into Extreme Value Theory, focusing on the limiting distributions of continuous Erlang mixtures and their mixing distributions. It categorizes Erlang mixtures based on their extreme value types, demonstrating that the limiting distributions of the Erlang mixtures can be either Type I (Gumbel) or Type II (Frechet), contingent on the mixing distribution. Further, this study derives the mean residual lifetime and equilibrium distributions of these mixed distributions.

Preventive maintenance policy optimization for a weighted k-out-of-n: G system using the survival signature

This paper presents a novel preventive maintenance (PM) policy for a weighted k-out-of-n: G system. The system consists of critical components with high weight and other low-weight components, while the critical ones significantly impact the system's total weight. The lifetime distribution of critical and other components follows the Weibull distribution with different shape and scale parameters. Different maintenance actions are performed on the component according to the number of failed critical components and the total weight of the working components. The expected cost per renewal cycle and system availability are analyzed based on survival signature. The optimal PM cycle and the inspection period are derived by minimizing the expected cost per renewal cycle or maximizing availability. Finally, the effectiveness of the presented strategy is illustrated by a numerical case.

A reliability model for non-isothermal isotropic damages

This study introduces a novel lifetime distribution originating from the Neyman Type A distribution. We built a Neyman Type A counting process and developed a survival function. Some statistical properties of the new distribution were presented, such as the resulting humped hazard function and its convergence. An accelerated test model structure with Arrhenius law was specified, and the effects of different accelerating stresses were analyzed. The hazard function implied by the model is inversely proportional to the stress, which results in interesting features and provides an efficient approach to describe the lifespan phenomena of some engineering metals and bulbs under low temperatures. The estimation of parameters of the accelerated model by maximum likelihood, mean time to failure, and expected number of failures are discussed in the numerical experiments.

New and Efficient Estimators of Reliability Characteristics for a Family of Lifetime Distributions under Progressive Censoring

Estimation of reliability and stress–strength parameters is important in the manufacturing industry. In this paper, we develop shrinkage-type estimators for the reliability and stress–strength parameters based on progressively censored data from a rich class of distributions. These new estimators improve the performance of the commonly used Maximum Likelihood Estimators (MLEs) by reducing their mean squared errors. We provide analytical asymptotic and bootstrap confidence intervals for the targeted parameters. Through a detailed simulation study, we demonstrate that the new estimators have better performance than the MLEs. Finally, we illustrate the application of the new methods to two industrial data sets, showcasing their practical relevance and effectiveness.

Optimal step stress accelerated degradation tests with the bivariate inverse Gaussian process

AbstractStep‐stress accelerated degradation test (SSADT) has become a prevailing approach to lifetime assessment for highly reliable products. In practice, many products suffer from multiple degradation processes that significantly contribute to failures. In this paper, we investigate the optimal SSADT plans for products subject to two dependent degradation characteristics modeled by a bivariate inverse Gaussian process. The drift parameter of each process is assumed to be influenced by a common stress factor. A bivariate Birnbaum‐Saunders (BVBS)‐type distribution is employed to approximate the lifetime distribution and facilitate the derivation of the objective function. The optimal plans are prescribed under three common optimality criteria in the presence of constraints on test units and inspections. A revisited example of fatigue crack is then presented to demonstrate the proposed methods. Finally, the sensitivity of the SSADT plans is studied, and the results exhibit fair robustness of the optimal plans.

Reliability Assessment of Bridge Structure Using Bilal Distribution

Reliability assessments are pivotal in evaluating system quality and have found extensive application in manufacturing. This research delves into a system comprising five components, one of which is a bridge network. The components are presumed to follow a Bilal lifetime distribution with a failure rate that changes over time. Four distinct methods are employed to enhance the components within the system. This study involves the computation of δ-fractiles and reliability equivalence factors (REFs). Additionally, a numerical case study is provided to elucidate the theoretical findings.

Estimating the parameter of a geometric distribution from series system data

In a traditional setup of estimation of an unknown parameter of component lifetime distribution, system’s continuous lifetime data is used. In this paper, we propose a simple and competitive estimator that is based on discrete lifetime data, i.e., the number of failed components at the time when the system fails. In particular, we consider the estimation of the parameter of a geometric distribution based on the system’s lifetime data, and the number of failed components upon the failure of the system when the system has a series structure. Two moment estimators that are based on the system lifetime data and the number of failed components at the moment of system failure are obtained and their performances are compared in terms of the mean square error. The associated Bayesian estimators with non-informative priors are also discussed.

