scholarly journals Multicomponent Stress-Strength Reliability Based on Progressive First Failure for Kumaraswamy Model: Bayesian and Non-Bayesian Estimation

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2120
Author(s):  
Manal M. Yousef ◽  
Ehab M. Almetwally
Keyword(s):  
Strength Function ◽  
Real Life ◽  
Interval Estimation ◽  
Real Data ◽  
Point Estimation ◽  
Operating Conditions ◽  
Loss Functions ◽  
Kumaraswamy Distribution ◽  
Censored Samples ◽  
Operating Environments

It is highly common in many real-life settings for systems to fail to perform in their harsh operating environments. When systems reach their lower, upper, or both extreme operating conditions, they frequently fail to perform their intended duties, which receives little attention from researchers. The purpose of this article is to derive inference for multicomponent reliability where stress-strength variables follow unit Kumaraswamy distributions based on the progressive first failure. Therefore, this article deals with the problem of estimating the stress-strength function, R when X,Y, and Z come from three independent Kumaraswamy distributions. The classical methods namely maximum likelihood for point estimation and asymptotic, boot-p and boot-t methods are also discussed for interval estimation and Bayes methods are proposed based on progressive first-failure censored data. Lindly’s approximation form and MCMC technique are used to compute the Bayes estimate of R under symmetric and asymmetric loss functions. We derive standard Bayes estimators of reliability for multicomponent stress–strength Kumaraswamy distribution based on progressive first-failure censored samples by using balanced and unbalanced loss functions. Different confidence intervals are obtained. The performance of the different proposed estimators is evaluated and compared by Monte Carlo simulations and application examples of real data.

scholarly journals Survival estimation for singly type one censored sample based on generalized Rayleigh distribution

2014 ◽  
Vol 11 (2) ◽  
pp. 193-201
Author(s):  
Baghdad Science Journal
Keyword(s):  
Current Model ◽  
Survival Function ◽  
Information Matrix ◽  
Interval Estimation ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Generalized Rayleigh Distribution

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

scholarly journals A New Modified Kies Family: Properties, Estimation Under Complete and Type-II Censored Samples, and Engineering Applications

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1345 ◽  
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Mohammed K. Shakhatreh ◽  
Mazen Nassar ◽  
Ahmed Z. Afify
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Real Data ◽  
Mean Residual Life ◽  
Type Ii ◽  
Censored Samples ◽  
New Family ◽  
Generalized Distributions ◽  
Two Parameters ◽  
New Distribution

In this paper, we introduce a new family of continuous distributions that is called the modified Kies family of distributions. The main mathematical properties of the new family are derived. A special case of the new family has been considered in more detail; namely, the two parameters modified Kies exponential distribution with bathtub shape, decreasing and increasing failure rate function. The importance of the new distribution comes from its ability in modeling positively and negatively skewed real data over some generalized distributions with more than two parameters. The shape behavior of the hazard rate and the mean residual life functions of the modified Kies exponential distribution are discussed. We use the method of maximum likelihood to estimate the distribution parameters based on complete and type-II censored samples. The approximate confidence intervals are also obtained under the two schemes. A simulation study is conducted and two real data sets from the engineering field are analyzed to show the flexibility of the new distribution in modeling real life data.

scholarly journals ON ESTIMATION OF STRESS-STRENGTH RELIABILITY USING LOWER RECORD VALUES FROM ODD GENERALIZED EXPONENTIAL - EXPONENTIAL DISTRIBUTION

2021 ◽  
pp. 1-12
Author(s):  
Marwa Mohamed ◽  
Ahmed Reda
Keyword(s):  
Interval Estimation ◽  
Simulated Data ◽  
Real Data ◽  
Record Values ◽  
Point Estimation ◽  
Estimation Methods ◽  
The Real ◽  
Lower Record ◽  
Lower Record Values ◽  
Lower Records

This research paper aims to find the estimated values closest to the true values of the reliability functionunder lower record values and to know how to obtain these estimated values using point estimation methodsor interval estimation methods. This helps researchers later in obtaining values of the reliability function intheory and then applying them to reality which makes it easier for the researcher to access the missing datafor long periods such as weather. We evaluated the stress–strength model of reliability based on point andinterval estimation for reliability under lower records by using Odd Generalize Exponential–Exponentialdistribution (OGEE) which has an important role in the lifetime of data. After that, we compared theestimated values of reliability with the real values of it. We analyzed the data obtained by the simulationmethod and the real data in order to reach certain results. The Numerical results for estimated values ofreliability supported with graphical illustrations. The results of both simulated data and real data gave us thesame coverage.

scholarly journals AnANN Model Trained on Regional Data in the Prediction of Particular Weather Conditions

