Lower quantile inference for constant stress accelerated life tests via P-spline modeling under type-II progressively censoring

Articles in Press

Document Type : Original Article

Authors
Bahareh Sedighi 1
Esmaile Khorram 2
Ali Aghamohammadi 3
1 Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
2 Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.
3 Department of Statistics, University of Zanjan, Zanjan, Iran
10.22034/jirss.2026.2087161.1188
Abstract
The purpose of this paper is to propose a semiparametric modeling approach for constant stress accelerated life test (CSALT) under the type-II progressively censoring scheme (T-II PCS). In the proposed model, the quantile regression (QR) approach based on the asymmetric Laplace distribution (ALD) is presented, and nonparametric functions are used to describe relationships between lifetime distribution characteristics and accelerated stresses. The relationships are approximated by the B-spline method. Additionally, a penalized expectationmaximization algorithm (EM) is developed for maximum likelihood estimation of parameters of the model at the τth quantile of the lifetime distribution, using a hierarchical representation of the ALD. The proposed model is appropriate to deal with one or more accelerated stresses scenarios. To demonstrate the performance and effectiveness of the proposed model, a simulation study and a real data set analysis are conducted.
Keywords
Constant Stress Accelerated Life Test
P-spline
Lower Quantile
Asymmetric Laplace Distribution
Penalized Expectation-Maximization Algorithm
Subjects
Abd El-Raheem AM. Optimal design of multiple constant-stress accelerated life testing for the extension of the exponential distribution under type-II censoring. Journal of Computational and Applied Mathematics. 2021;382:113094.
Anderson KM. A nonproportional hazards Weibull accelerated failure time regression model. Biometrics. 1991;p. 281–288.
Bae SJ, Lim M. A nonlinear quantile regression for accelerated destructive degradation testing data. IISE Transactions. 2025;57(6):621–638.
Balakrishnan N, Aggarwala R. Progressive Censoring: Theory, Methods, and Applications. Birkhäuser; 2000.
Balakrishnan N, Sandhu RA. A simple simulational algorithm for generating progressive typeII censored samples. The American Statistician. 1995;49(2):229–230.
Balakrishnan N. Progressive censoring methodology: an appraisal. Test. 2007;16(2):211–259.
Chen N, Tang Y, Ye ZS. Robust quantile analysis for accelerated life test data. IEEE Transactions on Reliability. 2015;65(2):901–913.
Davino C, Furno M, Vistocco D. Quantile Regression: Theory and Applications. John Wiley & Sons; 2013.
De Boor C. A practical guide to splines, vol. 27. springer New York; 1978.
Eilers PHC, Marx BD. Flexible smoothing with B-splines and penalties. Statistical science. 1996;11(2):89–121.
Elsayed EA, Zhang H. Design of PH-based accelerated life testing plans under multiple-stresstype. Reliability Engineering & System Safety. 2007;92(3):286–292.
Escobar LA, Meeker WQ. A review of accelerated test models. Statistical science. 2006;p.552–577.
Feng X, Tang J. Reliability Assessment for Dual Constant-Stress Accelerated Life Test Based on Weibull Distribution With type-II Censoring. Quality and Reliability Engineering International. 2025;41(3):1025–1040.
Feng X, Tang J, Balakrishnan N, Tan Q. Reliability inference for dual constant-stress accelerated life test with exponential distribution and progressively type-II censoring. Journal of Statistical Computation and Simulation. 2024;94(17):3864–3891.
Hastie T, Tibshirani R. Generalized Additive Models. London: Chapman and Hall; 1990.
Hirose H. Estimation of threshold stress in accelerated life-testing. IEEE Transactions on Reliability. 1993;42(4):650–657.
Koenker R, Machado JAF. Goodness of fit and related inference processes for quantile regression. Journal of the american statistical association. 1999;94(448):1296–1310.
Kozumi H, Kobayashi G. Gibbs sampling methods for Bayesian quantile regression. Journal of statistical computation and simulation. 2011;81(11):1565–1578.
Kumar D, Nassar M, Dey S, Alam FMA. On estimation procedures of constant stress accelerated life test for generalized inverse Lindley distribution. Quality and Reliability Engineering International. 2022;38(1):211–228.
Lee ER, Park S, Lee SK, Hong HG. Quantile forward regression for high-dimensional survival data: ER Lee et al. Lifetime data analysis. 2023;29(4):769–806.
Li Y, Pan G, Li Q, Wang C, Hu X. A novel accelerated life-test method under thermal cyclic loadings for electronic devices considering multiple failure mechanisms. Microelectronics Reliability. 2020;114:113766.
Lin CT, Hsu YY, Lee SY, Balakrishnan N. Inference on constant stress accelerated life tests for log-location-scale lifetime distributions with type-I hybrid censoring. Journal of statistical computation and simulation. 2019;89(4):720–749.
Journal of the Iranian Statistical Society

Articles in Press, Accepted Manuscript
Available Online from 14 September 2026

  • Receive Date 21 April 2026
  • Revise Date 02 August 2026
  • Accept Date 25 August 2026