Bayesian and non-bayesian inference for logistic-exponential distribution using improved adaptive type-II progressively censored data.

Improved adaptive type-II progressive censoring schemes (IAT-II PCS) are increasingly being used to estimate parameters and reliability characteristics of lifetime distributions, leading to more accurate and reliable estimates. The logistic exponential distribution (LED), a flexible distribution with five hazard rate forms, is employed in several fields, including lifetime, financial, and environmental data. This research aims to enhance the accuracy and reliability estimation capabilities for the logistic exponential distribution under IAT-II PCS. By developing novel statistical inference methods, we can better understand the behavior of failure times, allow for more accurate decision-making, and improve the overall reliability of the model. In this research, we consider both classical and Bayesian techniques. The classical technique involves constructing maximum likelihood estimators of the model parameters and their asymptotic covariance matrix, followed by estimating the distribution's reliability using survival and hazard functions. The delta approach is used to create estimated confidence intervals for the model parameters. In the Bayesian technique, prior information about the LED parameters is used to estimate the posterior distribution of the parameters, which is derived using Bayes' theorem. The model's reliability is determined by computing the posterior predictive distribution of the survival or hazard functions. Extensive simulation studies and real-data applications assess the effectiveness of the proposed methods and evaluate their performance against existing methods.

Static and dynamic stress analysis of different crown materials on a titanium base abutment in an implant-supported single crown: a 3D finite element analysis

BackgroundThis Finite Element Analysis was conducted to analyze the biomechanical behaviors of titanium base abutments and several crown materials with respect to fatigue lifetime and stress distribution in implants and prosthetic components.MethodsFive distinct designs of implant-supported single crowns were modeled, including a polyetheretherketone (PEEK), polymer-infiltrated ceramic network, monolithic lithium disilicate, and precrystallized and crystallized zirconia-reinforced lithium silicates supported by a titanium base abutment. For the static load, a 100 N oblique load was applied to the buccal incline of the palatal cusp of the maxillary right first premolar. The dynamic load was applied in the same way as in static loading with a frequency of 1 Hz. The principal stresses in the peripheral bone as well as the von Mises stresses and fatigue strength of the implants, abutments, prosthetic screws, and crowns were assessed.ResultsAll of the models had comparable von Mises stress values from the implants and abutments, as well as comparable maximum and minimum principal stress values from the cortical and trabecular bones. The PEEK crown showed the lowest stress (46.89 MPa) in the cervical region. The prosthetic screws and implants exhibited the highest von Mises stress among the models. The lithium disilicate crown model had approximately 9.5 times more cycles to fatique values for implants and 1.7 times more cycles to fatique values for abutments than for the lowest ones.ConclusionsWith the promise of at least ten years of clinical success and favorable stress distributions in implants and prosthetic components, clinicians can suggest using an implant-supported lithium disilicate crown with a titanium base abutment.

Bayesian reliability acceptance sampling plans under interval censoring

. This work considers Bayesian reliability acceptance sampling plan (RASP) under interval censoring. It is considered that the consumer and manufacturer agree on a common lifetime distribution of the product. However, they differ in their assessment of the prior distributions and utility functions because of the adversarial nature of the consumer and manufacturer, but the manufacturer knows the consumer’s utility and prior. The consumer accepts or rejects a lot of products based on his/her own priors about the quality of the product and a utility function. If the consumer rejects the lot, the manufacturer gives additional information on lifetime based on a life test to update the consumer’s belief. The consumer decides on accepting or rejecting the lot based on updated information. The life test is conducted under an interval censoring scheme, where the decision on acceptance or rejection of the lot can be taken sequentially at pre-specified inspection times. The manufacturer’s task is to determine the optimal interval-censoring life testing plan which maximizes his/her utility. Last, we discuss a methodology where the manufacturer does not require knowledge of the consumer’s utility function and prior distribution for planning the life test.

