Lifetime Distribution Function Research Articles

A novel lifetime analysis of repairable systems via Daubechies wavelets

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

Robust assessment of life insurance products

AbstractIn this paper we propose a robust assessment for the premium of a standard life insurance contract with respect to the uncertainty on the estimated residual lifetime distribution function. Specifically, we provide a method to derive the range of values that the premium of a given contract can attain when considering all residual lifetime distribution functions that satisfy an $$L^2$$ L 2 distance constraint to a reference distribution function. Furthermore, we show that the $$L^2$$ L 2 distance constraint can be used as flexible starting point to include further information regarding future mortality.

Dynamic Plastics Flow Analysis for Korea between 1982-2020

Objectives : This study analyzed Korea’s plastic flows and stocks over the past 40 years to provide a quantitative basis for the nation’s plastic management and circular economy.Methods : Dynamic material flow analysis was conducted to quantify plastic flows across lifecycle stages and to estimate the size of in-use stocks. Focusing on 10 resins and 7 products, the analysis was conducted between 1982 and 2020 and at a national level. Production and trade flows were mainly quantified based on statistical and literature data, while consumption and waste flows were estimated using transfer coefficients. Different from static material flow analysis, waste flows were calculated based on the products’ lifetime distribution functions, and the changes in in-use stocks were estimated.Results and Discussion : Between 1982 and 2020, Korea produced 237 million tons of resins and provided 242 million tons of primary plastic products after the trade. Approximately 207 million tons of final products were consumed, 71% of which was generated as post-consumption waste and additional 3.8 million tons of waste was generated from the manufacturing stage. The amount of in-use stock of plastics was estimated to be 60 million tons. Of the 151 million tons of plastic waste, 24% was landfilled, 29% was incinerated and 47% was entered into sorting and recycling facilities. After sorting and recycling, 27 million tons were estimated to be recycled into products. From 1982 to 2020, per-capita plastic consumption increased from 15 kg to 150 kg, and per-capita waste generation increased from 2 kg to 139 kg. Packaging and containers, or PP and PE represented a major share of plastic consumption as well as waste generation. On the other hand, about half of the plastic stock was used for buildings and more than 50% of the building plastic stock was PVC.Conclusion : This study used a dynamic material flow analysis to quantify plastic flows over time, identify the composition of plastic waste flows according to resins or products, and estimate the size of in-use stocks. Such information on the waste composition and in-use stocks would be useful to improve recycling systems and estimate future waste flows.

A new measure of inaccuracy for record statistics based on extropy

AbstractWe introduce a new measure of inaccuracy based on extropy between distributions of the nth upper (lower) record value and parent random variable and discuss some properties of it. A characterization problem for the proposed extropy inaccuracy measure has been studied. It is also shown that the defined measure of inaccuracy is invariant under scale but not under location transformation. We characterize certain specific lifetime distribution functions. Nonparametric estimators based on the empirical and kernel methods for the proposed measures are also obtained. The performance of estimators is also discussed using a real dataset.

Degradation Analysis of Organic Light-Emitting Diodes through Dispersive Magneto-Electroluminescence Response.

Understanding the stability and degradation of organic light-emitting diodes (OLEDs) under working conditions is a significant area of research for developing more effective OLEDs and further improving their performance. However, studies of degradation processes by in situ noninvasive methods have not been adequately developed. In this work, tris-(8-hydroxyquinolino) aluminum (Alq3)-based OLED degradation processes have been analyzed through the investigation of the device dispersive magneto-electroluminescence (MEL(B)) response measured at room temperature. By studying the change in the MEL(B) response during the device degradation under different external stimuli, such as exposing the device to the atmosphere and prolonged illumination by a strong visible light source, we have gained insight into the microscopic spin-dependent phenomena that control the recombination of e-h polaron pairs in the device. We found that the device degradation leads to a shorter e-h polaron lifetime, smaller dispersive parameter, and broader lifetime distribution function that shows increased disorder in the active layer. This study could offer a potential tool that may be beneficial for assessing the degradation of OLED devices based on various active layers.

English

Reliable data on e-waste generation is important for environmentally sound management systems. This study models e-waste generation from existing data on electrical electronics imports, consumption and e-waste generation from Nigerian households. Structured questionnaires were used to obtain information on Electrical Electronic Equipment (EEE) use, reuse, and disposal from households in Nigeria households. Data from placed on the market (POM) were obtained from United Nations University (UNU) for five EEE types (TV, DVD player, refrigerator, desktop and laptop) in Nigeria between 1995 and 2019 using the apparent consumption method. A forecast up to 2020 and backcasts to 1980 were made based on these data. The lifetime profile for these five EEEs was modeled using the Weibull distribution function characterized by a time-varying shape parameter and a scale parameter. The POM data from 1980 to 2020 and the lifetime of the selected EEE from households were analyzed and fit into the Weibull lifetime distribution functions. The differences between reuse and non-reuse options show that around 54 million units of DVD players; 106 million units of CRT TV; 22 million units of the refrigerator; 11 million units of laptops and 24 million units of desktop computers would have been delayed from transiting into e-waste stream between 1981 and 2020 through reuse options.   Key words: Electronic waste, electrical electronic equipment, lifetime distribution, re-use repair, recycling, Nigeria.

