Pub Date : 2021-03-08DOI: 10.13052/JRSS0974-8024.1412
Y. M. Bulut, F. Z. Doğru, O. Arslan
This study offers a newly proposed distribution called alpha power Lomax (APL) distribution as a new extension of the Lomax distribution using the alpha power transformation (APT) method. Some distributional properties of newly defined distribution such as density function, moments, hazard and survival functions, orders statistics etc. are investigated. Parameters of the APL distribution are estimated with the help of the maximum likelihood (ML) estimation method. The applicability of the APL distribution is conducted through a simulation study and a real data example.
本研究提出了一种新的分布，称为alpha power Lomax (APL)分布，作为使用alpha power transformation (APT)方法对Lomax分布的新扩展。研究了新定义分布的一些分布性质，如密度函数、矩、危险和生存函数、阶数统计量等。利用最大似然估计方法对APL分布参数进行估计。通过仿真研究和实际数据算例验证了APL分布的适用性。
{"title":"Alpha Power Lomax Distribution: Properties and Application","authors":"Y. M. Bulut, F. Z. Doğru, O. Arslan","doi":"10.13052/JRSS0974-8024.1412","DOIUrl":"https://doi.org/10.13052/JRSS0974-8024.1412","url":null,"abstract":"This study offers a newly proposed distribution called alpha power Lomax (APL) distribution as a new extension of the Lomax distribution using the alpha power transformation (APT) method. Some distributional properties of newly defined distribution such as density function, moments, hazard and survival functions, orders statistics etc. are investigated. Parameters of the APL distribution are estimated with the help of the maximum likelihood (ML) estimation method. The applicability of the APL distribution is conducted through a simulation study and a real data example.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48048290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.13052/jrss0974-8024.1426
P. Varghese, G. M. Rosario
The weaving machine’s reliability is assessed using newly introduced fuzzy numbers. The fuzzy numbers introduced in this study give a better method to improve the reliability than other techniques. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number are all introduced in this present study. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number,α-cuts are defined, as well as their mathematical operations. The numerical examples are utilised to conduct a comparative research of reliability using various Fuzzy Numbers, and their defuzzification is accomplished using various ways such as Signed Distance method, Graded Mean Integration Method and Centroid Method. The purpose of this study is to discover the most reliable value for a weaving machine.
{"title":"A Study On Reliability Using Pendant, Hexant, Octant Fuzzy Numbers","authors":"P. Varghese, G. M. Rosario","doi":"10.13052/jrss0974-8024.1426","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1426","url":null,"abstract":"The weaving machine’s reliability is assessed using newly introduced fuzzy numbers. The fuzzy numbers introduced in this study give a better method to improve the reliability than other techniques. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number are all introduced in this present study. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number,α-cuts are defined, as well as their mathematical operations. The numerical examples are utilised to conduct a comparative research of reliability using various Fuzzy Numbers, and their defuzzification is accomplished using various ways such as Signed Distance method, Graded Mean Integration Method and Centroid Method. The purpose of this study is to discover the most reliable value for a weaving machine.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66117022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.13052/jrss0974-8024.1424
S. K. Yadav, Dinesh K. Sharma, Ayodele Alade, A. Shukla
In this study, three novel regression models are introduced for estimating and forecasting peppermint yield production. Several indices of the goodness of fit are used to assess the quality of the suggested models. The proposed models for yield production are compared to current regression models that are well-known. Primary data from the Banki block of the Barabanki District of Uttar Pradesh State in India was used to validate the efficiency conditions for the suggested models to outperform the competition models. The empirical results suggest that the proposed models for estimating and predicting peppermint yield production are more efficient than competing estimators.