Parametric estimations of the mean value and variance functions in geometric process

The paper introduces novel parametric estimators for the mean value function (MVF) and variance function (VF) in geometric processes (GPs) based on a random sample which belongs to a GP. Specifically, it addresses scenarios where the distribution function of the first interarrival time of GP is analytically known, but its parameters, along with the ratio parameter of the GP, are unknown. It establishes a solid theoretical foundation for the estimators proposed and investigates some statistical properties such as strong consistency and asymptotic unbiasedness of the estimators. These results generalize some of the findings acquired in previous studies. To evaluate the performance of the proposed estimators, we conduct a comprehensive Monte Carlo simulation study. This involves using various lifetime distributions, such as gamma, Weibull, and lognormal considering different sample sizes and parameter values. A discussion of an application to software engineering is also provided to illustrate the applicability of the methods developed in this study.

A hybrid prognostic & health management framework across multi-level engineering systems with scalable convolution neural networks and adjustable functional regression models

With the rapid development of sensor technology and mechatronics integration, there are emerging demands for achieving prognostic and health management (PHM) within a general framework across multi-level engineering systems. However, current PHM frameworks are mainly supported either by field data or degradation models, which are always limited in inadequate robustness to systematically increase operational availability and reduce maintenance costs. For extending the scalability and flexibility of PHM services, this paper proposes a novel hybrid framework that integrates the scalable convolution neural network (SCNN) with the adjustable functional regression model (AFRM) through a modified linear filter. This proposed framework first establishes a data-driven SCNN with scalable time sequences and kernel sizes to enhance the remaining useful life (RUL) generalization. Then, enabled by an adjustable semi-parametric degradation process model, AFRM with flexible lifetime distributions is designed to evaluate time-to-failure (TTF) in real time. Finally, a modified Kalman filter has been explored to coordinate data-driven RUL results with model-based TTF values to schedule predictive maintenance (PdM). High-accuracy prediction, multi-level systems, high-flexibility evaluation are thus encompassed within the hybrid progressive modification. The proposed framework has been practically validated through multi-level studies including the component-level bearings, subsystem-level engines, and system-level machines. Results demonstrate that our hybrid PHM framework achieves significant improvements in prediction accuracy, evaluation adaptability, and scheduling effectiveness.

The component outage model for power systems using availability approximations

The traditional outage models with constant failure rates do not truly reflect the environmental and operating conditions nor the effect of repair operations on power systems. This paper proposes two useful approximations for the availability function based only on the first three of the lifetime distribution. We compare the availability function of a power transformer using the numerical inverse of the transformed availability function. It also suggests methods to verify the effectiveness of the approaches. Finally, it outlines the proposed approximations to validate the efficacy of the approximations.

Statistical Reliability Assessment with Generalized Intuitionistic Fuzzy Burr XII Distribution

Intuitionistic fuzzy sets provide a viable framework for modelling lifetime distribution characteristics, particularly in scenarios with measurement imprecision. This is accomplished by utilizing membership and non-membership degrees to accurately express the complexities of data uncertainty. Nonetheless, the complexities of some cases necessitate a more advanced approach of imprecise data, motivating the use of generalized intuitionistic fuzzy sets (GenIFSs). The use of GenIFSs represents a flexible modeling strategy that is characterized by the careful incorporation of an extra level of hesitancy, which effectively clarifies the underlying ambiguity and uncertainty present in reliability evaluations. The study employs a methodology based on generalized intuitionistic fuzzy distributions to thoroughly examine the uncertainty related to the parameters and reliability characteristics present in the Burr XII distribution. The goal is to provide a more accurate evaluation of reliability measurements by addressing the inherent ambiguity in the distribution’s shape parameter. Various reliability measurements, such as reliability, hazard rate, and conditional reliability functions, are derived for the Burr XII distribution. This extensive analysis is carried out within the context of the generalized intuitionistic fuzzy sets paradigm, improving the understanding of the Burr XII distribution’s reliability measurements and providing important insights into its performance for the study of various types of systems. To facilitate understanding and point to practical application, the findings are shown graphically and contrasted across various cut-set values using a valuable numerical example.

On the residual lifetimes of dependent components upon system failure

In this paper, we consider coherent systems composed of identical yet possibly dependent components. The dependence structure among components is modelled via copulas. We investigate residual lifetimes of components that survived the failure of the system. The main result of the paper is a new general formula describing the joint distribution of these residual lifetimes. Using the new formula we look more closely at this distribution in the cases of Clayton, Gumbel–Hougaard and Frank copulas and standard exponential and Weibull margins. In particular, we present some comparative numerical results that enable us to examine the influence of the dependence among components on the residual lifetimes of the surviving ones. We observe that the results obtained under the assumption of dependence and independence may differ significantly, especially when the system breaks down just after it started working.

