Lifetime Data Sets Research Articles

A New Extended Model with Bathtub-Shaped Failure Rate: Properties, Inference, Simulation, and Applications

Theoretical and applied researchers have been frequently interested in proposing alternative skewed and symmetric lifetime parametric models that provide greater flexibility in modeling real-life data in several applied sciences. To fill this gap, we introduce a three-parameter bounded lifetime model called the exponentiated new power function (E-NPF) distribution. Some of its mathematical and reliability features are discussed. Furthermore, many possible shapes over certain choices of the model parameters are presented to understand the behavior of the density and hazard rate functions. For the estimation of the model parameters, we utilize eight classical approaches of estimation and provide a simulation study to assess and explore the asymptotic behaviors of these estimators. The maximum likelihood approach is used to estimate the E-NPF parameters under the type II censored samples. The efficiency of the E-NPF distribution is evaluated by modeling three lifetime datasets, showing that the E-NPF distribution gives a better fit over its competing models such as the Kumaraswamy-PF, Weibull-PF, generalized-PF, Kumaraswamy, and beta distributions.

Estimation for two exponential life time models under joint multiply type-II censoring

Various types of censoring schemes basically type-I and type-II censoring schemes and their modified versions are used in life testing experiments. Most of the tests used in life testing experiments are based on a single sample. A joint censoring scheme is quite useful in conducting comparative life tests of products from different units within the same facility. In this article, we consider two exponential life time models under joint multiply type-II censoring scheme, which is a generalization of usual type-II censoring scheme, implemented on the two samples. We have considered maximum likelihood estimation and Bayesian estimation for estimating the reliability of the product under such a censoring scheme. The results are compared with the results obtained under usual type-II censoring scheme. In Bayes estimation the effect of prior parameters on mean life time and reliability of the product is discussed. We have used the local influence approach for identifying observations that strike a disproportionate effect in the maximum likelihood estimate of the reliability in the model. The life time data set of air-conditioning systems of two Boeing 720 jet airplanes “7914” and “7913” are used to apply the theory developed in the paper.

New class of Lindley distributions: properties and applications

A new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

A new length-biased power Lindley distribution with properties and its applications

The present paper introduces a new model namely length biased power Lindley distribution with two parameters. The survival function, failure rate and moments of the proposed distribution are derived. The maximum likelihood estimators of the parameters and their asymptotics are discussed and also the order statistics are derived. The potentiality of the proposed model has been tested by using two real life time data sets.

Fitmix: An R Package for Mixture Modeling of the Budding Yeast S. cerevisiae Replicative Lifespan (RLS) Distributions

Replicative lifespan (RLS) of the budding yeast is the number of mother cell divisions until senescence and is instrumental to understanding mechanisms of cellular aging. Recent research has shown that replicative aging is heterogeneous, which argues for mixture modeling. The mixture model is a statistical method to infer subpopulations of the heterogeneous population. Mixture modeling is a relatively underdeveloped area in the study of cellular aging. There is no open access software currently available that assists extensive comparison among mixture modeling methods. To address these needs, we developed an R package called fitmix that facilitates the computation of well-known distributions utilized for RLS data and other lifetime datasets. This package can generate a group of functions for the estimation of probability distributions and simulation of random observations from well-known finite mixture models including Gompertz, Log-logistic, Log-normal, and Weibull models. To estimate and compute the maximum likelihood estimates of the model parameters, the Expectation–Maximization (EM) algorithm is employed.

Remaining useful life prediction based on intentional noise injection and feature reconstruction

The accurate remaining useful life (RUL) prediction is the foundation of prognostics and health management (PHM). The accuracy of RUL prediction model depends on not only the quality and quantity of degradation feature but also the prediction model. In most of the existing deep-learning based RUL prediction models, noise is considered harmful and has to be removed. Further, the correlation among sensory measurements is ignored. However, noise can boost the prediction performance if judiciously used. This paper proposes a new RUL prediction method where noise is intentionally added into a long short-term memory (LSTM) network. Additionally, correlation analysis is conducted among the sensory measurements to construct new degradation features as the inputs of the LSTM network. Validation of the proposed method was carried out on the C-MAPSS aero-engine lifetime dataset. Finally, the proposed RUL prediction model is compared to other the-state-of-the-art techniques.

