Statistical Lifetime Research Articles

Stochastic attrition modeling

Lanchester’s equations provide a classical way in which to analyze the performance of two combat teams in battle, competing in the case where they are both equipped comparably and where each team’s survivability is a function of the size of the opposing force. This paper introduces a similar approach motivated by analysis of individual’s statistical lifetime distributions. Applying the same principle as in the design of Lanchester’s equations, a stochastic model is suggested, based upon individual’s lifetimes conditional on the size of the opposing force. This novel approach allows variation in individual team members to be included in the analysis, including the case where team members have correlated lifetimes. Hence, it provides a modeling methodology more general than that available through Lanchester’s equations. Based upon fits to real data, a specific model is then applied for individual lifetimes and it is shown how order statistics of the resultant lifetime distributions may be used to analyze combat team survivability.

Economic evaluation of vaccination against COVID-19: A systematic review.

Coronavirus has burdened considerable expenditures on the different health systems. Vaccination programs, the critical solution against pandemic diseases, are known as safe and effective interventions to prevent and control epidemics. We aimed to perform a systematic review to provide economic evidence of the value of different types of vaccines available to combat the Covid-19 to all health policymakers worldwide. Electronic searches conducted on Medline/PubMed, Cochrane Library, Web of Science, Scopus, Embase, and other economic evaluation databases. Related and published articles searched up to March 2022 by using keywords such as "Vaccination," "Covid-19," "Cost-benefit," "Cost-utility," "Cost-effectiveness," "Economic Assessment," and "Economic evaluation." Followed by choosing the most suitable articles according to inclusion and exclusion criteria, data captured and the results extracted. The quality assessment of the articles performed by the checklist of CHEERS 2022. Finally, 13 articles included in the review. All messenger RNA vaccines were dominant with approximately 70% coverage against no vaccination in the primary vaccination program except in one study that looked at booster effects. From a payer's perspective, a dollar invested in a vaccine would be less profitable than from a societal perspective. Therefore, primary mass vaccination can be considered a cost-effective intervention in primary vaccination to save more lives and produce more positive externalities. However, the cost-benefit ratio for all vaccines increases when statistical lifetime value and global economic and educational disadvantages are considered. The COVID-19 primary vaccination programs in regional outbreaks, from a long-term perspective, will demonstrate substantial cost-effectiveness. It is suggested that due to the positive externalities of vaccination, primary mass vaccination, with the help of COVAX-19TM, could be considered a reliable way to combat viral epidemics compared to the loss of individual lives and economic and educational disturbances around the world.

Generalization of the Lindley distribution with application to COVID-19 data.

Creating new distributions with more desired and flexible qualities for modeling lifetime data has resulted in a concentrated effort to modify or generalize existing distributions. In this paper, we propose a new distribution called the power exponentiated Lindley (PEL) distribution by generalizing the Lindley distribution using the power exponentiated family of distributions, that can fit lifetime data. Then the main statistical properties such as survival function, hazard function, reverse hazard function, moments, quantile function, stochastic ordering, MRL, order statistics, etc., of the newly proposed distribution have been derived. The parameters of the distribution are estimated using the MLE method. Then, a Monte Carlo simulation study is used to check the consistency of the parameters of the PEL distribution in terms of MSE, RMSE, and bias. Finally, we implement the PEL distribution as a statistical lifetime model for the COVID-19 case fatality ratio (in %) in China and India, and the new cases of COVID-19 reported in Delhi. Then we check whether the new distribution fits the data sets better than existing well-known distributions. Different statistical measures such as the value of the log-likelihood function, K-S statistic, AIC, BIC, HQIC, and p-value are used to assess the accuracy of the model. The suggested model seems to be superior to its base model and other well-known and related models when applied to the COVID-19 data set.

GIS의 수명특성 분석을 통한 고장대수 예측에 관한 연구

In the past, in accordance with the rapid development of industrial society, power facilities were replaced in order to expand the power grid and upgrade the performance. However, as the modernization of the industrial society is saturated, the replacement speed of facilities is slowing down, and the aging equipment is increasing. Therefore, interest in how to manage aging facilities is increasing, and research on the asset management of power facilities is required to establish a plan to efficiently operate facilities that are already in operation. It is necessary to diagnose the status of the facilities and analyze how the condition of the facilities will change in the future through an analysis of the remaining life. In order to establish the process, research on the statistical life of assets should be preceded. However, in the case of South Korea, power facilities are replaced before failure occurs in order to improve the reliability of power grid. Therefore, there is insufficient data to estimate the statistical life power assets. In this paper, a study on a system that analyzes the statistical lifetime using the data of gas insulated switchgear (GIS) published abroad and predicts the number of failures over time using the hazard rate.

