Failure Rate Function Research Articles

Statistical inference on the exponentiated moment exponential distribution and its discretization

Hasnain and Ahmad (2013) propose a two-parameter Exponentiated Moment Exponential (EME) Distribution and investigate its some characteristics. In this paper we study its additional properties in the context of its applications. The study classifies the EME distribution to homogeneous subfamilies with respect to hazard rate. A simulation study is conducted for EME distribution to observe the parameters for maximum likelihood and quartile estimates based on bias and mean square error. Based on EME distribution, we develop a discretized model that gives its importance in the industry. However, some important structural properties are studied for discrete Exponentiated moment exponential distribution with useful characterizations. Shapes of density and failure rate function of new discrete model are studied. Moreover, we provide justifications for the usefulness of the model and its enhanced scope as compared to the existing discretized model with the help of real-life data sets.

Integrated optimization for X-bar control chart, preventive maintenance and production rate

There are close relationships among statistical process control, maintenance, and production that have not fully explored in existing studies. In this study, we propose an economic model for jointly optimizing the X-bar control chart, preventive maintenance, and production rate. Unlike conventional studies relying on known failure rate functions, we employ a Gamma process to describe the system's deterioration. This approach allows us to consider not only the relationship between the production rate and the deterioration rate but also a broad range of deterioration scenarios and failure modes in the integrated optimization. After calculating the failure probability at each time point, we propose a recursive method to derive the production revenue, process control costs, and quality losses. This approach explores the close inner relationship between the production rate, deterioration, process monitoring and maintenance. Subsequently, we establish an optimization model aimed at maximizing the profit rate within a renewal cycle. The decision variables of this model include the production rate, control chart coefficient, sample size, length of the first sampling interval, and number of sampling intervals. Finally, we use a case study to illustrate the effectiveness and validity of our proposed model by identifying and explaining the interactions between production rate, deterioration, process control and maintenance.

Binomial Poisson Ailamujia model with statistical properties and application

In this study, an improved extension of the Poisson-Ailamujia distribution is introduced. The new distribution was derived using a binomial mixing approach, and the new model is named the “Binomial Poisson-Ailamujia (Bin-PA)” distribution. Some important statistical properties are derived, including mode, quantile function, moments and their associated measures, actuarial (risk) measures, and reliability features such as survival, hazard (failure) rate, and mean residual life function. The parameters of the proposed distribution are estimated using the maximum likelihood estimation method. A comprehensive simulation study is also carried out to access the behavior-derived maximum likelihood estimators. Furthermore, a new count-regression model was also introduced. Two datasets are utilized to demonstrate the applicability and usefulness of the new model. It is concluded that the Binomial Poisson-Ailamujia distribution is more flexible and efficiently analyzed both datasets as compared to competitive discrete distributions.

Theoretical framework and inference for fitting extreme data through the modified Weibull distribution in a first-failure censored progressive approach

The importance of biomedical physical data is underscored by its crucial role in advancing our comprehension of human health, unraveling the mechanisms underlying diseases, and facilitating the development of innovative medical treatments and interventions. This data serves as a fundamental resource, empowering researchers, healthcare professionals, and scientists to make informed decisions, pioneer research, and ultimately enhance global healthcare quality and individual well-being. It forms a cornerstone in the ongoing pursuit of medical progress and improved healthcare outcomes. This article aims to tackle challenges in estimating unknown parameters and reliability measures related to the modified Weibull distribution when applied to censored progressive biomedical data from the initial failure occurrence. In this context, the article proposes both classical and Bayesian techniques to derive estimates for unknown parameters, survival, and failure rate functions. Bayesian estimates are computed considering both asymmetric and symmetric loss functions. The Markov chain Monte Carlo method is employed to obtain these Bayesian estimates and their corresponding highest posterior density credible intervals. Due to the inherent complexity of these estimators, which cannot be theoretically compared, a simulation study is conducted to evaluate the performance of various estimation procedures. Additionally, a range of optimization criteria is utilized to identify the most effective progressive control strategies. Lastly, the article presents a medical application to illustrate the effectiveness of the proposed estimators. Numerical findings indicate that Bayesian estimates outperform other estimation methods by achieving minimal root mean square errors and narrower interval lengths.

Reliability and Residual Life of Cold Standby Systems

In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study proposes system equivalent models for various types of cold standby systems, all composed of components that follow the same exponential distribution. We use the equivalent model to determine the optimal timing for the use of cold spares and derive the reliability function and residual lifetime function for each type of system. To demonstrate the validity of our model, the Monte Carlo simulation is strategically designed based on the system failure rate function. The experimental results are then compared with those obtained from the numerical model, highlighting that the numerical method incurs a lower time cost.