2021 ◽  
Vol 11 (11) ◽  
pp. 4757
Author(s):  
Aleksandra Bączkiewicz ◽  
Jarosław Wątróbski ◽  
Wojciech Sałabun ◽  
Joanna Kołodziejczyk
Keyword(s):  
Atmospheric Pressure ◽  
Real Life ◽  
Real Data ◽  
Weather Conditions ◽  
Maximum Temperature ◽  
Air Masses ◽  
Weather Forecasts ◽  
Life Problems ◽  
The World ◽  
The City

Artificial Neural Networks (ANNs) have proven to be a powerful tool for solving a wide variety of real-life problems. The possibility of using them for forecasting phenomena occurring in nature, especially weather indicators, has been widely discussed. However, the various areas of the world differ in terms of their difficulty and ability in preparing accurate weather forecasts. Poland lies in a zone with a moderate transition climate, which is characterized by seasonality and the inflow of many types of air masses from different directions, which, combined with the compound terrain, causes climate variability and makes it difficult to accurately predict the weather. For this reason, it is necessary to adapt the model to the prediction of weather conditions and verify its effectiveness on real data. The principal aim of this study is to present the use of a regressive model based on a unidirectional multilayer neural network, also called a Multilayer Perceptron (MLP), to predict selected weather indicators for the city of Szczecin in Poland. The forecast of the model we implemented was effective in determining the daily parameters at 96% compliance with the actual measurements for the prediction of the minimum and maximum temperature for the next day and 83.27% for the prediction of atmospheric pressure.

scholarly journals Calibrating the CreditRisk+ Model at Different Time Scales and in Presence of Temporal Autocorrelation †

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1679
Author(s):  
Jacopo Giacomelli ◽  
Luca Passalacqua
Keyword(s):  
Time Series ◽  
Default Risk ◽  
Real Life ◽  
Statistical Error ◽  
Real Data ◽  
Sampling Period ◽  
Calibration Procedure ◽  
Industry Standards ◽  
Default Rate

The CreditRisk+ model is one of the industry standards for the valuation of default risk in credit loans portfolios. The calibration of CreditRisk+ requires, inter alia, the specification of the parameters describing the structure of dependence among default events. This work addresses the calibration of these parameters. In particular, we study the dependence of the calibration procedure on the sampling period of the default rate time series, that might be different from the time horizon onto which the model is used for forecasting, as it is often the case in real life applications. The case of autocorrelated time series and the role of the statistical error as a function of the time series period are also discussed. The findings of the proposed calibration technique are illustrated with the support of an application to real data.

scholarly journals Improving the performance of a radio-frequency localization system in adverse outdoor applications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Marcelo N. de Sousa ◽  
Ricardo Sant’Ana ◽  
Rigel P. Fernandes ◽  
Julio Cesar Duarte ◽  
José A. Apolinário ◽  
...  
Keyword(s):  
Random Forest ◽  
Ray Tracing ◽  
Real World ◽  
Practical Implication ◽  
Real Life ◽  
Simulated Data ◽  
Real Data ◽  
Gradient Boosting ◽  
Real World Data ◽  
Localization Accuracy

AbstractIn outdoor RF localization systems, particularly where line of sight can not be guaranteed or where multipath effects are severe, information about the terrain may improve the position estimate’s performance. Given the difficulties in obtaining real data, a ray-tracing fingerprint is a viable option. Nevertheless, although presenting good simulation results, the performance of systems trained with simulated features only suffer degradation when employed to process real-life data. This work intends to improve the localization accuracy when using ray-tracing fingerprints and a few field data obtained from an adverse environment where a large number of measurements is not an option. We employ a machine learning (ML) algorithm to explore the multipath information. We selected algorithms random forest and gradient boosting; both considered efficient tools in the literature. In a strict simulation scenario (simulated data for training, validating, and testing), we obtained the same good results found in the literature (error around 2 m). In a real-world system (simulated data for training, real data for validating and testing), both ML algorithms resulted in a mean positioning error around 100 ,m. We have also obtained experimental results for noisy (artificially added Gaussian noise) and mismatched (with a null subset of) features. From the simulations carried out in this work, our study revealed that enhancing the ML model with a few real-world data improves localization’s overall performance. From the machine ML algorithms employed herein, we also observed that, under noisy conditions, the random forest algorithm achieved a slightly better result than the gradient boosting algorithm. However, they achieved similar results in a mismatch experiment. This work’s practical implication is that multipath information, once rejected in old localization techniques, now represents a significant source of information whenever we have prior knowledge to train the ML algorithm.

scholarly journals Modeling of a Real-Life Industrial Reactor for Hydrogenation of Benzene Process

Catalysts ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 412
Author(s):  
Mirosław K. Szukiewicz ◽  
Krzysztof Kaczmarski
Keyword(s):  
Catalyst Activity ◽  
Real Life ◽  
Operating Conditions ◽  
Reactor Operation ◽  
Reactor Model ◽  
High Scale ◽  
Industrial Reactor ◽  
Knowledge Based ◽  
Operation Conditions ◽  
Insight Into