{"title":"Naive Regression Growth Models for Prediction of Peppermint Yield Production","authors":"S. K. Yadav, Dinesh K. Sharma, Ayodele Alade, A. Shukla","doi":"10.13052/jrss0974-8024.1424","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1424","url":null,"abstract":"In this study, three novel regression models are introduced for estimating and forecasting peppermint yield production. Several indices of the goodness of fit are used to assess the quality of the suggested models. The proposed models for yield production are compared to current regression models that are well-known. Primary data from the Banki block of the Barabanki District of Uttar Pradesh State in India was used to validate the efficiency conditions for the suggested models to outperform the competition models. The empirical results suggest that the proposed models for estimating and predicting peppermint yield production are more efficient than competing estimators.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66116516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.13052/jrss0974-8024.1425
Dushyant Tyagi, Vipin Yadav
Statistical Process Control (SPC) is an efficient methodology for monitoring, managing, analysing and recuperating process performance. Implementation of SPC in industries results in biggest benefits, as enhanced quality products and reduced process variation. While dealing with the theory of control chart we generally move with the assumption of independent process observation. But in practice usually, for most of the processes the observations are autocorrelated which degrades the ability of control chart application. The loss caused by autocorrelation can be obliterated by making modifications in the traditional control charts. The article presented here refers to a combination of EWMA and CUSUM charting techniques supplementing modifications in the control limits. The performance of the referred scheme is measured by comparing average run length (ARL) with existing control charts. Also, the referred scheme is found reasonably well for detecting particularly smaller displacements in the process.
{"title":"The Modified Mixed Exponentially Weighted Moving Average-Cumulative Sum Control Charts for Autocorrelated Process","authors":"Dushyant Tyagi, Vipin Yadav","doi":"10.13052/jrss0974-8024.1425","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1425","url":null,"abstract":"Statistical Process Control (SPC) is an efficient methodology for monitoring, managing, analysing and recuperating process performance. Implementation of SPC in industries results in biggest benefits, as enhanced quality products and reduced process variation. While dealing with the theory of control chart we generally move with the assumption of independent process observation. But in practice usually, for most of the processes the observations are autocorrelated which degrades the ability of control chart application. The loss caused by autocorrelation can be obliterated by making modifications in the traditional control charts. The article presented here refers to a combination of EWMA and CUSUM charting techniques supplementing modifications in the control limits. The performance of the referred scheme is measured by comparing average run length (ARL) with existing control charts. Also, the referred scheme is found reasonably well for detecting particularly smaller displacements in the process.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66116965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.13052/jrss0974-8024.1427
Aamir Raza, Muhammad Noor-ul-Amin
The estimation of population mean is not meaningful using ordinary least square method when data contains some outliers. In the current study, we proposed efficient estimators of population mean using robust regression in two phase sampling. An extensive simulation study is conduct to examine the efficiency of proposed estimators in terms of mean square error (MSE). Real life example and extensive simulation study are cited to demonstrate the performance of the proposed estimators. Theoretical example and simulation studies showed that the suggested estimators are more efficient than the considered estimators in the presence of outliers.
{"title":"Regression-in-Ratio Estimators for Population Mean by Using Robust Regression in Two Phase Sampling","authors":"Aamir Raza, Muhammad Noor-ul-Amin","doi":"10.13052/jrss0974-8024.1427","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.1427","url":null,"abstract":"The estimation of population mean is not meaningful using ordinary least square method when data contains some outliers. In the current study, we proposed efficient estimators of population mean using robust regression in two phase sampling. An extensive simulation study is conduct to examine the efficiency of proposed estimators in terms of mean square error (MSE). Real life example and extensive simulation study are cited to demonstrate the performance of the proposed estimators. Theoretical example and simulation studies showed that the suggested estimators are more efficient than the considered estimators in the presence of outliers.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66117035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-30DOI: 10.13052/jrss0974-8024.13243
Çaǧatay Çetinkaya
The Pareto distribution takes part in life-testing experiments as a finite range distribution. In this study, inference studies for the scale and shape parameters of the Pareto distribution under type-II hybrid censoring scheme are considered. The main reason for choosing this censoring scheme is its advantage of guaranteeing at least particular failures to be observed by the end of the experiment. Maximum likelihood and Bayes estimation methods are used with their approximate confidence intervals. Proposed estimation methods are compared numerically based on simulation studies. A numerical example is also used to illustrate the theoretical outcomes.