A novel transmuted lomax exponential distribution: Properties and applications

Statistical lifetime distributions play a very important role in modeling data sets in various fields. Extending the existing distributions is of great interest in statistical research. The modification of the distributions provides more flexible model as compared to existing one. In this article, we propose a new probability model using Quadratic Rank Transmutation Map technique, named as Transmuted Lomax Exponential Distribution (TLED). The new distribution can model data sets with increasing, decreasing and bathtub shape hazard rates. Various statistical properties of the proposed distribution such as moments, order statistics, quantile function, mean residual life function and characteristic function are derived. Further, the parameter estimates are obtained through Maximum Likelihood method along with asymptotic confidence intervals. The utility of the new model is evaluated by analyzing two real data sets. In order to access the performance of the new model, several goodness of fit measures is used. The results indicate that the new model best fits the data as compared to the other extensions of the Lomax distribution.

On Modeling Cancer and Tuberculosis Data Using the Birnbaum–Saunders Lifetime Model Established on a Logistic Kernel

Due to their importance in representing, explaining, and analyzing phenomena, statistical lifetime distributions are widely used in science. As a result, this paper discusses a modern lifetime model called Birnbaum–Saunders logistic distribution. This distribution extends the Birnbaum–Saunders distribution, as it has proven to be characterized by great flexibility in data modeling in practice. Different features of this distribution have been discussed. The parameters of the model are estimated using the maximum likelihood and modified moment estimation methods. To evaluate the performance of the methods, a simulation study with data contamination scenarios is presented. Finally, the new model’s flexibility is tested using real datasets.

Statistical Inferences: Based on Exponentiated Exponential Model to Assess Novel Corona Virus (COVID-19) Kerala Patient Data.

In this article, we use exponentiated exponential distribution as a suitable statistical lifetime model for novel corona virus (covid-19) Kerala patient data. The suitability of the model has been followed by different statistical tools like the value of logarithm of likelihood, Kolmogorov–Smirnov distance, Akaike information criterion, Bayesian information criterion. Moreover, likelihood ratio test and empirical posterior probability analysis are performed to show its suitability. The maximum-likelihood and asymptotic confidence intervals for the parameters are derived from Fisher information matrix. We use the Markov Chain Monte Carlo technique to generate samples from the posterior density function. Based on generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct highest posterior density credible intervals. Further we discuss the Bayesian prediction for future observation based on the observed sample. The Gibbs sampling technique has been used for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample.

An exact method for quantifying the reliability of end-of-epidemic declarations in real time.

We derive and validate a novel and analytic method for estimating the probability that an epidemic has been eliminated (i.e. that no future local cases will emerge) in real time. When this probability crosses 0.95 an outbreak can be declared over with 95% confidence. Our method is easy to compute, only requires knowledge of the incidence curve and the serial interval distribution, and evaluates the statistical lifetime of the outbreak of interest. Using this approach, we show how the time-varying under-reporting of infected cases will artificially inflate the inferred probability of elimination, leading to premature (false-positive) end-of-epidemic declarations. Contrastingly, we prove that incorrectly identifying imported cases as local will deceptively decrease this probability, resulting in delayed (false-negative) declarations. Failing to sustain intensive surveillance during the later phases of an epidemic can therefore substantially mislead policymakers on when it is safe to remove travel bans or relax quarantine and social distancing advisories. World Health Organisation guidelines recommend fixed (though disease-specific) waiting times for end-of-epidemic declarations that cannot accommodate these variations. Consequently, there is an unequivocal need for more active and specialised metrics for reliably identifying the conclusion of an epidemic.