B-spline Estimation for Force of Mortality

The paper focuses on the estimation of the force of mortality of living time distribution. We use a third-order B-spline function to construct the logarithm for force of mortality of living time. The number of the knots, their locations and B-spline coefficients based on a sample of observations are estimated by the maximum likelihood estimation method. Evaluation of B-spline parameters estimated by maximum likelihood estimation tested with criteria of the modified chi-squared goodness of the fit statistic. An algorithm developed to calculate Sequential Procedure for the modified chi-squared goodness of the fit testing. The Matlab code was written using the algorithm. Within this evaluation, the number of knots in the model has significantly reduced. The developed method was used to explain the mortality rate of women aged 0 to 69 among the Mongolian population in 2019 and estimate the life expectancy of Mongolians. The results of this experiment provided an excellent estimation of the force of mortality. Construction of a mortality rate estimation gives possibilities to determine mortality trends and force of mortality. Here, force of mortality is further used to construct a survival function, a lifetime distribution function, and a lifetime distribution probability density function. The method can also be used in financial market models and in models that estimate the useful life of equipment.

Impact of aircraft lifetime change on lifecycle CO2 emissions and costs in Japan

Airline industry CO2 emissions have increased rapidly; air transportation released approximately 2.8% of global fuel-combustion-based CO2 emissions in 2019. Focusing on Japan, this study explored the introduction of new passenger aircraft as a CO2-reduction policy. To this end, the lifetime distribution function for passenger aircraft was specified. Lifecycle CO2 emissions and the associated costs between 1965 and 2019 were then estimated. The results showed that single-aisle aircraft followed a Rayleigh distribution with a mean of 13.42, while twin-aisle aircraft followed a normal distribution with a mean of 19.82. The reduction potential of lifecycle CO2 emissions is 28.2 Mt. over 55 years by extending the lifetime +11 years of single-aisle aircraft and shortening the lifetime −8 years of twin-aisle aircraft. If the average fuel intensity of aircraft inflow improves steadily, the shortened lifetime and introduction of more fuel-efficient aircraft contribute to a decrease in lifecycle CO2 emissions. However, the cost associated with the lifecycle CO2 emission reductions is USD 94.0 billion, and airlines need to pay USD 3.4 thousand to reduce CO2 emissions by one unit. In sum, the introduction of new aircraft was shown to be cost-ineffective as a CO2-reduction policy, and airlines need to switch to less costly alternatives.

Flexible time reduction method for burn‐in of high‐quality products

AbstractBurn‐in is an effective method to screen out early failures of electronic devices. Typically, this is achieved by operating the devices under accelerated stress conditions. This paper focuses on a burn‐in concept where a random sample of devices is drawn out of the running production, put to burn‐in, and investigated for early failures. This procedure is called burn‐in study. In parallel, as long as the burn‐in study is ongoing, all other produced devices are subjected to burn‐in screening. In this article, new flexible sampling plans for burn‐in studies are introduced. These are based on the progress of these studies and defined quality targets. Furthermore, these sampling plans enable fast burn‐in time reductions and various time reduction strategies. From a statistical point of view, this requires to combine the proportion of early failures in a population with their lifetime distribution function. The new model is illustrated by case studies and simulations. It contributes to burn‐in cost reductions, while controlling quality levels at the same time.

Accelerated Life Test Planning for Minimizing Misclassification Risks

The optimal plan of a time-censored accelerated life test (ALT) depends on unknown parameters in the ALT model. The general strategy for coping with this problem is to replace the unknown parameters with their a priori estimated values, after which we can design test plans that are robust to deviations of the estimated values. In an ALT with log-location-scale lifetime distribution and linear acceleration relation function, the slope parameter of the acceleration relation function usually has the highest uncertainty. Instead of prespecifying the slope parameter in the ALT design, in this article, we propose a new design criterion that minimizes the risk of misclassifying whether the product's pth quantile meets the design specification. Through a case study of a circular electric connector, we illustrate the proposed method, and compare it with other test criteria. The comparison result shows that the proposed plan exhibits good performance in both estimating and s-testing the product's pth quantile.

