Probability Distribution Of Lifetime Research Articles

A study of attribute control charts for censored lifetime data

In many recent articles authors have advocated the use of attribute charts based on the number of censored values for monitoring censored lifetime data. In this article we compare the average run-length performance of one-sided and two-sided Shewhart charts based on the conditional expected value (CEV) with the corresponding attribute charts. The overall findings indicate that using an attribute chart to monitor the mean of a Weibull lifetime probability distribution with right censoring does not perform as well as the CEV-based chart.

A Statistical Model of Hazard Rate Change Caused by a Random Shock

In the framework of statistical reliability analysis, we propose a model describing the change of reliability of a technical component after certain event, as for instance a shock, or the failure and maintenance. Two kinds of failure rate changes are considered, namely a shift of virtual age of analyzed component and the acceleration of its subjective time. The objective is to estimate both the baseline lifetime probability distribution and the magnitude of these changes. The estimation procedure is based on the maximum likelihood method, both parametric and nonparametric distributions of lifetime are considered. Further, a graphical method of the goodness-of-fit test is proposed. The method is then checked on artificial examples, finally a real data problem is solved.

Long-Term Orbital Lifetime Prediction of Highly Eccentric Orbits: A Statistical Approach

This paper concentrates on the long-term orbital lifetime prediction of highly eccentric orbits (HEOs) based on two-line element sets via a statistical approach. Due to the significantly different evolution characteristics of low- and high-inclination HEOs induced by different orbital resonances, two area-to-mass estimation methods are proposed, respectively. The resonance phenomena encountered in the HEO region strongly affect the orbital evolution and cause high sensitivity. Therefore, a statistical approach is adopted to handle these effects and correctly estimate low-inclination HEO lifetime. We use the Monte Carlo method and kernel-density estimation to calculate the probability distribution of the orbital lifetime. Finally, the performance of the method is assessed by the actual orbital lifetimes of space objects that reentered from HEOs in the past 50 years. The results indicate that our statistical approach can improve the orbital lifetime prediction accuracy to a large extent, especially for the low-inclination HEOs. If a relative error of 15% is adopted as the error tolerance, compared with the traditional method based on a single orbital propagation, our statistical method can increase the success rate from 40% to more than 70%. For the high-inclination HEOs, the objects with a relative error below 15% account for more than 90%.

On the inverse power law‐normal model for life prediction of organic light emitting diodes

AbstractIn accelerated life testing analysis with nonthermal accelerating stress, the inverse power law (IPL) is often solely merged with a particular lifetime probability distribution with a shape parameter. Although many fundamental lifetime distributions, such as the normal distribution, are excellent fits to the experimental lifetime data, they have not been considered as they lack the shape parameter. As such, this paper, for the first time, demonstrates that the shape parameter can be replaced by the coefficient of variation, allowing the use of normal distributions in this context. The work further introduces the IPL‐normal model in a rigorous mathematical setup that precisely leads to the least squares estimating equations and maximum likelihood estimates of the IPL‐normal accelerating parameters and the general coefficient of variation. The proposed model uses accelerated experimental data to successfully predict the lifetime of organic light‐emitting diodes (OLEDs) at use conditions. Based on these fundamentals, the predictions are benchmarked with prior works that were validated by market studies.

On Intractability in G-Class of Lifetime Probability Distributions: Properties and Applications

This research seeks to project the relevance of incorporating intractability in G-Class probability model development. Juchez distribution represents intractability among the conventional tractable distributions, as comparatively studied in their different G-Class dimensions. Some properties were derived; although nonintegrable properties really were a confirmation note to the intractable nature of the distribution. The L-shape hazard function as a special feature across the G-Class derived distributions suggests that the distribution is fit to model outcomes that do not wear out as time or cycle elapses. Finally, the performance comparison reveals that intractability could be embraced in the development of probability models, as the derived distributions showed to be a better fit than the existing G-class baseline-tractable distributions.