Limitations and Guidelines for Damage Estimation Based on Lifetime Models for High-Power IGBTs in Realistic Application Conditions

Statistical lifetime models for high-power insulated-gate bipolar transistors (IGBTs) are developed based on results from power-cycling experiments and relate lifetime expectancy to the well-defined conditions of a laboratory experiment. In most cases, predefined cyclic-stress conditions are repeatedly applied until the power device under test reaches its end of life. However, in real applications, power modules are exposed to nonrepetitive stress patterns that can be very different from the power-cycling conditions. A well-established lifetime estimation method suggests decomposing the stress pattern into individual components, whose damage can be calculated using a lifetime model. These damage contributions are then summed up in order to estimate the consumed or the remaining lifetime of a device. When comparing the estimation results to field measurements though, they often fail to match the real behavior of a power device. This article points out the uncertainties that appear in this process of applying a lifetime model on stress patterns deriving from field applications. The main purpose is to present typical sources of errors and discuss how severely these may impact the lifetime estimation.

A Model-Ranking Approach for Estimation Based on Accelerated Degradation Test Data

Motivated by an accelerated degradation test (ADT) on the power gain of microwave power amplifiers, in this article we propose a model-ranking approach for the estimation of some important reliability characteristics. Different degradation models and statistical lifetime distributions are applied to model the data obtained from the ADT. We study the effect of model misspecification in estimating the reliability characteristics when the behavior of the degradation process and the underlying degradation-data-generating mechanism are unknown. We then propose a model-ranking approach with weighted estimation procedures when multiple candidate models are under consideration. Through a Monte Carlo simulation study, we show that the proposed approach is robust and insensitive to model misspecification. Finally, the ADT data from the motivating example are used to illustrate the proposed methodologies.

Statistical life prediction of unidirectional carbon fiber/polypropylene tape under creep tension load

Recently, a carbon fiber/polypropylene unidirectional sheet has been developed by Mitsui Chemicals, Inc. from a new polyolefin-based sizing agent for carbon fiber. Its effective polypropylene modification brings good compatibility with polypropylene to improve the fiber matrix adhesion. This study examines the prediction of the statistical lifetime of this developed carbon fiber/polypropylene unidirectional sheet under creep tension loading. First, a tensile test method for static and creep strengths at elevated temperatures was developed for carbon fiber/polypropylene unidirectional tape cut from a carbon fiber/polypropylene unidirectional sheet. Second, the static tensile strengths of carbon fiber/polypropylene tape were measured statistically at various constant temperatures under a constant strain rate. The statistical creep failure times under tension loading for carbon fiber/polypropylene tape were predicted at a constant temperature by substituting the statistical static strengths into the formulation based on the matrix resin viscoelasticity. Third, the validity of the predicted results was clarified by comparison with the creep failure times measured statistically using creep tests for carbon fiber/polypropylene tape. Finally, the relation between the failure probability and creep failure times for carbon fiber/polypropylene unidirectional tape at various loads and temperature conditions was discussed.

ATLASGAL – physical parameters of dust clumps associated with 6.7 GHz methanol masers

Abstract We have constructed the largest sample of dust-associated class II 6.7 GHz methanol masers yet obtained. New measurements from the the Methanol MultiBeam (MMB) Survey were combined with the 870 $\mu$m APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) and the 850 $\mu$m JCMT Plane Survey (JPS). Together with two previous studies we have now identified the host clumps for 958 methanol masers across the Galactic Plane, covering approximately 99 per cent of the MMB catalogue and increasing the known sample of dust-associated masers by over 30 per cent. We investigate correlations between the physical properties of the clumps and masers using distances and luminosities drawn from the literature. Clumps hosting methanol masers are significantly more compact and have higher volume densities than the general population of clumps. We determine a minimum volume density threshold of n(H2) ≥ 104 cm−3 for the efficient formation of intermediate- and high-mass stars. We find 6.7 GHz methanol masers are associated with a distinct part of the evolutionary process (Lbol/Mfwhm ratios of between 100.6 and 102.2) and have well defined turning on and termination points. We estimate the lower limit for the mass of embedded objects to be ≥6 M⊙ and the statistical lifetime of the methanol maser stage to be ∼3.3 × 104 yrs. This suggests that methanol masers are indeed reliable tracers of high mass star formation, and indicates that the evolutionary period traced by this marker is relatively rapid.

Analysis of the antidote requirements and outcomes of different radionuclide decorporation strategies for a scenario of a "dirty bomb" attack.