Estimating the Lifetime of Rotary Dryer Flights Based on Experimental Data

The studies carried out address an important problem for the concrete and asphalt industry, referring to the wear phenomena that affect the elements (flights) of rotary dryers used to dry mineral aggregates. In this article, the authors propose a lifetime estimation method for rotary dryer flights. In order to benefit from greater credibility, the proposed method was applied based on the experimental results obtained, by the authors, in the laboratory, on a stand that reproduces a portion of the real equipment. Starting from these results, the authors identified the mathematical functions used to model the failure rates (wear) of the flights by referring to characteristic quantities for wear evaluation: mass loss of material; reduction in the thickness of the part; surface affected by wear. The experimental data—the input data for the proposed algorithm—correspond to six steels used in industrial applications. The wear phenomenon was modeled considering both the situation of uniform wear and the situation of differentiated wear on the flight surface. Therefore, the steel type with the highest service life values could be identified, namely, steel grades E and G. The method proposed in this paper can be extended to any category of material or part provided that the failure rate function is identified beforehand, possibly based on a laboratory experiment.

Estimating the survival function Maximum Likelihood and Cramér-Von Mises Method use of amixture distribution weibull and ailamujia with apractical application

Tow failure distributions were mixed ,weibull distribution and ailamujia distribution it's called weibull –ailamujia distribution which consists of four features, the two distributions were mixed by adding a mixing parameter ,the mixture of two distributions would be more efficient ,and representative of the data than the single distributions. A group of statistical properties of the mixture distribution were studied , such as the probability function ,the survival function and the failure rate function .classical estimation method were used to estimate the parameters of the mixture distribution, which are maximum likelihood of method ,the cramer –von mises method ,The method were compared using monte carlo simulations real data were taken regarding drug –resistant tuberculosis (TB) Multi Drug Resistance(MDR) methods were compared using the MSE statistical criterion ,and the result should a preference for the method cramer-von mises for having the lowest MSE

A stochastic model of preventive maintenance strategies for wind turbine gearboxes considering the incomplete maintenance

In contemporary large wind farms, the combination of condition-based maintenance (CBM) and time-based maintenance (TBM) has become a prevalent approach in preventive maintenance, which is an indispensable part to ensure the safe, stable and environmental operation of equipment. However, the utilization of an inappropriate maintenance strategy may result in over-maintenance or under-maintenance, leading to unstable equipment operation. Furthermore, the majority of preventive maintenance involves replacement maintenance, which may have adverse effects on the performance of wind turbines with excessive maintenance time. Therefore, this paper takes the gearbox as a case study to introduce the incomplete maintenance parameters into the failure rate function to establish a state model based on the stochastic differential equation (SDE) and describing the state change of incomplete maintenance. And then simulating the state model of the gearbox and the joint preventive maintenance strategy of TBM and CBM through examples, resulting the time-based incomplete maintenance (TBIM) is proposed based on the TBM and the incomplete maintenance, and a new joint preventive maintenance strategy incorporating TBIM and CBM is proposed. Through developing the decision-making process of the maintenance strategy to optimize the inappropriate maintenance which including over-maintenance and under-maintenance and simulating the optimized preventive maintenance strategy to compare with that of TBM and CBM and verify the superiority and effectiveness of the proposed maintenance method.

Reliability analysis of wind turbines considering seasonal weather effects

The failure rate of wind turbines shows obvious fluctuation due to seasonal environmental factors. However, few efforts have been devoted to modeling the seasonal failure rate. This paper develops a novel model that consists of a baseline failure rate function, seasonal indices, and a residual term to describe the monthly failure rate of wind turbines. A two-stage procedure is developed to estimate the 16 unknown parameters in the model. The first stage explores the relationship between the parameters in the baseline function and the monthly coefficients by maximum likelihood estimation and then integrates the properties into the genetic algorithm to estimate the main parameters. In the second stage, the variance of the residual term is estimated based on the analysis of the differences between the observed and predicted failure rates. The failure history of 48 months has been used to illustrate the proposed approach. The results show that the monthly failure rate function can well fit the real failure history of wind turbines, and it outperforms the traditional reliability model.

Statistical inference for a two-parameter distribution with a bathtub-shaped or increasing hazard rate function based on record values and inter-record times with an application to COVID-19 data

In this paper, we study the problem of estimation and prediction for a two-parameter distribution with a bathtub-shaped or increasing failure rate function based on lower records and inter-record times, and based on lower records without considering the inter-record times. The maximum likelihood and Bayesian approaches are employed to estimate the unknown parameters. As it seems that the Bayes estimates cannot be derived in a closed form, the Metropolis-Hastings within Gibbs algorithm is implemented to obtain the approximate Bayes point estimates. Bayesian prediction of a future record value is also discussed. A simulation study is conducted to evaluate the proposed point and interval estimators. A real data set consisting of COVID-19 data from Iran is analyzed to illustrate the application of the theoretical results of the paper. Moreover, a simulated data example is presented. Several concluding remarks end the paper.

