Point and interval evaluation of nanoparticles censored sample in the spray process

Document Type: Research Paper

Authors

1 Department of Mathematics and Statistics, Lahijan branch, Islamic Azad University, Lahijan, Iran

2 Department of Mechanical Engineering, Payame Noor University (PNU), Tehran, Iran

Abstract

A good nano coating depends on the quality of the collision and spreading behavior of the nanoparticles. Unfortunately, in many cases, nanoparticle spreading data has not been recorded. In this paper, we have extended the evaluation model to predict the unavailable or censored maximum spreading diameter of nanoparticle data. Different point and interval methods have been considered for this problem. Choosing Bayesian evaluation, the Markov Chain Monte Carlo (MCMC) has been proposed as an efficient procedure for estimating the predictive inference for future observation. An important implication of the present study is that the censored maximum diameter data can be predicted well using the proposed methods. Results showed the proposed point predictions are close to real data, the predictive intervals contain the real values, and it verifies the applicability of the prediction techniques for real problems.

Graphical Abstract

Point and interval evaluation of nanoparticles censored sample in the spray process

Highlights

  • Evaluation of the maximum spreading diameter of nanoparticle data on hydrophobic surface was studied.
  • The generalized inverted exponential model was proposed as an appropriate model.
  • The Markov Chain Monte Carlo procedure and likelihood approach were used to predict the censored data.

Keywords


[1] S.C. Maroo, J.N. Chung, Nanodroplet impact on a homogenous surface using molecular dynamics, ASME 2008 3rd Energy Nanotechnology International Conference, ENIC2008-53036 (2008) 113-121.
[2] N. Sedighi, S. Murad, S.K. Aggarwal, Molecular dynamics simulations of nanodroplet spreading on solid surfaces, effect of droplet size, Fluid Dyn. Res. 42 (2010) 035501.

[3] S. Asadi, Simulation of nanodroplet impact on a solid surface, Int. J. Nano Dimens. 3 (2012) 19-26.
[4] H. Hai-Bao, C. Li-Bin, B. Lu-Yao, H. Su-He, Molecular dynamics simulations of the nanodroplet impact process on hydrophobic surfaces, Chinese Phys. B, 23 (2014) 074702.
[5] X.-H. Li, X.-X. Zhang, M. Chen, Estimation of viscous dissipation in nanodroplet impact and spreading, Phys. Fluids, 27 (2015) 052007.
[6] K. Kobayashi, K. Konno, H. Yaguchi, H. Fujii, T. Sanada, M. Watanabe, Early stage of nanodroplet impact on solid wall, Phys. Fluids, 28 (2016) 032002.
[7] S. Asadi, Simulation of nanodroplet impact on an oblique surface in nanocoating processes by molecular dynamics, Iran. J. Surface Sci. Eng. 13 (2017) 41-50.
[8] H. Panahi, S. Asadi, Statistical modeling for oblique collision of nano- and microdroplets in plasma spray processes, Int. J. Nanosci. Nanotech. 14 (2018) 71-83.
[9] H.M. Khan, S.B. Provost, A. Singh, Predictive inference from a two-parameter Rayleigh life model given a doubly censored sample, Commu. Stat.-Theor. M. 39 (2010) 1237-1246.
[10] E.A. Ahmed, Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application, J. Appl. Stat. 44 (2017) 1576-1608.
[11] H. Panahi, S. Asadi, Modeling of splat particle splashing data during thermal spraying with the Burr distribution, J. Part. Sci. Technol. 3 (2017) 41-50.
[12] J.Y. Chiang, S. Wang, T.-R. Tsai, T. Li, Model selection approaches for predicting future order statistics from Type II censored data, Math. Probl. Eng. 4 (2018) 3465909.
[13] I. Basak, N. Balakrishnan, A note on the prediction of censored exponential lfetimes in a simple step-stress model with type-II censoring, Calcutta Stat. Assoc. 70 (2018) 57-73.
[14] A.M. Abouammoh, M.A. Alshingiti, Reliability estimation of generalized inverted exponential distribution, J. Stat. Comput. Sim. 79 (2009) 1301-1315.
[15] S. Nadarajah, S. Kotz, The exponentiated type distributions, Acta Appl. Math. 92 (2006) 97-111.
[16] S. Kotz, S. Nadarajah, Extreme value distributions: Theory and applications, Imperial College Press, London (2000).

[17] H. Panahi, Estimation methods for the generalized inverted exponential distribution under Type II progressively hybrid censoring with application to spreading of microdrops data, Commun. Math. Stat. 5 (2017) 159-174.
[18] E.A., Ahmed, Estimation and prediction for the generalized inverted exponential distribution nased on progressively first-failure censored data with application, J. Appl. Stat. 44 (2017) 1576-1608.
[19] B. Chandrasekar, A. Childs, N. Balakrishnan, Exact likelihood inference for the exponential distribution under generalized Type‐I and Type‐II hybrid censoring, Nav. Res. Log. 51 (2004) 994-1004.
[20] A. Shafay, Bayesian estimation and prediction based on generalized Type-II hybrid censored sample, J. Stat. Comput. Sim. 86 (2016) 1970-1988.
[21] R. Valiollahi, A. Asgharzadehb, D. Kundu, Prediction of future failures for generalized exponential distribution under Type-I or Type-II hybrid censoring, Braz. J. Probab. Stat. 31 (2015) 1-21.
[22] A.J. Fernández, On maximum likelihood prediction based on Type II doubly censored exponential data, Metrika, 3 (2000) 211-220.
[23] D. kundu, H. Howlader, Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data, Comput. Stat. Data Anal. 54 (2010) 1547-1558.
[24] S.O. Bleed, Gibbs sampling and Bayesian estimators for time censoring constant stress reliability/life prediction, J. Hum. Appl. Sci. 28 (2016) 166-182.
[25] E. Saraiva, A. Suzuki, L. Milan, Bayesian computational methods for sampling from the posterior distribution of a bivariate survival model, based on AMH copula in the presence of right-censored data, Entropy, 20 (2018) 35-42.
[26] S. Sel, M. Jung, Y. Chung, Bayesian and maximum likelihood estimations from parameters of McDonald Extended Weibull model based on progressive Type-II censoring, J. Stat. Theor. Pract. 12 (2018) 231-254.
[27] H. Panahi, Inference for exponentiated Pareto distribution based on progressive first-failure censored data with application to cumin essential oil data, J. Stat. Manag. Sys. 21 (2018) 1433-1457.
[28] H.L. Lu, Prediction intervals of an ordered observation from one-parameter exponential distribution based on multiple Type II censored samples, J. Chin. Inst. Ind. Eng. 21 (2004) 494-503.