In radiological emergencies, there is a risk of radionuclide incorporation. The radiological doses absorbed can be reduced by decorporation treatment. Antidote requirements depend on the scenario and treatment strategy ("urgent approach": immediate treatment of all patients with possible incorporation; "precautionary approach": treatment only after confirmation of incorporation). We calculated the number of daily antidote doses for different scenarios and the differences in outcome for both treatment strategies. The number of potentially contaminated victims was varied from 1,000 to 60,000 (a maximum that might seem plausible for "dirty bomb" scenarios in Germany), the proportion of patients actually needing decorporation treatment from 0.1 percent to 100 percent, the radioactive screening capacities from 250 to 2,500 people/day and treatment duration from 10 to 90 days. The outcomes were assessed as total statistical lifetime saved assuming an inhalation of 1 mCi cesium-137 and the achievable dose reductions by a Prussian Blue treatment. Assuming 1 percent of the potentially contaminated people actually needing treatment, applying an "urgent approach" the requirements for 1,000 victims range from 1,100 to 3,400 and for 60,000 victims from 489,000 to 4,400,000 daily doses, depending on treatment duration and screening capacities. The "urgent approach" is associated with larger stockpile requirements than the "precautionary approach", up to several hundred times in large-scale scenarios if the proportion of people actually needing treatment is low. The impact of the screening capacities is particularly important in large-scale scenarios, a low proportion of people needing treatment and extended treatment duration. The outcome is better for an "urgent approach" particularly in large-scale scenarios and low screening capacities. If only a small fraction of the victims actually needs treatment, their timely identification by enhancing screening capacities may be the most efficacious way to reduce antidote requirements. In large-scale scenarios, it might be necessary to abandon the medically preferable "urgent approach" for an antidote-sparing "precautionary approach".

ATLASGAL – properties of a complete sample of Galactic clumps★

Abridged: ATLASGAL is an unbiased 870 micron submillimetre survey of the inner Galactic plane. It provides a large and systematic inventory of all massive, dense clumps in the Galaxy (>1000 Msun) and includes representative samples of all embedded stages of high-mass star formation. Here we present the first detailed census of the properties (velocities, distances, luminosities and masses) and spatial distribution of a complete sample of ~8000 dense clumps located in the Galactic disk. We derive highly reliable velocities and distances to ~97% of the sample and use mid- and far-infrared survey data to develop an evolutionary classification scheme that we apply to the whole sample. Comparing the evolutionary subsamples reveals trends for increasing dust temperatures, luminosities and line-widths as a function of evolution indicating that the feedback from the embedded proto-clusters is having a significant impact on the structure and dynamics of their natal clumps. We find 88\,per\,cent are already associated with star formation at some level. We also find the clump mass to be independent of evolution suggesting that the clumps form with the majority of their mass in-situ. We estimate the statistical lifetime of the quiescent stage to be ~5 x 10^4 yr for clump masses ~1000 Msun decreasing to ~1 x 10^4 yr for clump masses >10000 Msun. We find a strong correlation between the fraction of clumps associated with massive stars and peak column density. The fraction is initially small at low column densities but reaching 100\,per\,cent for column densities above 10^{23} cm^{-2}; there are no clumps with column density clumps above this value that are not already associated with massive star formation. All of the evidence is consistent with a dynamic view of star formation wherein the clumps form rapidly and are initially very unstable so that star formation quickly ensues.

Characterization and Modelling of an Physico-Chemical Impedance Battery Model Based on the Tesla Model S Cell with the Help of Half-Cell Measurements