Lattice thermal conductivity of quartz at high pressure and temperature from the Boltzmann transport equation

The thermal conductivities along the basal and hexagonal directions of α-quartz silica, the low-temperature form of crystalline SiO2, are predicted from the solution of the Boltzmann transport equation combined with the van Beest, Kramer, and van Santen potential for the temperature up to 900 K and the pressure as high as 4 GPa. The thermal conductivities at atmospheric pressure, which show a negative and nonlinear dependence on temperature, are in reasonable agreement with the experimental data. The influence of pressure on thermal conductivity is positive and linear. The pressure (P) and temperature (T) dependences of the thermal conductivity (λ) in basal and hexagonal directions are fitted to a function of the form λ=(b+cP)Ta. The thermal conductivity, influenced by temperature and pressure, is analyzed based on phonon properties, including spectral thermal conductivity, dispersion relation, phonon density of states, phonon lifetime, and phonon probability density distribution function.

Accelerated Degradation Model of Nonlinear Wiener Process Based on Fixed Time Index

In the process of extrapolating a lifetime distribution function under normal storage conditions through nonlinear accelerated degradation data, time indexes under the normal storage conditions are usually set to the mean value of time indexes under various accelerated stresses. However, minor differences in time indexes may lead to great changes in the assessment results. For such a problem, an accelerated degradation model of a nonlinear Wiener process based on a fixed time index is established first and meanwhile, the impact of the measurement error is considered. Then, the probability density function is normalized, and multiple unknown parameters are estimated by using fminsearch function in MATLAB and multiple iterations. Finally, the model is validated by accelerated degradation test data of accelerometers and the O-type rubber sealing rings. The results show that there is a difference of 30,710 h for accelerometers between the mean time to failure under normal storage conditions obtained by the proposed method and the mean time to failure when the time indexes are the mean value of those under various accelerated stresses, and the main cause of the difference is compared and analyzed. A similar phenomenon is observed in the case study of O-type rubber sealing rings.

A model for first‐estimates of species‐specific, age‐specific mortality from centralized band‐recovery databases

AbstractPopulation mortality curves, otherwise known as lifetime distribution functions, can be indispensable in many areas of ecology and environmental management including population viability and stock management analyses, disaster‐recovery monitoring, and fundamental evolutionary biology. Yet available modeling tools are often unable to estimate population mortality curves from commonly available datasets because these datasets fail to meet stringent experimental‐design requirements. Here, we present a new method for estimating population mortality curves from records of marked individuals found dead. Such data are increasingly accessible in some of the largest biological datasets, such as continent‐ or nation‐wide marking‐and‐recovery schemes for birds and other animals. The method accounts for known biases in availability by age class, variable monitoring effort through time, and mark loss. We show that our modeling approach generates accurate estimates of population mortality structure across a range of populations differing in marking histories, true mortality curves, monitoring regimes, and mark loss rates. Our approach can be applied to multiple species or groups at a time and can provide estimates of inter‐annual adult, immature, and first‐year survival rates, required by predictive modeling applications such as population viability analyses. Our approach is also capable of estimating apparent senescence rates for each population and facilitates evolutionary analyses of life‐history traits. For example, our method is potentially useful for exploring the evolution of senescence or for inter‐group comparisons of mortality rates where groups that differ by environment may be identified within mark‐recovery records. To demonstrate the efficacy of this method, we present fitted population mortality curves for a suite of seabird species represented in a national mark–recapture database.

The joint signature of coherent systems

AbstractWe investigate the joint signature of coherent systems, under the assumption that the components have independent and identically distributed lifetimes. The joint signature, for a particular ordering of failure times, is an ‐dimensional matrix depending solely on the composition of the systems and independent of the underlying distribution function of the component lifetimes. The elements of the ‐dimensional matrix are formulated based on the joint signatures of numerous series of parallel systems. The number of the joint signatures involved is an exponential function of the number of the minimal cut sets of each original system and may, therefore, be significantly large. We prove that although this number is typically large, a great number of the joint signatures are repeated, or removed by negative signs. We determine the maximum number of different joint signatures based on the number of systems and components. It is independent of the number of the minimal cut sets of each system and is polynomial in the number of components. Moreover, we consider all permutations of failure times and demonstrate that the results for one permutation can be of use for the others. Our theorems are applied to various examples. The main conclusion is that the joint signature can be computed much faster than expected.