{"title":"Inference Based on Type-II Hybrid Censored Data from a Pareto Distribution","authors":"Çaǧatay Çetinkaya","doi":"10.13052/jrss0974-8024.13243","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.13243","url":null,"abstract":"The Pareto distribution takes part in life-testing experiments as a finite range distribution. In this study, inference studies for the scale and shape parameters of the Pareto distribution under type-II hybrid censoring scheme are considered. The main reason for choosing this censoring scheme is its advantage of guaranteeing at least particular failures to be observed by the end of the experiment. Maximum likelihood and Bayes estimation methods are used with their approximate confidence intervals. Proposed estimation methods are compared numerically based on simulation studies. A numerical example is also used to illustrate the theoretical outcomes.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43750005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-30DOI: 10.13052/jrss0974-8024.13245
Rahila Yousaf, Sajid Ali, M. Aslam
In this article, we aim to estimate the parameters of the transmuted Weibull distribution (TWD) using Bayesian approach, as the Weibull distribution plays an important role in reliability engineering and life testing problems. Informative and non-informative priors under squared error loss function (SELF), precautionary loss function (PLF) and quadratic loss function (QLF) are assumed to estimate the scale, the shape and the transmuted parameter of the TWD. In addition to this, we also compute the Bayesian credible intervals (BCIs). To estimate parameters, we adopt Markov Chain Monte Carlo (MCMC) technique assuming uncensored and censored environments in terms of different sample sizes and censoring rates. The posterior risks, associated with each estimator are used to compare the performance of different estimators. Two real data sets are analyzed to illustrate the flexibility of the proposed distribution.
{"title":"Bayesian Estimation of Transmuted Weibull Distribution under Different Loss Functions","authors":"Rahila Yousaf, Sajid Ali, M. Aslam","doi":"10.13052/jrss0974-8024.13245","DOIUrl":"https://doi.org/10.13052/jrss0974-8024.13245","url":null,"abstract":"In this article, we aim to estimate the parameters of the transmuted Weibull distribution (TWD) using Bayesian approach, as the Weibull distribution plays an important role in reliability engineering and life testing problems. Informative and non-informative priors under squared error loss function (SELF), precautionary loss function (PLF) and quadratic loss function (QLF) are assumed to estimate the scale, the shape and the transmuted parameter of the TWD. In addition to this, we also compute the Bayesian credible intervals (BCIs). To estimate parameters, we adopt Markov Chain Monte Carlo (MCMC) technique assuming uncensored and censored environments in terms of different sample sizes and censoring rates. The posterior risks, associated with each estimator are used to compare the performance of different estimators. Two real data sets are analyzed to illustrate the flexibility of the proposed distribution.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46491081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we have proposed Bayes estimators of shape parameter of Pareto distribution as well as reliability function under SELF, QLF and APLF loss functions. For better understanding of Bayesian approach, we consider Jeffrey’s prior as non-informative prior, exponential and gamma priors as informative priors. The proposed estimators have been compared with Maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). Moreover, the current study also derives the expressions for risk function under these three loss functions. The results obtained have been illustrated with the real as well as simulated data set.
{"title":"Bayes Estimation of the Reliability Function of Pareto Distribution Under Three Different Loss Functions","authors":"Gaurav Shukla, U. Chandra, Vinod Kumar","doi":"10.13052/0974-8024.1318","DOIUrl":"https://doi.org/10.13052/0974-8024.1318","url":null,"abstract":"In this paper, we have proposed Bayes estimators of shape parameter of Pareto distribution as well as reliability function under SELF, QLF and APLF loss functions. For better understanding of Bayesian approach, we consider Jeffrey’s prior as non-informative prior, exponential and gamma priors as informative priors. The proposed estimators have been compared with Maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE). Moreover, the current study also derives the expressions for risk function under these three loss functions. The results obtained have been illustrated with the real as well as simulated data set.","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48858816","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-14DOI: 10.13052/jrss2229-5666.12210
Azeem Ali, Sajid Ali, Shama Khaliq
The paper deals with the Bayes estimation of Extended Weibull-Geometric (EWG) distribution. In particular, we discuss Bayes estimators and their posterior risks using the noninformative and informative priors under different loss functions. Since the posterior summaries cannot be obtained analytically, we adopt Markov Chain Monte Carlo (MCMC) technique to assess the performance of Bayes estimates for different sample sizes. A real life example is also part of this study.