The Alpha Power Topp-Leone Distribution: Properties, Simulations and Applications

This paper presents an extended lifetime probability distribution based on the alpha power transformation. We refer to the proposed distribution as “the Alpha Power Topp-Leone (APTL) distribution”. Mathematical properties of the APTL distribution such as the density and cumulative distribution functions, survival and hazard rate functions, quantile function, median, moments and its relative measures, probability weighted moment, moment generating function, Renyi entropy, and the distribution of order statistics were derived. The method of maximum likelihood estimation was employed to estimate the unknown parameters of the APTL distribution. Finally, we used two real data sets obtained from the literature to illustrate the applicability of the APTL distribution in real-life data fitting.

Data pooling for multiple single-component systems under population heterogeneity

We consider multiple newly designed single-component systems with a known finite lifespan. The component in each system can be replaced preventively to avoid a costly failure. This component is also in use for the first time, and therefore, there is no historical data on the lifetime of the component. In this case, the probability distribution of the component lifetime can be estimated based on expert opinions. However, there can be different opinions on the lifetime distribution. There are two populations where components can come from: a weak and a strong population. We assume that the components always come from the same population. However, the true type of the population is unknown. We build a discrete-time partially observable Markov decision process model to find the optimal replacement policy which minimizes the expected total cost throughout the lifespan. To resolve the uncertainty regarding population heterogeneity, we update the belief by using the data collected from all systems, allowing us to investigate the effect of so-called data pooling. First, we generate insights about the structure of the optimal policy. We then compare the cost per system under the optimal policy with the cost per system under two benchmark heuristics that follow the single-system optimal policy with and without data pooling, respectively. In our numerical experiments, we show that the cost reduction relative to the worst benchmark heuristic can be up to 5.6% for data pooling with two systems, and this increases up to 14% for 20 systems. Additionally, the effect of various input parameters on the costs is analyzed.

The effects and mechanism of the magnetic field on the hydrogen abstraction reaction of benzophenone and isopropanol

The effects of magnetic fields ranging from 0 T to 0.13 T on the photochemical reactions between benzophenone and isopropanol in the complete reaction cycle were explored. The results showed that with the increase of the applied magnetic field strength, the production rate of the product benzopinacol increased, and the induction period of the reaction was shortened. A new theoretical model suitable for the excitation process was used to explain the magnetic phenomenon in the initiation process of radical reaction, in which the magnetic field was believed to change the lifetime distribution of the excited reactant BP*, thereby affecting the rate of product generation. Specific parameters were used to calculate the lifetime probability distribution of excited state reactant molecules, which provides support for the quantitative analysis of the magnetic field effects of the reaction.

A New Probability Model Based on a Coherent System with Applications

The notion of a coherent system allows us to formalize how the random lifetime of the system is connected to the random lifetimes of its components. These connections are also generators of new pliant distributions, being those of various mixes of minimum and maximum of random variables. In this paper, a new four-parameter lifetime probability distribution is introduced by using the notion of a coherent system. Its structural properties are assessed and evaluated, including the analytical study of its main functions, stochastic dominance results, moments, and moment generating function. The proposed distribution, in particular, is proving to be efficient at fitting data with slight negative skewness and platykurtic as well as leptokurtic nature. This is illustrated by the analysis of three relevant real-life data sets, two in reliability and another in production, exhibiting the significance of the introduced model in comparison to various well-known models in statistical literature.

Prospects on end of life electric vehicle batteries through 2050 in Catalonia

As electric mobility gains prominence, the demand for electric vehicle batteries is rapidly rising. Although the amount of these batteries reaching their end of life is presently negligible, studies to quantify their flows and stocks will progressively gain importance as they have a high potential for reuse and contain some economic valuable materials. This study aims at forecasting the number of batteries due to be collected yearly from 2020 to 2050 in Catalonia (Northeast Spain). Product flow analyses are developed considering two different future electric vehicle sales, and two lifespan scenarios for batteries, assuming they follow a Weibull lifetime probability distribution. The volume of batteries reaching their first-use end of life will not reach significance until 2050, however strategies to optimise their use can be placed earlier to get prepared to the coming influxes. If future electric vehicle sales are to meet the Spanish Climate Change Law, influxes of batteries can increase up to 25-fold in 2030 and 72-fold in 2040. Under the extended battery service scenarios, the storage capacity is estimated to be 4 to 5 times larger than in scenarios where batteries are recycled earlier. The potential supply of secondary materials from end of life batteries will increase up to 80% of cobalt, copper and nickel, and 60% of lithium in 2050. The results urge to place proper management strategies for batteries in the coming years to help optimising their use and their potential recovery.