A new modified Lehmann type – II G class of distributions: exponential distribution with theory, simulation, and applications to engineering sector

Background: Modeling against non-normal data a challenge for theoretical and applied scientists to choose a lifetime model and expect to perform optimally against experimental, reliability engineering, hydrology, ecology, and agriculture sciences, phenomena. Method: We have introduced a new G class that generates relatively more flexible models to its baseline and we refer to it as the new modified Lehmann Type – II (ML–II) G class of distributions. A list of new members of ML–II-G class is developed and as a sub-model the exponential distribution, known as the ML-II-Exp distribution is considered for further discussion. Several mathematical and reliability characters along with explicit expressions for moments, quantile function, and order statistics are derived and discussed in detail. Furthermore, plots of density and hazard rate functions are sketched out over the certain choices of the parametric values. For the estimation of the model parameters, we utilized the method of maximum likelihood estimation. Results: The applicability of the ML–II–G class is evaluated via ML–II–Exp distribution. ML–II–Exp distribution is modeled to four suitable lifetime datasets and the results are compared with the well-known competing models. Some well recognized goodness–of–fit including -Log-likelihood (-LL), Anderson-Darling (A*), Cramer-Von Mises (W*), and Kolmogorov-Smirnov (K-S) test statistics are considered for the selection of a better fit model. Conclusion: The minimum value of the goodness–of–fit is the criteria of a better fit model that the ML–II–Exp distribution perfectly satisfies. Hence, we affirm that the ML–II–Exp distribution is a better fit model than its competitors.

ON THE PROPERTIES AND MLEs OF GENERALIZED ODD GENERALIZED EXPONENTIAL- EXPONENTIAL DISTRIBUTION

For proper actualization of the phenomenon contained in some lifetime data sets, a generalization, extension or modification of classical distributions is required. In this paper, we introduce a new generalization of exponential distribution, called the generalized odd generalized exponential-exponential distribution. The proposed distribution can model lifetime data with different failure rates, including the increasing, decreasing, unimodal, bathtub, and decreasing-increasing-decreasing failure rates. Various properties of the model such as quantile function, moment, mean deviations, Renyi entropy, and order statistics. We provide an approximation for the values of the mean, variance, skewness, kurtosis, and mean deviations using Monte Carlo simulation experiments. Estimating of the distribution parameters is performed using the maximum likelihood method, and Monte Carlo simulation experiments is used to assess the estimation method. The method of maximum likelihood is shown to provide a promising parameter estimates, and hence can be adopted in practice for estimating the parameters of the distribution. An application to real and simulated datasets indicated that the new model is superior to the fits than the other compared distributions

The AGU-F distribution : Properties and applications on over and underdispersed data

In this paper, we introduced a one-parameter lifetime distribution called the Agu-F distribution (Agu-F-D) and explored some of its useful statistical properties. The numerical applications of the Agu-F-D was examined using over and under dispersed, low and high kurtosis, positively, and negatively skewed three lifetime data sets. The parameter of the distribution was obtained using the maximum likelihood estimation method. The results obtained indicated that the proposed Agu-F-D performed best to the high kurtosis, positively, skewed, over and under dispersed data sets under consideration than the Lindley, Exponential and Ishita distributions. Thus, it can be used as an alternative model.

QUALITY PAPERA new rapid and robust multi-factorial screening for low-percentile use-rate accelerated reliability analysis

PurposeThe study aims to provide a quick-and-robust multifactorial screening technique for early detection of statistically significant effects that could influence a product's life-time performance.Design/methodology/approachThe proposed method takes advantage of saturated fractional factorial designs for organizing the lifetime dataset collection process. Small censored lifetime data are fitted to the Kaplan–Meier model. Low-percentile lifetime behavior that is derived from the fitted model is used to screen for strong effects. A robust surrogate profiler is employed to furnish the predictions.FindingsThe methodology is tested on a difficult published case study that involves the eleven-factor screening of an industrial-grade thermostat. The tested thermostat units are use-rate accelerated to expedite the information collection process. The solution that is provided by this new method suggests as many as two active effects at the first decile of the data which improves over a solution provided from more classical methods.Research limitations/implicationsTo benchmark the predicted solution with other competing approaches, the results showcase the critical first decile part of the dataset. Moreover, prediction capability is demonstrated for the use-rate acceleration condition.Practical implicationsThe technique might be applicable to projects where the early reliability improvement is studied for complex industrial products.Originality/valueThe proposed methodology offers a range of features that aim to make the product reliability profiling process faster and more robust while managing to be less susceptible to assumptions often encountered in classical multi-parameter treatments.