Modelling of batteries has become an important part in the design process of battery application. Especially for electric vehicles the design options can become very complex. To be able to make better design decisions, powerful modelling tools are necessary. However, one of the major drawbacks of complex models is the additional effort that is needed to parametrize the model [1, 2]. This work aims to simplify the parametrization of an impedance battery model, but keeping the parameters still physical and chemical meaningful.The project openBat [3], funded by the German government, examines the effect of a massive parallelization on the failure rate of lithium-ion-battery-packs and creates a statistical lifetime model. To create a lifetime model, a decent understanding of the battery and modelling is needed. Exemplarily cells from a barely used Tesla Motors Model S are used and will be characterized over the lifetime. To get a starting point for the lifetime prediction, some cells were intensively investigated. The batteries were tested using electrochemical impedance spectroscopy (EIS) and time domain relaxation measurements (TDM). The EIS and TDM experiments have been performed on 5 temperature levels between -5 °C and 45 °C and under different states of charge. A physical-chemical modeling routine derived by H. Witzenhausen [4] was used to determine physical meaningful parameters. The parametrization routine was implemented in a graphical user interface [5] and is available under an open source MIT license. In this routine, the measured EIS data are processed with the so called distribution of relaxation times (DRT), which was formerly successful applied for fuel-cells [6] and later on for lithium-ion batteries [7]. The DRT is a transformation that allows calculating the relaxation time constants which are present in a system and thus can help reducing the parameters for a curve fitting. The determined time constants by the DRT are used to stabilize a non-linear equation fitting algorithm. The validation of the parameters is done firstly by implementing the parameters into an impedance based battery modelling framework [8] and comparing them to time domain measurements. This model implementation is freely available under GNU General Public License version 3. Secondly, a small number of specimens were opened for further analysis to verify the parameter set. The components, i.e. anode, cathode and separator were separated, samples of the electrodes were taken and analyzed for their chemical composition. Other samples were used for building coin cells, anode vs lithium and cathode vs lithium. These samples underwent several experiments. At first, the samples were checked for electrochemical stability by cycling with a very low current for three cycles and checking for voltage anomalies between each cycle. After creating stable samples, the open circuit voltage was measured. Furthermore, the relaxation behavior was analyzed and both were correlated with the full cell and therefore with the derived parameter set. In this work the parametrization approach by H. Witzenhausen will be explained as well as the modelling. Furthermore the conducted experiments on the full cell and the half cells will be shown. Finally the validation of the parametrized model is presented.

A nonparametric Bayesian modeling approach for heterogeneous lifetime data with covariates

Lifetime data collected at product design and production stage or field operational stage often exhibit heterogeneity patterns, making the homogeneity assumption in conventional statistical lifetime models invalid. Mixture models are important modeling approaches that account for data heterogeneity. However, existing mixture models are constrained by assuming an known number of sub-populations. This paper proposes a new Bayesian statistical model to analyze heterogeneous lifetime data by assuming an unknown number of sub-populations. Each sub-population is characterized by an accelerated failure time model to quantify the effects of possible reliability impact factors. The proposed model allows simultaneous identification of the number of sub-populations and the model parameters of sub-populations. Convenient sampling strategies are further proposed to address the challenges of model estimation. Both numerical case study and real case study are provided to illustrate the proposed approach and demonstrate its validity.

Analysis of Residence Time in the Measurement of Radon Activity by Passive Diffusion in an Open Volume: A Micro-Statistical Approach

Residence time in a flow measurement of radioactivity is the time spent by a pre-determined quantity of radioactive sample in the flow cell. In a recent report of the measurement of indoor radon by passive diffusion in an open volume (i.e. no flow cell or control volume), the concept of residence time was generalized to apply to measurement conditions with random, rather than directed, flow. The generalization, leading to a quantity Δtr, involved use of a) a phenomenological alpha-particle range function to calculate the effective detection volume, and b) a phenomenological description of diffusion by Fick’s law to determine the effective flow velocity. This paper examines the residence time in passive diffusion from the micro-statistical perspective of single-particle continuous Brownian motion. The statistical quantity “mean residence time” Tr is derived from the Green’s function for unbiased single-particle diffusion and is shown to be consistent with Δtr. The finite statistical lifetime of the randomly moving radioactive atom plays an essential part. For stable particles, Tr is of infinite duration, whereas for an unstable particle (such as 222Rn), with diffusivity D and decay rate λ, Tr is approximately the effective size of the detection region divided by the characteristic diffusion velocity . Comparison of the mean residence time with the time of first passage (or exit time) in the theory of stochastic processes shows the conditions under which the two measures of time are equivalent and helps elucidate the connection between the phenomenological and statistical descriptions of radon diffusion.

