Estimating reliability parameters for inverse Gaussian distributions under complete and progressively type-II censored samples

ABSTRACT In this paper, we study estimation of stress-strength reliability, assuming the stress and strength variables are inverse Gaussian distributed with unknown parameters. When the coefficient of variations of the distributions is unknown but equal, we develop MLE, Bayes estimator, bootstrap interval of the reliability. The profile likelihood Bayes estimator of the coefficient of variation is also derived. When all parameters are different, we derive the MLE, UMVUE, Bayes estimator, bootstrap interval, and highest posterior density credible interval of the stress-strength reliability. The predictive Bayes estimators of the reliability functions are derived. Under progressive type-II censoring, we derive the MLE, Bayes estimator and bootstrap confidence interval. Monte-Carlo simulation results and real data-based examples are also presented. We analyze lung cancer and air pollution data sets as applications of the stress-strength model.

[1]  H. Panahi,et al.  Estimation of stress–strength reliability based on censored data and its evaluation for coating processes , 2022, Quality Technology & Quantitative Management.

[2]  Nabakumar Jana,et al.  On estimating common mean of several inverse Gaussian distributions , 2021, Metrika.

[3]  M. Z. Raqab,et al.  Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution , 2020, Statistical Papers.

[4]  K. Chatterjee,et al.  Inference on stress–strength reliability for exponential distributions with a common scale parameter , 2019, Journal of Applied Statistics.

[5]  N. Nematollahi,et al.  Estimation of stress–strength reliability in the inverse Gaussian distribution under progressively type II censored data , 2019, Mathematical Sciences.

[6]  Sumith Gunasekera,et al.  Inference for the reliability function based on progressively type II censored data from the Pareto model: The generalized variable approach , 2018, J. Comput. Appl. Math..

[7]  Fatma Gül Akgül,et al.  Estimation of P(X < Y) using ranked set sampling for the Weibull distribution , 2017 .

[8]  A. Baklizi.  Bayesian inference for Pr (Y, 2014 .

[9]  Chien-Tai Lin,et al.  Estimation of P(Y, 2013 .

[10]  Narayanaswamy Balakrishnan,et al.  Estimation for the three-parameter inverse Gaussian distribution under progressive Type-II censoring , 2012 .

[11]  Laura Ventura,et al.  Recent advances on Bayesian inference for $P(X < Y)$ , 2011 .

[12]  Ajit Srividya,et al.  Applying mechanistic models to reliability evaluation of mechanical components – An illustration , 2011 .

[13]  Ren-Dao Ye,et al.  Inferences on the common mean of several inverse Gaussian populations , 2010, Comput. Stat. Data Anal..

[14]  G. Mazzanti,et al.  Bayesian reliability estimation based on a weibull stress-strength model for aged power system components subjected to voltage surges , 2006, IEEE Transactions on Dielectrics and Electrical Insulation.

[15]  Xue Li,et al.  Statistical inference for the common mean of two log-normal distributions and some applications in reliability , 2006, Comput. Stat. Data Anal..

[16]  Ramalingam Shanmugam,et al.  The Stress-Strength Model and Its Generalizations: Theory and Applications , 2004, Technometrics.

[17]  T G Clark,et al.  Survival Analysis Part I: Basic concepts and first analyses , 2003, British Journal of Cancer.

[18]  S. Kotz,et al.  The stress-strength model and its generalizations : theory and applications , 2003 .

[19]  N. Balakrishnan,et al.  Point and interval estimation for Gaussian distribution, based on progressively Type-II censored samples , 2003, IEEE Trans. Reliab..

[20]  Narayanaswamy Balakrishnan,et al.  Estimation of parameters from progressively censored data using EM algorithm , 2002 .

[21]  W. J. Padgett,et al.  Inference for Reliability and Stress-Strength for a Scaled Burr Type X Distribution , 2001, Lifetime data analysis.

[22]  N. Balakrishnan,et al.  Progressive Censoring: Theory, Methods, and Applications , 2000 .

[23]  S. Ramakrishnan,et al.  Point and Interval Estimation of P(X < Y): The Normal Case with Common Coefficient of Variation , 1999 .

[24]  Thomas A. Severini,et al.  Likelihood functions for inference in the presence of a nuisance parameter , 1998 .

[25]  Z. F. Jaheen,et al.  Empirical Bayes estimation of P(Y < X) and characterizations of Burr-type X model , 1997 .

[26]  Ramesh C. Gupta,et al.  On the reliability studies of a weighted inverse Gaussian model , 1995 .

[27]  Narayanaswamy Balakrishnan,et al.  A Simple Simulational Algorithm for Generating Progressive Type-II Censored Samples , 1995 .

[28]  A. C. Kimber,et al.  Exploratory Data Analysis for Possibly Censored Data from Skewed Distributions , 1990 .

[29]  S. Sinha.  Bayesian estimation of the reliability function of the inverse gaussian distribution , 1986 .

[30]  E. M. Roberts,et al.  Review of Statistics of Extreme Values with Applications to Air Quality Data: Part II. Applications , 1979 .

[31]  W. J. Padgett,et al.  Confidence Bounds on Reliability for the Inverse Gaussian Model , 1979, IEEE Transactions on Reliability.

[32]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[33]  Wayne A. Woodward,et al.  Minimum Variance Unbiased Estimation of P[Y < X] in the Normal Case , 1977 .

[34]  F. Downton.  The Estimation of Pr (Y < X) in the Normal Case , 1973 .

[35]  Alessia Dorigoni,et al.  Inverse Gaussian Distribution , 2015 .

[36]  A. Basu,et al.  The Inverse Gaussian Distribution , 1993 .

[37]  H. K. Hsieh.  INFERENCES ON THE COEFFICIENT OF VARIATION OF AN INVERSE GAUSSIAN DISTRIBUTION , 1990 .

[38]  N. Balakrishnan,et al.  Computational Statistics and Data Analysis Estimation for the Three-parameter Lognormal Distribution Based on Progressively Censored Data , 2022 .