The joint signature of parallel systems for different permutations of failure times

The joint signature of m coherent systems is an extension of the joint signature of two systems introduced in 2010. It is interesting because the joint signature depends only on the mechanism of the systems’ composition rather than the underlying distribution function of the component lifetimes. It also depends on the permutation of the failure times. As there are m! permutations we need to compute m! joint signatures, many of which are the same. Even if the joint signatures for two different orderings of the system lifetimes are different, it is sometimes possible to obtain one of them via the other one by a transformation. In this article, we consider several parallel systems with independent and identically distributed component lifetimes and investigate how to classify the m! permutations of the failure times according to the same joint signature. Further, we partition the result into sets based on transformed joint signatures. Moreover, we establish a relationship between the different sets in the last partition so that the related joint signatures can be converted into each other by small modifications. By this procedure, we are able to compute the m! joint signatures together efficiently. Using several examples, we illustrate that our classifications save us a large number of calculations. We introduce an algorithm to determine the partitions and present a computer program for the algorithm. The case of series-parallel systems is quite complicated and is discussed briefly.

Service Lifetime, Storage Time, and Disposal Pathways of Electronic Equipment: A Swiss Case Study

SummaryProduct lifetime is an essential aspect of dynamic material flow analyses and has been modeled using lifetime distribution functions, mostly average lifetimes. Existing data regarding the lifetime of electronic equipment (EE) are based on diverging definitions of lifetime as well as different temporal and regional scopes. After its active use, EE is often not disposed of immediately, but remains in storage for some time. Specific data on the share of EE that is stored and the time they remain in storage are scarce. This article investigates the service lifetime, storage time, and disposal pathways of ten electronic device types, based on data from an online survey complemented by structured interviews. We distinguish between new and secondhand devices and compute histograms, averages, and medians of the different lifetimes and their change over time. The average service lifetime varies from 3.3 years for mobile phones to 10.8 years for large loudspeakers, the average storage time from 0.8 years for flat panel display televisions to 3.6 years for large loudspeakers. Most service lifetime histograms are positively skewed and show substantial differences among device types. The storage time histograms, being more similar to one another, indicate that the storage behavior is similar for most device types. The data on disposal pathways show that a large proportion of devices are stored and reused before they reach the collection scheme.

Extremum sieve estimation in k-out-of-n systems

ABSTRACTThis article considers the non parametric estimation of absolutely continuous distribution functions of independent lifetimes of non identical components in k-out-of-n systems, 2 ⩽ k ⩽ n, from the observed “autopsy” data. In economics, ascending “button” or “clock” auctions with n heterogeneous bidders with independent private values present 2-out-of-n systems. Classical competing risks models are examples of n-out-of-n systems. Under weak conditions on the underlying distributions, the estimation problem is shown to be well-posed and the suggested extremum sieve estimator is proven to be consistent. This article considers the sieve spaces of Bernstein polynomials which allow to easily implement constraints on the monotonicity of estimated distribution functions.

Semi-parametric survival function estimators deduced from an identifying Volterra type integral equation

Based on an identifying Volterra type integral equation for randomly right censored observations from a lifetime distribution function F , we solve the corresponding estimating equation by an explicit and implicit Euler scheme. While the first approach results in some known estimators, the second one produces new semi-parametric and pre-smoothed Kaplan–Meier estimators which are real distribution functions rather than sub-distribution functions as the former ones are. This property of the new estimators is particular useful if one wants to estimate the expected lifetime restricted to the support of the observation time. Specifically, we focus on estimation under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. We show that some estimated linear functionals which are based on the new semi-parametric estimator are strong consistent, asymptotically normal, and efficient under SRCM. In a small simulation study, the performance of the new estimator is illustrated under moderate sample sizes. Finally, we apply the new estimator to a well-known real dataset.

Bayesian Analysis of Step-Stress Accelerated Life Tests and Its Use in Planning

ABSTRACTA Bayesian analysis of step-stress accelerated life test data is introduced and illustrated by an experiment on cryogenic cables. A cumulative damage model is used to describe the cumulative distribution function of Weibull lifetimes. The analysis methodology can then be used to evaluate a step-stress accelerated life test plan through simulation and calculation of appropriate criteria. Such planning is illustrated with the cryogenic cable example.

Optimization of reliability centered predictive maintenance scheme for inertial navigation system

The goal of this study is to propose a reliability centered predictive maintenance scheme for a complex structure Inertial Navigation System (INS) with several redundant components. GO Methodology is applied to build the INS reliability analysis model—GO chart. Components Remaining Useful Life (RUL) and system reliability are updated dynamically based on the combination of components lifetime distribution function, stress samples, and the system GO chart. Considering the redundant design in INS, maintenance time is based not only on components RUL, but also (and mainly) on the timing of when system reliability fails to meet the set threshold. The definition of components maintenance priority balances three factors: components importance to system, risk degree, and detection difficulty. Maintenance Priority Number (MPN) is introduced, which may provide quantitative maintenance priority results for all components. A maintenance unit time cost model is built based on components MPN, components RUL predictive model and maintenance intervals for the optimization of maintenance scope. The proposed scheme can be applied to serve as the reference for INS maintenance. Finally, three numerical examples prove the proposed predictive maintenance scheme is feasible and effective.