Lifetime Prediction of Massively Parallelized Lithium-Ion Batteries

Batteries need to pass several stress tests before deployment. These tests can range in complexity from seconds (short-time electrochemical impedance spectroscopy) to several years during life time estimation tests. Several publications have shown that at the end of life, the behavior of specimens can drastically differ, even though initial measurements indicate identical behavior [1,2]. The effect of highly volatile ageing in specimens can be attributed to mainly two factors, discrepancies during production batches [3] and thermal inhomogeneities [4]. Cooling and pack design can be optimized to minimize the thermal effects on ageing. However, it is still unclear to what extent the risk of a single faulty battery cell, which might impact the whole pack performance, can be minimized. Therefore, it is useful to design tests that have a statistical significance to estimate and reduce the risk of faulty battery packs. One way to design a test setup is to create a serial connection of batteries and measure voltage over every specimen and the current in the string. This method has decisive drawbacks. Depending on the number of test subjects, the total voltage of the string might exceed extra-low voltage regulation and therefore only specialized personnel are allowed to handle the test equipment. Another drawback is that the weakest battery limits the total amount of energy that can be used. The discharge voltage limit of the weakest battery will be reached faster and therefore the measurement has to be stopped. Thus, it leads to inhomogeneities in the depth of discharge. To overcome these disadvantages the specimens can be connected in parallel, forcing an equal voltage and a homogeneous depth of discharge. This setup is especially challenging as the current of every parallel path has to be measured separately. To research the influence on the specimen and the accuracy of the measurement, the project openBat has been established. The project openBat examines the effect of a mass parallelization on the failure rate of lithium-ion-battery-packs and creates a statistical lifetime model. Overall, more than 600 specimens of the type NCR 18650B of Panasonic with a rated capacity of 3.20 Ah will be measured over the lifetime of the cells. The operating temperature and the cycle depth will be varied. The specimens are connected in smaller packages (30 specimens), each with its own synchronous current and voltage measurement. Each channel can be sampled at a maximum sampling rate of 1 kHz with 24 bit resolution. This enables the calculation of the impedance during the different stages of the life cycle without changing the test setup. Likewise, it is possible to measure the capacity of every single cell and the total pack. The impedance and capacity allow modeling the terminal voltage behavior and the heat generated by the batteries. To minimize temperature differences, all cells are closely fitted into an aluminum block and therefore allow temperature to be distributed evenly. The aluminum block is placed inside a temperature chamber and is actively cooled by a special cooling system. The submission will cover the hardware setup and preliminary measurement results. References x [1] Thorsten Baumhöfer, Manuel Brühl, Susanne Rothgang, and Dirk Uwe Sauer, "Production caused variation in capacity aging trend and correlation to initial cell performance," Journal of Power Sources, vol. Volume 247, pp. 332-338, February 2014. [2] Matthieu Dubarry, Cyril Truchot et all., "Evaluation of commercial lithium-ion cells based on composite positive electrode for plug-in hybrid electric vehicle applications," Journal of Power Sources, vol. 196, no. 23, pp. 10336 – 10343, 2011. [3] Shriram Santhanagopalan and Ralph E. White, "Quantifying cell-to-cell variations in lithium ion batteries," International Journal of Electrochemistry, 2012. [4] Sebastian Paul, Christian Diegelmann, Herbert Kabz, and Werner Tillmetz, "Analysis of ageing inhomogeneities in lithium-ion battery systems," Journal of Power Sources, 2013. x Figure 1

Statistical Lifetime Modeling of Fe-Ni-Cr Alloys Subject to High-Temperature Corrosion in Waste-to-Energy Production Units

The incineration of municipal solid waste as the main process of waste-to-energy (WtE) plants is often associated with high-temperature corrosion problems. With the idea of further increasing the efficiency of electric power generation and reducing the total cost of WtE units, it is important to develop preventive maintenance strategies based on accurate predictive methods resulting in economic savings and resource optimization. The main purpose of this study is to propose a statistical methodology for lifetime prediction modeling over a wide range of conditions of these complex environments and discuss the results regarding the mechanisms described in the literature. In order to create a quantitative tool to evaluate material corrosion performances based on adapted corrosion tests and the definition of accurate criteria for life assessment, a database with 1,595 test results has been built from several published high-temperature corrosion studies. The data distribution was analyzed by descriptive statist...

Data Requisites for Transformer Statistical Lifetime Modelling—Part II: Combination of Random and Aging-Related Failures

Statistical lifetime modeling is of importance for replacement management of aged power transformers. Survival data are recognized as important as failure data in improving the accuracy level of the lifetime models since transformer failures are rare events and most of the units are still in operating condition. This paper argues that differentiating random failures and aging-related failures is also important. Different data requisites for modeling random failures and aging-related failures are analyzed and compared through Monte Carlo simulations. The transformer life-cycle failure model can be built by combining the random and aging-related failure models. A case study is presented to show that through postmortem analysis, the two failure modes can be distinguished and, hence, it helps to improve the accuracy of the combined model.