Abstract
In this paper, we propose a new non-parametric test for testing mean time to failure order. The asymptotic properties of the proposed test statistic are studied. We also develop a jackknife empirical likelihood (JEL) ratio test for testing the mean time to failure order. Using the Monte Carlo simulation study, we establish that the JEL ratio test has good power under various alternatives. Finally, we illustrate the proposed test procedure using two real data sets.
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References
Asha G, Nair UN (2010) Reliability properties of mean time to failure in age replacement models. Int J Reliab Qual Saf Eng 17:15–26
Barlow RE, Proschan F (1965) Mathematical theory of reliability. Wiley, New York
Bhattacharyya D, Khan RA, Mitra M (2020) A test of exponentiality against DMTTF alternatives via L-statistics. Stat Probab Lett 165:108853
Bhattacharyya D, Khan RA, Mitra M (2021) Two-sample nonparametric test for comparing mean time to failure functions in age replacement. J Stat Plan Inference 212:34–44
Bhattacharyya D, Ali Khan R, Mitra M (2021) A goodness of fit test for mean time to failure function in age replacement. J Stat Comput Simul. https://doi.org/10.1080/00949655.2021.1944141
Bhattacharyya D, Khan RA, Mitra M (2021) A new family of tests for DMTTF alternatives under complete and censored samples. Commun Stat. https://doi.org/10.1080/03610918.2021.1965164
Bouadoumou M, Zhao Y, Lu Y (2015) Jackknife empirical likelihood for the accelerated failure time model with censored data. Commun Stat 44:1818–1832
Izadi M, Sharafi M, Khaledi BE (2018) New nonparametric classes of distributions in terms of mean time to failure in age replacement. J Appl Probab 55:1238–1248
Izadi M, Manesh SF (2021) Testing exponentiality against a trend change in mean time to failure in age replacement. Commun Stat Theory Methods 50:3358–3370
Jeske DR, Zhang X (2005) Some successful approaches to software reliability modeling in industry. J Syst Softw 74:85–99
Jing BY, Yuan J, Zhou W (2009) Jackknife empirical likelihood. J Am Stat Assoc 104:1224–1232
Kayid M, Ahmad IA, Izadkhah S, Abouammoh AM (2013) Further results involving the mean time to failure order and the decreasing mean time to failure class. IEEE Trans Reliab 62:670–678
Khan RA, Bhattacharyya D, Mitra M (2020) A change point estimation problem related to age replacement policies. Oper Res Lett 48:105–108
Khan RA, Bhattacharyya D, Mitra M (2021) Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives. Stat Pap 62:3015–3045
Khan RA, Bhattacharyya D, Mitra M (2021) On classes of life distributions based on the mean time to failure function. J Appl Probab 58:289–313
Klefsjö B (1982) On ageing properties and total time on test transforms. Scand J Stat 9:37–41
Knopik L (2005) Some results on ageing class. Control Cybern 34:1175–1180
Knopik L (2006) Characterization of a class of lifetime distributions. Control Cybern 35:407–414
Lai CD, Xie M (2006) Stochastic ageing and dependence for reliability. Springer, New York
Lee AJ (1990) \(U\)-statistics: theory and practice. CRC Press, Boca Raton
Lehmann EL (1951) Consistency and unbiasedness of certain nonparametric tests. Ann Math Stat 22:165–179
Proschan F (1963) Theoretical explanation of observed decreasing failure rate. Technometrics 5:375–383
Qi Y (2018) Jackknife empirical likelihood methods. Biostat Biom Open Access J 7:20–22
Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer Science and Business Media, New York
Sudheesh KK, Anisha P (2019) A simple non-parametric test for decreasing mean time to failure. Stat Pap 60:73–87
Sudheesh KK, Asha G, Jagathnath Krishna KM (2021) On the mean time to failure of an age-replacement model in discrete time. Commun Stat 51:2569–2585
Sudheesh KK, Deemat CM (2021) A Family of non-parametric tests for decreasing mean time to failure with censored data. Commun Stat 50:203–215
Wang X (2010) Empirical likelihood with applications, [Doctoral dissertation]. National University of Singapore
Wang R, Peng L, Qi Y (2013) Jackknife empirical likelihood test for equality of two high dimensional means. Stat Sin 23:667–690
Wang D, Zhao Y (2016) Jackknife empirical likelihood for comparing two Gini indices. Can J Stat 44:102–119
Yang H, Liu S, Zhao Y (2016) Jackknife empirical likelihood for linear transformation models with right censoring. Ann Inst Stat Math 68:1095–1109
Yu X, Zhao Y (2018) A short ode to jackknife empirical likelihood procedures. Biom Biostat Int J 7(1):7–8
Zhang Z, Liu T, Zhang B (2016) Jackknife empirical likelihood inferences for the population mean with ranked set samples. Stat Probab Lett 108:16–22
Zhao Y, Meng X, Yang H (2015) Jackknife empirical likelihood inference for the mean absolute deviation. Comput Stat Data Anal 91:92–101
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We thank the anonymous reviewers for their valuable suggestions which resulted in this improved version of the manuscript.
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Mathew, D.C., Alex, R.M. & Kattumannil, S.K. Jackknife empirical likelihood ratio test for testing mean time to failure order. Stat Papers 65, 79–92 (2024). https://doi.org/10.1007/s00362-022-01385-x
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DOI: https://doi.org/10.1007/s00362-022-01385-x