A New Flexible Logarithmic‐X Family of Distributions with Applications to Biological Systems

Probability distributions play an essential role in modeling and predicting biomedical datasets. To have the best description and accurate prediction of the biomedical datasets, numerous probability distributions have been introduced and implemented. We investigate a novel family of lifetime probability distributions to represent biological datasets in this paper. The proposed family is called a new flexible logarithmic‐X (NFLog‐X) family. The suggested NFLog‐X family is obtained by applying the T‐X method together with the exponential model having the PDF m(t) = e−t. Based on the NFLog‐X approach, a three parameters probability distribution, namely, a new flexible logarithmic‐Weibull (NFLog‐Wei) distribution is introduced. The method of maximum likelihood estimation is adopted for estimating the parameters of the NFLog‐X family. In the end, we examine three different biological datasets in order to give a thorough numerical research that illustrates the NFLog‐Wei distribution. Comparisons are made between the analytical goodness‐of‐fit metrics of the suggested distribution. We made comparison with the (i) alpha power transformed Weibull, (ii) exponentiated Weibull, (iii) Weibull, (iv) flexible reduced logarithmic‐Weibull, and (v) Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions.

A Novel Approach to Increase the Goodness of Fits with an Application to Real and Simulated Data Sets

In practice, the data sets with extreme values are possible in many fields such as engineering, lifetime analysis, business, and economics. A lot of probability distributions are derived and presented to increase the model flexibility in the presence of such values. The current study also focuses on investigations to derive a new probability model New Flexible Family (NFF) of distributions. The significance of NFF is carried out using the Weibull distribution called New Flexible Weibull distribution or in short NFW. Various mathematical properties of NFW have been discussed including the estimation of parameters and entropy measures. Two real data sets with extreme values and a simulation study have been conducted so as to delineate the importance of NFW. Furthermore, NFW is compared with other existing probability distributions; numerically, it has been observed that the new mechanism of producing the lifetime probability distributions plays a significant role in making predictions about the population than others using the data sets with extreme values.

Marshall-Olkin Lehmann Lomax Distribution: Theory, Statistical Properties, Copulas and Real Data Modeling

In this work, a new four-parameter lifetime probability distribution called the Marshall-Olkin Lehmann Lomax distribution is defined and studied. The density function of the new distribution "asymmetric right skewed" and "symmetric" and the corresponding hazard rate can be monotonically increasing, increasing-constant, constant, upside down and monotonically decreasing. The coefficient of skewness can be negative and positive. We derive some new bivariate versions via Farlie Gumbel Morgenstern family, modified Farlie Gumbel Morgenstern family, Clayton Copula and Renyi's entropy.The method of maximum likelihood is used to estimate the unknown parameters. Using "biases" and "mean squared errors", a simulation study is performed for assessing the finite behavior of the maximum likelihood estimators.

Modeling of COVID-19 Cases in Pakistan Using Lifetime Probability Distributions.

The Coronavirus Disease (COVID-19) is a respiratory disease that caused a large number of deaths all over the world since its outbreak. The World Health Organization (WHO) has declared the outbreak a global pandemic. The understanding of the random process related to the behavior infection of COVID-19 is an important health and economic problem. In the proposed study, we analyze the frequency of daily confirmed cases of COVID-19 using different two-parameter lifetime probability distributions. We consider the data from the period of March 11, 2020, to July 25, 2020, of Pakistan. We consider nine lifetime probability distributions for the analysis purpose and the selection of best fit was carried out using log-likelihood, AIC, BIC, RMSE, and R2 goodness-of-fit measures. Results indicate that Weibull distribution provides generally the best-fit probability distribution.

Reliability analysis of wind turbine based on degradation threshold

The time-dependent reliability model of the structure was established by using the Gamma process and combined with the stress-strength interference model to describe the product strength degradation process. The characteristics of the failure threshold based on strength degradation was analyzed, and the life distribution of the product can be calculated under the condition of given degradation threshold was pointed out. Taking a vertical axis wind turbine as an example, ANSYS finite element analysis software was used to calculate the load at the stress concentration of the shaft end of the wind turbine. According to the distribution of load and based on the threshold of product degradation, the product lifetime distribution subject to Gamma degradation was analyzed, the variation law of reliability at the shaft end of the wind turbine with time was studied, and the probability distribution of lifetime under a given threshold of degradation was solved. By using this method, the product reliability subject to Gamma degradation and the lifetime distribution under a given threshold could be obtained, which provides a method for product reliability evaluation with difficulty in obtaining reliability data.