A dynamic model of the hydrogenation of benzene to cyclohexane reaction in a real-life industrial reactor is elaborated. Transformations of the model leading to satisfactory results are presented and discussed. Operating conditions accepted in the simulations are identical to those observed in the chemical plant. Under those conditions, some components of the reaction mixture vanish, and the diffusion coefficients of the components vary along the reactor (they are strongly concentration-dependent). We came up with a final reactor model predicting with reasonable accuracy the reaction mixture’s outlet composition and temperature profile throughout the process. Additionally, the model enables the anticipation of catalyst activity and the remaining deactivated catalyst lifetime. Conclusions concerning reactor operation conditions resulting from the simulations are presented as well. Since the model provides deep insight into the process of simulating, it allows us to make knowledge-based decisions. It should be pointed out that improvements in the process run, related to operating conditions, or catalyst application, or both on account of the high scale of the process and its expected growth, will remarkably influence both the profits and environmental protection.

scholarly journals Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 934
Author(s):  
Yuxuan Zhang ◽  
Kaiwei Liu ◽  
Wenhao Gui
Keyword(s):  
Bayesian Method ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Statistical Efficiency ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Bayesian Estimations ◽  
Generalized Type

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

A Solution Framework for Response Surface-Based Multiple Quality Characteristics Optimization

2018 ◽  
Vol 25 (05) ◽  
pp. 1850025
Author(s):  
Sasadhar Bera ◽  
Indrajit Mukherjee
Keyword(s):  
Response Surface ◽  
Optimization Problems ◽  
Real Life ◽  
Quality Characteristics ◽  
Operating Conditions ◽  
Simultaneous Optimization ◽  
Trade Off ◽  
Multiple Quality Characteristics ◽  
Pin On Disc ◽  
Application Potential

A common problem generally encountered during manufacturing process improvement involves simultaneous optimization of multiple ‘quality characteristics’ or so-called ‘responses’ and determining the best process operating conditions. Such a problem is also referred to as ‘multiple response optimization (MRO) problem’. The presence of interaction between the responses calls for trade-off solution. The term ‘trade-off’ is an explicit compromised solution considering the bias and variability of the responses around the specified targets. The global exact solution in such types of nonlinear optimization problems is usually unknown, and various trade-off solution approaches (based on process response surface (RS) models or without using process RS models) had been proposed by researchers over the years. Considering the prevalent and preferred solution approaches, the scope of this paper is limited to RS-based solution approaches and similar closely related solution framework for MRO problems. This paper contributes by providing a detailed step-by-step RS-based MRO solution framework. The applicability and steps of the solution framework are also illustrated using a real life in-house pin-on-disc design of experiment study. A critical review on solution approaches with details on inherent characteristic features, assumptions, limitations, application potential in manufacturing and selection norms (indicative of the application potential) of suggested techniques/methods to be adopted for implementation of framework is also provided. To instigate research in this field, scopes for future work are also highlighted at the end.

Combined Statistical-Mechanical Characterization of a Next Generation Textured PTFE for Extreme Environments

2018 ◽  
Author(s):  
Sannmit Shinde ◽  
Ali P. Gordon ◽  
Zachary Poust ◽  
Steve Pitolaj ◽  
Jim Drago ◽  
...  
Keyword(s):  
Extreme Environments ◽  
Viscoelastic Behavior ◽  
Ceramic Particle ◽  
Operating Conditions ◽  
Operating Environments ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
Statistical Mechanical ◽  
Relaxation Responses

Pressurized vessels that transfer media from one location to another often contain a bolted connection. Gaskets are essential for these systems since they confer high levels of leak mitigation across of range of operating environments (i.e., internal pressure and temperature). The balance of both sealability and compressibility must be displayed in candidate gasket materials to be subjected to aggressive operating conditions. Historically, thin gauge gasket (i.e., 1/16” thick) confer high sealability while thick gaskets offer superior compressibility (i.e., 1/8”). Fabricated with skive cut, ceramic particle-reinforced PTFE, these materials display linear viscoelastic behavior that allow consolidation to occur. For example, GYLON® 3504 is filled with Aluminosilicate Microspheres, GYLON®3510 is filled with barium sulfate, respectively, to efficiently fill crevices along the surfaces of the flange. Novel textured PTFE gasket (3504 EPX and 3510 EPX) have been developed to simultaneously confer sealability and compressibility compared to flat products. A design of experiments (DoE) approach is applied to characterize the factors that influence load relaxation responses of the both candidate textured PTFE (dual-face honeycomb) and existing (flat) gasket styles. Using an instrumented test platform analyzed. A new parameter is presented to quantify gasket efficiency. The collection of efficiency measurement methods and approach to re-torque optimization convey a novel framework that designers can invoke to facilitate improved flange performance.

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