A Novel Degradation Feature Extraction Technique Based on Improved Base-Scale Entropy

In order to track the performance degradation trend accurately, a novel degradation feature extraction technique is proposed based on improved base-scale entropy. A unified base scale is proposed and a new symbol standard is defined to overcome the disadvantages of the base-scale entropy method, so as to symbolize signal amplitude to characterize information amount under different degradation conditions quantitatively. A lifetime dataset of rolling bearing from the IMS Bearing Experiment Center is introduced. For instance, analysis and some entropy-based techniques including fuzzy entropy, approximate entropy and sample entropy are imported for comparison. The results show that the improved basic-scale technique is able to characterize information amount of the signal amplitude distribution, so that the characterizing performance degradation degree of bearing shows a proportional relationship. When comparing the entropy-based techniques, the improved base-scale entropy technique has a faster calculation speed and better algorithm stability.

A consistent method of estimation for three-parameter generalized exponential distribution

In this article, we provide a consistent method of estimation for the parameters of a three-parameter generalized exponential distribution which avoids the problem of unbounded likelihood function. The method is based on a maximum likelihood estimation of the shape parameter, which uses location and scale invariant statistic, originally proposed by Nagatsuka et al. (A consistent method of estimation for the three-parameter weibull distribution, Computational Statistics & Data Analysis 58:210–26). It has been shown that the estimators are unique and consistent for the entire range of the parameter space. We also present a Monte-Carlo simulation study along with the comparisons with some prominent estimation methods in terms of the bias and root mean square error. For the illustration purpose, the data analysis of a real lifetime data set has been reported.

The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data.

The paper addresses a new four-parameter probability distribution called the Exponentiated Exponential Burr XII or abbreviated as EE-BXII. We derive various statistical properties in addition to the parameter estimation, moments, and asymptotic confidence bounds. We estimate the precision of the maximum likelihood estimators via a simulation study. Furthermore, the utility of the proposed distribution is evaluated by using two lifetime data sets and the results are compared with other existing probability distributions. The results clarify that the proposed distribution provides a better fit to these data sets as compared to the existing probability distributions.

Statistical Properties of a New Bathtub Shaped Failure Rate Model With Applications in Survival and Failure Rate Data

In this study, we proposed a flexible lifetime model identified as the modified exponentiated Kumaraswamy (MEK) distribution. Some distributional and reliability properties were derived and discussed, including explicit expressions for the moments, quantile function, and order statistics. We discussed all the possible shapes of the density and the failure rate functions. We utilized the method of maximum likelihood to estimate the unknown parameters of the MEK distribution and executed a simulation study to assess the asymptotic behavior of the MLEs. Four suitable lifetime data sets we engaged and modeled, to disclose the usefulness and the dominance of the MEK distribution over its participant models.

A New Generalized Two Parameter Lindley Distribution

A new generalized two-parameter Lindley distribution which offers more flexibility in modeling lifetime data is proposed and some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, mean residual life function, moment generating function, quantile function, moments, Renyi entropy and stochastic ordering are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study was carried out to examine the performance and accuracy of the maximum likelihood estimators of the parameters. Finally, an application of the proposed distribution to a real lifetime data set is presented and its fit was compared with the fit attained by some existing lifetime distributions.

An Extended Fr echet Distribution: Properties and Applications

In this paper, we introduce an extended four-parameter Fr´echet model called the exponentiated exponential Fr´echet distribution, which arises from the quantile function of the standard exponential distribution. Various of its mathematical properties are derived including the quantile function, ordinary and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, generating function, Shannon entropy and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new distribution is illustrated by means of three real lifetime data sets. In fact, the new model provides a better fit to these data than the Marshall-Olkin Fr´echet, exponentiated-Fr´echet and Fr´echet models.