{"title":"ON THE BAYESIAN ANALYSIS OF EXTENDED WEIBULL-GEOMETRIC DISTRIBUTION","authors":"Azeem Ali, Sajid Ali, Shama Khaliq","doi":"10.13052/jrss2229-5666.12210","DOIUrl":"https://doi.org/10.13052/jrss2229-5666.12210","url":null,"abstract":"The paper deals with the Bayes estimation of Extended Weibull-Geometric (EWG) distribution. In particular, we discuss Bayes estimators and their posterior risks using the noninformative and informative priors under different loss functions. Since the posterior summaries cannot be obtained analytically, we adopt Markov Chain Monte Carlo (MCMC) technique to assess the performance of Bayes estimates for different sample sizes. A real life example is also part of this study. \u0000 ","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43508576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-14DOI: 10.13052/jrss2229-5666.1228
N. Nandal, S. Malik
The preference to the use of single unit systems over the redundant systems has been given due to their intrinsic reliability and affordability. And, stochastic modeling of repairable systems of one or more unit has been done by assuming negative exponential distribution for failure and repair times. In fact, the repairable systems may or may not have constant failure and repair rates. In such situations some other distributions possessing monotonic nature of the random variables associated with different time points may be considered. Gamma distribution is one of the distributions that may offer a good fit to some set of failure data. Also, negative exponential distribution is a special case of this distribution. Hence, in this paper reliability and availability of a single unit system by considering Gamma distribution for the random variables associated with failure and repair times of the system have been evaluated. A single server is employed to carry out the repair activities. The server is allowed to take some time to arrive at the system (called arrival time). The system has all the transit points as regenerative and so regenerative point has been used to derive the expressions for reliability measures. The values of reliability and availability are obtained for particular situations of the parameters. The behavior of these measures has been observed for the arbitrary values of the parameters.
{"title":"ON USE OF GAMMA DISTRIBUTION FOR EVALUATION OF RELIABILITY AND AVAILABILITY OF A SINGLE UNIT SYSTEM SUBJECT TO ARRIVAL TIME OF THE SERVER","authors":"N. Nandal, S. Malik","doi":"10.13052/jrss2229-5666.1228","DOIUrl":"https://doi.org/10.13052/jrss2229-5666.1228","url":null,"abstract":"The preference to the use of single unit systems over the redundant systems has been given due to their intrinsic reliability and affordability. And, stochastic modeling of repairable systems of one or more unit has been done by assuming negative exponential distribution for failure and repair times. In fact, the repairable systems may or may not have constant failure and repair rates. In such situations some other distributions possessing monotonic nature of the random variables associated with different time points may be considered. Gamma distribution is one of the distributions that may offer a good fit to some set of failure data. Also, negative exponential distribution is a special case of this distribution. Hence, in this paper reliability and availability of a single unit system by considering Gamma distribution for the random variables associated with failure and repair times of the system have been evaluated. A single server is employed to carry out the repair activities. The server is allowed to take some time to arrive at the system (called arrival time). The system has all the transit points as regenerative and so regenerative point has been used to derive the expressions for reliability measures. The values of reliability and availability are obtained for particular situations of the parameters. The behavior of these measures has been observed for the arbitrary values of the parameters. \u0000 ","PeriodicalId":42526,"journal":{"name":"Journal of Reliability and Statistical Studies","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2019-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42330183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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