Published Paper by Shuo-jye Wu
Taylor & Francis
We consider the problem of making statistical inference on unknown parameters of a lognormal dist... more We consider the problem of making statistical inference on unknown parameters of a lognormal distribution under the assumption that samples are progressively censored. The maximum likelihood estimates (MLEs) are obtained by using the expectation-maximization algorithm. The observed and expected Fisher information matrices are provided as well. Approximate MLEs of unknown parameters are also obtained. Bayes and generalized estimates are derived under squared error loss function. We compute these estimates using Lindley's method as well as importance sampling method. Highest posterior density interval and asymptotic interval estimates are constructed for unknown parameters. A simulation study is conducted to compare proposed estimates. Further, a data set is analysed for illustrative purposes. Finally, optimal progressive censoring plans are discussed under different optimality criteria and results are presented.
Papers by Shuo-jye Wu
Communications in Statistics - Theory and Methods, 2019
This research deals with classical, Bayesian, and generalized estimation of stress-strength relia... more This research deals with classical, Bayesian, and generalized estimation of stress-strength reliability parameter, R s,k = Pr(at least s of (X 1 , X 2 , ..., X k) exceed Y) = Pr(X k−s+1:k > Y) of an s-out-of-k : G multicomponent system, based on progressively type-II right-censored samples with random removals when stress and strength are two independent Chen random variables. Under squared-error and LINEX loss functions, Bayes estimates are developed by using Lindley's approximation and Markov Chain Monte Carlo method. Generalized estimates are developed using generalized variable method while classical estimates-the maximum likelihood estimators, their asymptotic distributions, asymptotic confidence intervals, bootstrap-based confidence intervals-are also developed. A simulation study and a real-world data analysis are provided to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected lengths of the confidence intervals, and biases of the estimators are also computed, compared and contrasted. iv DEDICATION This thesis is dedicated to my family. To my loving parents, Titus and Ibijoke Ajumobi who supported me emotionally and financially, and whose words of encouragement and unwavering support molded me into the man I am today. To my siblings, Oyinda, Siji and Damilare who have always believed in me and pushed me to be the best that I can be. Thank you for teaching me that life comes in phases and to take the time to enjoy the little moments. v ACKNOWLEDGMENTS This journey would not have been possible without the support of my family, professors and mentors, and friends. To my family, thank you for encouraging me in all of my pursuits, never giving up on me and inspiring me to follow my dreams. I am forever indebted and hope my work makes you proud. I must give special acknowledgment to my advisor, Dr. Sumith Gunasekera (Associate Professor of Statistics, Department of Mathematics) who I have been extremely fortunate to work with and has served as a mentor throughout my academic journey. For his advice, his encouragement and guidance, I am eternally grateful and humbled. In addition, I would like to acknowledge the entire faculty and staff in the Department of Mathematics at The University of Tennessee at Chattanooga. It has been an absolute privilege working alongside such a dedicated and generous group of people. I would like to give special thanks to my thesis committee; I owe a debt of gratitude to Dr. Ossama Saleh for his time and careful attention to detail. To Dr. Lakmali Weerasena, I thank her for her untiring support and guidance throughout my journey. To Dr. Hong Qin, I am grateful for the well needed critiques and feedback. I look up to them as the epitome of the researcher and teacher I
Journal of Statistical Computation and Simulation, 2013
The accuracy of the Content should not be relied upon and should be independently verified with p... more The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &
gazi university journal of science, 2012
In this paper, a progressive type I group-censoring life test for Burr XII distribution is consid... more In this paper, a progressive type I group-censoring life test for Burr XII distribution is considered. We use the maximum likelihood method to obtain the point estimators of the Burr XII parameters. The approximate confidence intervals for the parameters of Burr XII distribution are also obtained. We use modified algorithm proposed by Kus et al. [19] to decide the number of test units, number of inspections, and length of inspection interval under a restricted budget of experiment such that the determinant of the asymptotic variances-covariance of estimators of parameters is minimum . A numerical example is presented to illustrate the proposed approach. T he sensitivity analysis is also investigated .
Quality and Reliability Engineering International, 2021
In this paper, reliability estimation of multicomponent system under a multilevel accelerated lif... more In this paper, reliability estimation of multicomponent system under a multilevel accelerated life testing. When the lifetime of components follows Weibull distribution, the problem of point and interval estimates are discussed from different perspectives. Under a general life‐stress assumption that there are multiple nonconstant and stress‐dependent scale and shape parameters, the maximum likelihood estimates of unknown parameters along with associated existence and uniqueness are established. Approximate confidence intervals are constructed correspondingly via expected Fisher information matrix. Furthermore, some pivotal quantities are constructed and alternative generalized point and interval estimates are also proposed for comparison. In addition, predictive intervals for the lifetime of the multicomponent system are discussed under classical and generalized pivotal approaches, respectively. The results show that the proposed generalized estimates are superior to the conventional likelihood approach in terms of the accuracy. A real data example is carried out to illustrate the implementations of the proposed methods.
American Journal of Mathematical and Management Sciences, 2018
We consider estimation of unknown parameters of a two-parameter Kumaraswamy distribution with hyb... more We consider estimation of unknown parameters of a two-parameter Kumaraswamy distribution with hybrid censored samples. We obtain maximum likelihood estimates using an expectation-maximization algorithm. Bayes estimates are derived under the squared error loss function using different approximation methods. In addition, an importance sampling technique is also discussed. Interval estimation is considered as well. We conduct a simulation study to compare the performance of different estimates, and based on this study, recommendations are made. A real data set and a simulated data set are analyzed for illustration purposes.