Rapid and lean multifactorial screening methods for robust product lifetime improvement

Reliability enhancement is indispensable in modern operations. It aims to ensure the viability of complex functionalities in competitive products. We propose a full-robust screening/optimization method that promotes the rapid multi-factorial profiling of censored highly-fractionated lifetime datasets. The method intends to support operational conditions that demand quick, practical and economical experimentation. The innovative part of this proposal includes the robust split and quantification of structured lifetime information in terms of location and dispersion tendencies. To accomplish the robust data-reduction of lifetimes, maximum breakdown-point estimators are introduced to stabilize potential external-noise intrusions, which might be manifested as outliers or extremities. The novel solver provides resilience by robustifying the location (median) and dispersion (Rousseeuw-Croux Qn) estimations. The proposed profiler fuses dichotomized and homogenized lifetime information in a distribution-free manner. The converted and consolidated lifetime dataset is non-parametrically pre-screened to ensure error balances across effects. Consequently, any strong effects that maximize the lifetime response are diagnosed as long as the error symmetry has been previously established. We discuss problems that may be encountered in comparison to other multi-factorial profilers/optimizers upon application to densely-fractionated-and-saturated experimental schemes. We comment on the lean and agile advantages of the proposed technique with respect to several traditional treatments for the difficult case that implicates small and censored survival datasets. The robust screening procedure is illustrated on an industrial-level paradigm that concerns the multi-factorial reliability improvement of a thermostat; the trial units have been subjected to conditions of censoring and use-rate acceleration.

A new one-parameter lifetime distribution and its regression model with applications.

Lifetime distributions are an important statistical tools to model the different characteristics of lifetime data sets. The statistical literature contains very sophisticated distributions to analyze these kind of data sets. However, these distributions have many parameters which cause a problem in estimation step. To open a new opportunity in modeling these kind of data sets, we propose a new extension of half-logistic distribution by using the odd Lindley-G family of distributions. The proposed distribution has only one parameter and simple mathematical forms. The statistical properties of the proposed distributions, including complete and incomplete moments, quantile function and Rényi entropy, are studied in detail. The unknown model parameter is estimated by using the different estimation methods, namely, maximum likelihood, least square, weighted least square and Cramer-von Mises. The extensive simulation study is given to compare the finite sample performance of parameter estimation methods based on the complete and progressive Type-II censored samples. Additionally, a new log-location-scale regression model is introduced based on a new distribution. The residual analysis of a new regression model is given comprehensively. To convince the readers in favour of the proposed distribution, three real data sets are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other extensions of half-logistic distribution.

Modeling of Survival of HIV Patients by Stages of Immune Suppression and Opportunisic Infections

Globally, there are many people living with Human Immune Deficiency Virus (HIV), and the rate increases every day. Research has shown that Nigeria is the second largest country with HIV epidemic, as many are living with advanced HIV. People with advanced stage of HIV infection are vulnerable to secondary infections and malignancies, generally termed Opportunistic Infections (OIs). This is because, these infections take advantage of the opportunity offered by a weakened immune system, thereby causing complications in HIV infected persons and causing harm to individuals. The aim of this work is to investigate and model the survival, by stages of immune suppression and opportunistic infections on patients undergoing Antiretroviral Therapy (ART), in a population in South-South Nigeria. 221 Human Immune Deficiency Virus (HIV) patients data obtained from St. Luke’s Hospital, Anua, for the period of 2008 to 2017 were used. Four different parametric models, the extreme, lognormal, logistics, log-logistics distributions and nonparametric Kaplan-Meier method were considered in order to carry out modeling of survival, and survival of patients respectively. The models were subjected to life application using lifetime datasets and a test of goodness of fit was made using Akaike’s Information Criteria (AIC) and Bayesian Information Criteria (BIC) criteria. From the results obtained, extremedistribution had the lowest AIC and BIC value, indicating that it is the best parametric model for modeling survival of HIV patients in the hospital. Also, the Kaplan-Meier method indicates that the survival experience of female patients were favorable than male patients.

Predicting future order statistics with random sample size

<abstract> We suggest a new method for constructing an efficient point predictor for the future order statistics when the sample size is a random variable. The suggested point predictor is based on some characterization properties of the distributions of order statistics. For several distributions, including the mixture distribution, the performance of the suggested predictor is evaluated by means of a comprehensive simulation study. Three examples of real lifetime data-sets are analyzed by using this method and compared with an efficient recent method given by Barakat et al. ^{[<xref ref-type="bibr" rid="b1">1</xref>]}, that deals with non-random sample sizes. One of these examples predicts the accumulative new cases per million for infection of the new Coronavirus (COVID-19). </abstract>