Bound lengths for Burr-XII distribution under step-stress PALT

Authors

  • Gyan Prakash Assistant Professor

DOI:

https://doi.org/10.14419/ijsw.v5i2.8242

Published:

2017-09-26

Keywords:

Partially Accelerated Life Test (PALT), Step-Stress Partially Accelerated Life Test (SS-PALT), Progressive Type-II censoring with Random Removal scheme (PRR-censoring), Approximate Confidence Length (ACL), One-Sample Bayes Prediction Bound Length (BPBL).

Abstract

Some inferences based on Step-Stress Partially Accelerated Life Test (SS-PALT) are discussed in the present article. The Progressive Type-II censoring criterion with Random Removal scheme is used for determining the Approximate Confidence Lengths and One-Sample Bayes Prediction Bound Lengths for the unknown parameters of the Burr Type-XII distribution. Based on the simulated data, the analysis of the present discussion has been carried out.

References

[1] Burr, W. I. 1942. Cumulative frequency distribution, Annals of Mathematical Statistics, 13, 215 - 232.

[2] Soliman, A. A., Abd-Ellah, A. H., Abou-Elheggag, N. A. & Modhesh, A. A. 2011. Bayesian inference and prediction of Burr Type – XII distribution for progressive first failure censored sampling. Intelligent Information Management, 3, 175 - 185.

[3] Nadar, M. & Papadopoulos, A. S. (2011). Bayesian analysis for the Burr Type - XII distribution based on record values, Statistica, 71 (4), 421 - 435.

[4] Danish, M. Y. & Aslam, M. 2014. Bayesian analysis of censored Burr-XII distribution. Electronic Journal of Applied Statistical Analysis, 7 (2), 326 - 342.

[5] Jang, D.-H., Jung, M., Park, J.-H., & Kim, C. 2014. Bayesian estimation of Burr Type-XII distribution based on general Progressive Type - II censoring. Applied Mathematical Sciences, 8 (69), 3435 - 3448.

[6] Li, X., Shi, Y., Wei, J., & Chai, J. 2007. Empirical Bayes estimators of reliability performances using LINEX loss under progressively Type - II censored samples. Mathematics and Computers in Simulation, 73 (5), 320 - 326.

[7] Lee, W. C., Wu, J. W. & Hong, C. W. 2009. Assessing the lifetime performance index of products from progressively Type - II right censored data using Burr - XII model. Mathematics and Computers in Simulation, 79 (7), 2167 - 2179.

[8] Al-Hussaini, E. K. & Hussein, M. 2011. Estimation using censored data from exponentiated Burr Type - XII population. American Open Journal of Statistics, 1, 33 - 45.

[9] Rao, G. S., Aslam, M. & Kundu, D. 2015. Burr - XII distribution parametric estimation and estimation of reliability of multicomponent stress-strength. Communications in Statistics - Theory and Methods, 44, 4953 - 4961.

[10] Prakash, G. 2017 a. Progressive censored Burr Type - XII distribution under random removal scheme: Some inferences. Afrika Statistika, 12 (2), 1273 - 1284.

[11] Prakash, G. 2017 b. Confidence limits for progressive censored Burr Type - XII data under Constant-Partially ALT. Journal of Statistics Applications & Probability, 6 (2), 295 - 303.

[12] Prakash, G. 2015. A comparative study based on Bayes estimation under different censoring criterion. Journal of Data Science, 13 (2), 261 - 280.

[13] Bhattacharyya, G. K. & Soejoeti, Z. 1989. A tampered failure rate model for step-stress accelerated life test. Communication in Statistics Theory & Method, 18, 1627 - 1643.

[14] Abdel-Hamid, A. H. & Al-Hussaini, E. K. 2007. Progressive stress accelerated life tests under finite mixture models. Metrika, 66, 213 - 231.

[15] Ismail, A. A. & Aly, H. M. 2009. Optimal planning of failure-step stress partially accelerated life tests under Type - II Censoring. International Journal of Mathematical Analysis, 3 (31), 1509 - 1523.

[16] Srivastava, P. W. & Mittal, N. 2010. Optimum step-stress partially accelerated life tests for the truncated logistic distribution with censoring. Applied Mathematical Modelling, 34, 3166 - 3178.

[17] Tangi, Y., Guani, Q., Xu, P., & Xu, H. 2012. Optimum design for Type - I step-stress accelerated life tests of two-parameter Weibull distributions. Communication in Statistics - Theory and Methods, 41, 3863 - 3877.

[18] Hyun, S. & Lee, J. 2015. Constant-stress partially accelerated life testing for Log-Logistic distribution with censored data. Journal of Statistics Applications and Probability, 4 (2), 293 - 201.

[19] Abdel-Hamid, A. H. 2016. Estimations in step-partially accelerated life tests for an Exponential lifetime model under Progressive Type-I censoring and general entropy loss function. Journal of Mathematics and Statistical Science, 2016, 75 - 93.

[20] DeGroot, M. H. & Goel, P. K. 1979. Bayesian and optimal design in partially accelerated life testing. Naval Research Logistics, 16(2), 223 - 235.

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