Journal of Computational and Applied Mathematics, 2020
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Journal of Statistical Computation and Simulation, 2019
In this paper, we investigate some inference and design problems related to multiple constant-str... more In this paper, we investigate some inference and design problems related to multiple constant-stress accelerated life test with progressive type-I interval censoring. A Weibull lifetime distribution at each stress-level combination is considered. The scale parameter of Weibull distribution is assumed to be a log-linear function of stresses. We obtain the estimates of the unknown parameters through the method of maximum likelihood, and also derive the Fisher's information matrix. The optimal number of test units, number of inspections, and length of the inspection interval are determined under D-optimality, T-optimality, and E-optimality criteria with cost constraint. An algorithm based on nonlinear mixed-integer programming is proposed to the optimal solution. The sensitivity of the optimal solution to changes in the values of the different parameters is studied.
Reliability Engineering & System Safety, 2017
In this article, we investigate the optimization problem when the competing risks data come from ... more In this article, we investigate the optimization problem when the competing risks data come from a progressive type II censoring in an accelerated life test with multiple levels of constant stress. The failure times of the individual causes are assumed to be independent and exponentially distributed with different parameters. We propose three criteria related to the Fisher's information matrix to determine the optimal stress level as well as the optimal sample allocation at each stress level. A real data set is studied to illustrate the application of the proposed criteria.
International Journal of Information and Management Sciences
ABSTRACT
Statistica Neerlandica, 2006
Accelerated life testing of products is used to get information quickly on their lifetime distrib... more Accelerated life testing of products is used to get information quickly on their lifetime distributions. This paper discusses a k-stage step-stress accelerated life test under progressive type I censoring with grouped data. An exponential lifetime distribution with mean life that is a loglinear function of stress is considered. A cumulative exposure model is also assumed. We use the maximum likelihood method to obtain the estimators of the model parameters.The methods for obtaining the optimum test plan are investigated using the variance-optimality and D-optimality criteria. Some numerical studies are discussed to illustrate the proposed criteria.
Journal of Information and Optimization Sciences, 2002
ABSTRACT
International Journal of Reliability, Quality and Safety Engineering, 2012
In material manufacturing applications, the lower percentiles of breaking strength of products co... more In material manufacturing applications, the lower percentiles of breaking strength of products contain critical reliability information. To promote the quality of product, it is important to ensure the lower percentiles of product breaking strength meet a satisfactory level. In this paper, two acceptance sampling plans are developed based on the percentiles of Weibull distribution and lognormal distribution with truncated life testing samples. An algorithm is provided to obtain acceptance sampling plans under the specified points of producer's risk and consumer's risk. Some tables are presented for numerical study, and an example of real data set regarding the first failure times of small electric carts used for internal transportation and delivery is provided for illustration.
Computational Statistics & Data Analysis, 2012
In this article, reliability sampling plans are developed for the Weibull distribution when the l... more In this article, reliability sampling plans are developed for the Weibull distribution when the life test is progressively first-failure censored. We use the maximum likelihood method to obtain the point estimators of the model parameters. We propose an approach to establish reliability sampling plans which minimize three different objective functions under the constraint of total cost of experiment and given consumer's and producer's risks. The results are tabulated for selected specifications under progressive first-failure censoring scheme, and the sensitivity analysis is also studied. A Monte Carlo simulation is performed to study the accuracy of large-sample approximation.
Journal of Information and Optimization Sciences, 2002
ABSTRACT
IEEE Transactions on Reliability, 1994
General purpose: Define bounds on life-test duration Special math needed for explanations: Statis... more General purpose: Define bounds on life-test duration Special math needed for explanations: Statistical inference Special math needed to use results: Same Results useful to: Reliability data analysts. Summary & Conclusions-The prediction of future ordered observations shows how long a sample of units might run until all fail in life testing. This paper presents the prediction intervals on future ordered-observation s in a sample of she n from a Pareto distribution with known shape parameter where the f i t k ordered observations have been observed. A useful method is defined for obtaining a bound on life-test duration for sample from a population having Pareto distributed lifetimes. [ (nP-2)-(P + 1) + ((nk) .P-2) .BJI(P + 2) 8/ U U2 / U1 Pr (s-prediction interval includes true value of future order statistics} (x (s)-x (k)) I u = y (s)y(k)
Reliability Engineering & System Safety
International Journal of Statistics and Probability
Based on progressive type-II censored sample with random removals, point and interval estimations... more Based on progressive type-II censored sample with random removals, point and interval estimations for the shape parameters of the exponentiated Weibull distribution are discussed. Computational formula for the expected total test time are derived for different situations of sampling plans. This is useful in planning a life test experiment. The efficiency of the estimators are compared in terms of the root mean square error, the variance and the coverage probability of the corresponding confidence intervals. A simulation study is presented for several values of removal probability and different values of failure percentage. Also, numerical applications are conducted to illustrate and compare the usefulness of the different sampling plans in terms of expected test times for different patterns of failure rates.
Hacettepe Journal of Mathematics and Statistics
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Published Paper by Shuo-jye Wu
Papers by Shuo-jye Wu