An exponentiated XLindley distribution with properties, inference and applications

In this paper, we propose exponentiated XLindley (EXL) distribution. The novel model is adaptable due to the mixt shapes of its density and failure rate functions. The following key statistical properties of EXL distribution are derived: quantile function, moments, hazard function, mean residual life, and Rényi entropy. The parameters are estimated using the maximum likelihood, Anderson Darling, Cramer von Misses, maximum product spacing, ordinary and weighted least square estimation procedures. To examine the behavior of the estimate, Monte Carlo simulation is used. Further Bayesian technique is also utilized to estimate the EXL parameters. The traceplot and Geweke diagnostics are used to track the convergence of simulated processes. The applicability of the EXL distribution is demonstrated by three datasets from different domains such as mortality rate due to COVID-19, precipitation in inches, and failure time for repairable items. The proposed distribution provides efficient results as compared to renowned competitive distributions.

Randomly Censored Kumaraswamy Distribution

In this paper, inferential procedures based on classical and Bayesian framework for the Kumaraswamy distribution under random censoring model are studied. We first propose estimators for the distribution parameters, reliability function, failure rate function, and Mean time to system failure based on the maximum likelihood estimation method. Then, we calculate asymptotic confidence intervals for the parameters based on the observed Fisher’s information matrix. Also, for the parameters and reliability characteristics, Bayesian estimates are derived using the importance sampling and Gibbs sampling procedures. Highest posterior density credible intervals for the parameters are constructed using Markov Chain Monte Carlo method. Expected time on test of experiment with random censoring is also calculated. A simulation study is conducted to compare the efficiency of the derived estimates. Finally, the analysis of a real data set is presented for the illustration purpose.

A discrete extension of the Burr-Hatke distribution: Generalized hypergeometric functions, different inference techniques, simulation ranking with modeling and analysis of sustainable count data

<abstract><p>The intertwining relationship between sustainability and discrete probability distributions found its significance in decision-making processes and risk assessment frameworks. Count data modeling and its practical applications have gained attention in numerous research studies. This investigation focused on a particular discrete distribution characterized by a single parameter obtained through the survival discretization method. Statistical attributes of this distribution were accurately explicated using generalized hypergeometric functions. The unveiled characteristics highlighted its suitability for analyzing data displaying "right-skewed" asymmetry and possessing extended "heavy" tails. Its failure rate function effectively addressed scenarios marked by a consistent decrease in rates. Furthermore, it proved to be a valuable tool for probabilistic modeling of over-dispersed data. The study introduced various estimation methods such as maximum product of spacings, Anderson-Darling, right-tail Anderson-Darling, maximum likelihood, least-squares, weighted least-squares, percentile, and Cramer-Von-Mises, offering comprehensive explanations. A ranking simulation study was conducted to evaluate the performance of these estimators, employing ranking techniques to identify the most effective estimator across different sample sizes. Finally, real-world sustainability engineering and medical datasets were analyzed to demonstrate the significance and application of the newly introduced model.</p></abstract>

Joint optimization of two-dimensional warranty period and maintenance strategy considering availability and cost constraints

Abstract Warranty can improve customer satisfaction and increase product sales, but it will bring additional economic burden to manufacturers, so making reasonable warranty decisions is particularly important. The current research focuses more on the interests of manufacturers, while there is less attention paid to indicators that consumers are concerned about, such as system availability. To solve this problem, a joint optimization model of the two-dimensional warranty period and preventive maintenance (PM) strategy considering availability and cost constraints was established. Based on the failure dependence analysis of multi-component systems, the actual failure rate function is constructed by using the failure dependence coefficient matrix. Based on the comprehensive consideration of imperfect PM and minimum maintenance, the two-dimensional warranty cost model and system availability model are established, respectively. Aiming at maximum availability and considering the warranty cost budget constraint, a joint optimization model of the two-dimensional warranty period and PM strategy was built, and a model-solving algorithm combining grid search and binary search was introduced. The effectiveness of the model is verified by the case analysis, and the necessity of the PM strategy and considering failure dependence are reflected in the model comparative analysis and parameter sensitivity analysis. Finally, reasonable suggestions are put forward for manufacturers’ warranty decisions through the result analysis.