Semiparametric evaluation of first‐passage distribution for step‐stress accelerated degradation tests

AbstractIn reliability engineering, different types of accelerated degradation tests have been used to obtain reliability information for evaluating highly reliable or expensive products. The step‐stress accelerated degradation test (SSADT) is one of the useful experimental schemes that can be used to save the resources of an experiment. Motivated by the SSADT data for operational amplifiers collected in Xi'an Microelectronic Technology Institute, in which the underlying degradation mechanism of the operational amplifiers is unknown, we propose a semiparametric approach for SSADT data analysis that does not require strict distributional assumptions. Specifically, the empirical saddlepoint approximation method is proposed to estimate the items' lifetime (first‐passage time) distribution at both stress levels included and not included in the SSADT experiment. Monte Carlo simulation studies are used to evaluate the performance and illustrate the advantages of the proposed approach. Finally, the proposed semiparametric approach is applied to analyze the motivating data set.

Evaluating the lifetime distribution parameters and reliability of products using successive approximation method

AbstractThe Weibull distribution is an extensively used statistical model for analyzing the reliability of mechanical and electrical components. Due to the complexity of the nonlinear equations and the scarcity of failure data, the common method may not provide satisfactory results of the reliability. In this case, a new approach for Weibull parameter estimation and reliability analysis, based on successive approximation schemes, is presented. The shape and scale parameters are estimated by maximizing the likelihood functions, and the location parameter is obtained by constructing an approximate correction model between it and the failure data. In order to show the performance of the proposed method, an extensive Monte‐Carlo simulation study is conducted. Simulation results show that the proposed method provides better estimates and efficient confidence intervals for Weibull parameters. In addition, the proposed method works well in presence of small sample sizes. Finally, two real examples are analyzed to illustrate the application of the proposed method.

A Physics-Based Tweedie Exponential Dispersion Process Model for Metal Fatigue Crack Propagation and Prognostics

Most structural faults in metal parts can be attributed to fatigue crack propagation. The analysis and prognostics of fatigue crack propagation play essential roles in the health management of mechanical systems. Due to the impacts of different uncertainty factors, the crack propagation process exhibits significant randomness, which causes difficulties in fatigue life prediction. To improve prognostic accuracy, a physics-based Tweedie exponential dispersion process (TEDP) model is proposed via integrating Paris Law and the stochastic process. This TEDP model can capture both the crack growth mechanism and uncertainty. Compared with other existing models, the TEDP taking Wiener process, Gamma process, and inverse process as special cases is more general and flexible in modeling complex degradation paths. The probability density function of the model is derived based on saddle-joint approximation. The unknown parameters are calculated via maximum likelihood estimation. Then, the analytic expressions of the distributions of lifetime and product reliability are presented. Significant findings include that the proposed TEDP model substantially enhances predictive accuracy in lifetime estimations of mechanical systems under varying operational conditions, as demonstrated in a practical case study on fatigue crack data. This model not only provides highly accurate lifetime predictions, but also offers deep insights into the reliability assessments of mechanically stressed components.

Four-Dimensional Physical Unclonable Functions and Cryptographic Applications Based on Time-Varying Chaotic Phosphorescent Patterns.

Physical unclonable functions (PUFs) have attracted interest in demonstrating authentication and cryptographic processes for Internet of Things (IoT) devices. We demonstrated four-dimensional PUFs (4D PUFs) to realize time-varying chaotic phosphorescent randomness on MoS2 atomic seeds. By forming hybrid states involving more than one emitter with distinct lifetimes in 4D PUFs, irregular lifetime distribution throughout patterns functions as a time-varying disorder that is impossible to replicate. Moreover, we established a bit extraction process incorporating multiple 64 bit-stream challenges and experimentally obtained physical features of 4D PUFs, producing countless random 896 bit-stream responses. Furthermore, the weak and strong PUF models were conceptualized and demonstrated based on 4D PUFs, exhibiting superior cryptological performances, including randomness, uniqueness, degree of freedom, and independent bit ratio. Finally, the data encryption and decryption in pictures were performed by a single 4D PUF. Therefore, 4D PUFs could enhance the counterfeiting deterrent of existing optical PUFs and be used as an anticounterfeiting security strategy for advanced authentication and cryptographic processes of IoT devices.