Use of Graphical Methods in The Diagnostic Of Parametric Probability Distributions for Bivariate Lifetime Data in Presence of Censored Data

The choice of an appropriate bivariate parametrical probability distribution for pairs of lifetime data in presence of censored observations usually is not a simple task in many applications. Each existing bivariate lifetime probability distribution proposed in the literature has different dependence structure. Commonly existing classical or Bayesian discrimination methods could be used to discriminate the best among different proposed distributions, but these techniques could not be appropriate to say that we have good fit of some particular model to the data set. In this paper, we explore a recent dependence measure for bivariate data introduced in the literature to propose a graphical and simple criterion to choose an appropriate bivariate lifetime distribution for data in presence of censored data.

Strategic formulation of industrial maintenance based on equipment reliability in a sugar and ethanol production plant

Maintenance and management have substantial importance in the search of the company’s competitive advantages. In this direction, a reliability analysis of equipments is very important for the definition of the most suitable maintenance strategy. The main goal of this paper is to assess the reliability-centered maintenance of the industrial reliability curve of a sugar cane department of an industry located in São Paulo State, Brazil. The proposed research method was based on the application of existing statistical modeling for the times between failures (TBF) of all reported equipment failures or the interruption times in the production line. These times were modeled by standard lifetime probability distributions as log-normal and Weibull distributions. The results showed that the company's strategy for preventive maintenance during the off-season is not adequate and the statistical analysis also identified important factors that affect the company's maintenance strategy. These results could be of great interest for the company and for engineering applications in general.

A novel family of lifetime distribution with applications to real and simulated data.

The paper investigates a new scheme for generating lifetime probability distributions. The scheme is called Exponential- H family of distribution. The paper presents an application of this family by using the Weibull distribution, the new distribution is then called New Flexible Exponential distribution or in short NFE. Various statistical properties are derived, such as quantile function, order statistics, moments, etc. Two real-life data sets and a simulation study have been performed so that to assure the flexibility of the proposed model. It has been declared that the proposed distribution offers nice results than Exponential, Weibull Exponential, and Exponentiated Exponential distribution.

On past geometric vitality function of order statistics

In this article, we propose geometric vitality function introduced by Nair and Rajesh (IAPQR Trans 25(1):1–8, 2000) for the past lifetime of a random variable. This measure plays a vital role in analysing different characteristics of a system/component when it fails in the interval (0, t). The monotonic behaviour and some ordering properties in terms of the proposed measure were studied under certain conditions. Similar properties of the proposed measure were analysed for order statistics as well. Further, bounds were obtained for the past geometric vitality function of order statistics. Apart from this, characterizations of some lifetime probability distributions with respect to order statistics were also discussed.

Distributionally Robust Design for Redundancy Allocation

In this paper, we consider a redundancy allocation problem for a series parallel system with uncertain component lifetimes that minimizes system costs while safeguarding system reliability over a given threshold level. We consider mixed redundancy strategies of cold standby and active redundancy with multiple types of components. We address lifetime uncertainty in the framework of distributionally robust optimization. In particular, we assume the probability distributions of the component lifetimes are not exactly known with only limited distributional information (e.g., mean, dispersion, and support) being available. We protect the worst-case system reliability constraint over all the possible component lifetime distributions that are consistent with the given distributional characteristics. The proposed modeling framework enjoys computationally attractive structures. The evaluation of the worst-case system reliability in our redundancy allocation problem can be transformed into a linear program, and the resulting overall redundancy allocation optimization problem can be cast as a mixed integer linear program that does not induce any additional integer variables (other than original allocation variables). In addition, the extreme joint distribution of component lifetimes can be efficiently recovered by solving a linear program. Our modeling framework can also be extended to incorporate the startup failures and common-cause failures for cold standbys and active parallels, respectively, to cater to more computationally complex settings. Finally, the computational experiments positively demonstrate the performance of the proposed approach in protecting system reliability.