A New Life-Time Model with Bathtub and Inverted Bathtub Failure Rate Function

In this paper, a three parameter model called Zubair- Kumaraswamy (Z-Kum) distribution is proposed. The extension was done using Zubair G-Family [1] of continuous probability distribution to extend the well knownKumaraswamy distribution to make it more flexible in modeling and predicting real world phenomenon. Some basic structural properties of the new distributions like cdf, pdf, quantile functions, moments, moment generating functions, characteristics functions and order statistics was obtained. Survival function, hazard function, reversed hazard rate function and a cumulative hazard rate function was also obtained. Behavior of the hazard rate plot exhibit increase, decrease, Bathtub and inverted Bathtub shape. Maximum likelihood estimate was used to estimate the Z-Kum distribution parameters. Monte Carlo simulation was carried out to evaluate the performance of MLE method adopted. Result of the simulation studies indicates that MLE is good for the estimation of our distribution parameters. To compare the proposed model with the other fitted existing models, analytical measure of goodness of fit of some information criterion was considered using three real life data sets. From the results obtained, it is evident that our proposed model gives better fit than the other competing models and therefore, our proposed model provide greater flexibility in modeling real world phenomenon.

A novel refined maintenance strategy for full life cycle of high‐speed automatic train protection system

AbstractAutomatic train protection (ATP) system is essential for ensuring the safe operation of high‐speed trains. However, the existing extensive and fixed maintenance mode of the ATP system results in a waste of resources. To achieve a state of operation and maintenance that ensures both protection capability and economic efficiency, a lean method in a dynamic maintenance mode for the full life cycle of the ATP system is proposed. Firstly, reliability tests are carried out based on historical failure data. The parameter values of the possible life distribution are estimated by maximum likelihood method, and the optimal life distribution of different devices is obtained through the Kolmogorov–Smirnov hypothesis test. Secondly, a dynamic failure rate function is introduced to describe the impact of maintenance on device performance. A refined maintenance model is then established within the life cycle, and the dynamically changing preventive maintenance intervals and frequencies are obtained using a genetic algorithm. Finally, to mitigate the impact of the intermittent operation of ATP system on maintenance, the multidimensional relationships among the maintenance strategy, service time and operation mileage are revealed. The effectiveness of the proposed method is verified through an example test on a type of driver machine interface device.

A new extension of Poisson distribution for asymmetric count data: theory, classical and Bayesian estimation with application to lifetime data.

Several research investigations have stressed the importance of discrete data analysis and its relevance to actual events. The current work focuses on a new discrete distribution with a single parameter that can be derived using the Poisson mixing technique. The new distribution is named the Poisson Entropy-Based Weighted Exponential Distribution. It is useful for discussing asymmetric "right-skewed" data with "heavy" tails. Its failure rate function can be used to explain situations with increasing failure rates. The statistical properties of the new distribution are expressed explicitly. The proposed model is simple to manage for under-, equal-, and over-dispersed datasets. The model parameters are estimated using the maximum likelihood method. We consider the parameter estimation for the new model based on right-censored data with a cure fraction. One more focus of the present study is the Bayesian estimation of the model parameters. In the end, three real-world dataset examples were utilized to show the value of the new distribution. These applications revealed that the new model outperforms other standard discrete models.

Estimation of the Parameters of the Modified Weibull Distribution with Bathtub-shaped Failure Rate Function

Estimation of the Parameters of the Modified Weibull Distribution with Bathtub-shaped Failure Rate Function

Statistical inference of joint competing risks models from comparative bathtub shape distributions with hybrid censoring

In reliability engineering studies, the class of lifetime distributions with bathtub-shaped failure rate functions is particularly important since the lifetimes of electro-mechanical, electronic, and mechanical goods are frequently modelled with this characteristic. Comparative competing risk data are obtained in a variety of applications, including engineering, biological, medical, and other related fields. In this study, we adopted the statistical inference of joint distributions with a bathtub shape or increasing failure rate function (Chen distributions). The problem of determining the relative merits of products according to their lifetime duration is discussed under the hybrid type-I censoring scheme. Also, under consideration of independent causes of failure, a survival analysis and the assessment of one risk in the presence of other risks are discussed. The maximum likelihood (ML) method and the Bayes approach relative to the symmetric loss function are used to estimate the model parameters. Additionally, we build the classical confidence intervals (CIs) (asymptotic CI and bootstrap CI) to compare with the Bayes credible intervals. Moreover, theoretical results are evaluated and contrasted using a Monte Carlo simulation study. Finally, for illustration purposes, a real data set obtained from a laboratory experiment is evaluated using the suggested model with some brief comments.

A family of tests for trend change in failure rate function with right censored data

In this paper we extend the family of test proposed by Majumder and Mitra [Detecting trend change in failure functions-an L-statistic approach. Stat Pap. 2019;62:31–52. doi: 10.1007/s00362-018-01074-8] for testing exponentiality against bathtub (BT) failure rate (upside down bathtub (UBT)) to randomly right censored case. We derive the asymptotic distribution of the test statistic and using Monte Carlo simulation we obtain the empirical powers for certain alternative distributions. As a special case the asymptotic distribution of the test statistic proposed by Park [Testing whether failure rate changes its trend. IEEE Trans Reliab. 1988;37(4):375–378. doi: 10.1109/24.9842] is obtained. Finally some examples of real life data are given for illustrative purpose.