# zbMATH — the first resource for mathematics

Inference of constant-stress accelerated life test for a truncated distribution under progressive censoring. (English) Zbl 1443.62323
Summary: Accelerated life test (ALT) provides a feasible and efficient way to obtain information quickly on lifetime of products by testing them at higher-than-use operating conditions. In this paper, the lifetime of products is assumed to follow a lower truncated family of distributions, when both resilience and threshold parameters are nonconstant and affected by operating stress, inference is discussed for simple constant-stress ALT under progressive Type-II censoring. Point estimates for unknown parameters are presented based on maximum likelihood and pivotal quantities based estimation methods. Meanwhile, generalized, asymptotic and bootstrap confidence intervals for the parameters of interest are constructed as well. Simulation studies and illustrative examples are carried out to investigate the performance of the proposed methods.

##### MSC:
 62N05 Reliability and life testing 62F10 Point estimation 62F25 Parametric tolerance and confidence regions
Full Text:
##### References:
 [1] Zhang, T. L.; Xie, M., On the upper truncated Weibull distribution and its reliability implications, Reliab. Eng. Syst. Saf., 96, 194-200 (2011) [2] Aban, I. B.; Meerschaert, M. M.; Panorska, A. K., Parameter estimation for the truncated Pareto distribution, J. Am. Stat. Assoc., 101(473), 270-277 (2006) · Zbl 1118.62312 [3] Nadarajah, S., Some truncated distributions, Acta Appl. Math., 106, 105-123 (2009) · Zbl 1379.60017 [4] Marshall, A. W.; Olkin, I., Life Distributions; Structure of Nonparametric, Semiparametric, and Parametric Families (2007), New York: Springer · Zbl 1304.62019 [5] Nelson, W., Accelerated Testing: Statistical Models, Test Plans and Data Analysis (1990), New York: Wiley [6] Han, D.; Kundu, D., Inference for a step-stress model with competing risks for failure from the generalized exponential distribution under Type-I censoring, IEEE T. Reliab., 64(1), 31-43 (2015) [7] Mitra, S.; Ganguly, A.; Samanta, D.; Kundu, D., On the simple step-stress model for two-parameter exponential distribution, Stat. Methodol., 15, 95-114 (2013) · Zbl 07035618 [8] Nelson, W.; Meeker, W. Q., Theory for optimum accelerated censored life tests for Weibull and extreme value distributions, Technometrics, 20, 171-177 (1987) · Zbl 0391.62074 [9] Watkins, A. J.; John, A. M., On constant stress accelerated life tests terminated by Type-II censoring at one of the stress levels, J. Stat. Plan. Infer., 138, 768-786 (2008) · Zbl 1133.62087 [10] Balakrishnan, N.; Han, D., Exact inference for a simple step stress model with competing risks for failure from exponential distribution under Type-II censoring, J. Stat. Plan. Infer., 138, 4172-4186 (2008) · Zbl 1146.62076 [11] Bagdonavicius, V.; Nikulin, M., Accelerated Life Models: Modeling and Statistical Analysis (2002), Boca Raton: Chapman & Hall · Zbl 1001.62035 [12] Li, P. C.; Ting, W.; Kwong, D. L., Time-dependent dielectric breakdown of chemical-vapour-deposited $$SiO_2$$ gate dielectrics, Elec. Lett., 25, 665-666 (1989) [13] Hiergeist, P.; Spitzer, A.; Rohl, S., Lifetime of oxide and oxide-nitro-oxide dielectrics within trench capacitors for DRAMs, IEEE T. Electron Dev., 36, 913-919 (1989) [14] Nelson, W., Fitting of fatigue curves with nonconstant standard deviation to data with runouts, J. Test. Eval., 12, 69-77. (1984) [15] Boyko, K. C.; Gerlach, D. L., Times dependent dielectric breakdown of 210Aoxides, Proceedings of the 1989 Reliability Physics Symposium, pp.1-8 (1989) [16] Meeter, C. A.; Meeker, W. Q., Optimum accelerated life tests with a nonconstant scale parameter, Technometrics, 36, 71-83 (1994) · Zbl 0800.62624 [17] Balakrishnan, N.; Ling, M. H., Best constant-stress accelerated life-test plans with multiple stress factors for one-shot device testing under a Weibull distribution, IEEE T. Reliab., 63(4), 944-952 (2014) [18] Seo, J. H.; Jung, M.; Kim, C. M., Design of accelerated life test sampling plans with a nonconstant shape parameter, Eur. J. Oper. Res., 197, 659-666 (2009) · Zbl 1159.91463 [19] Tang, L. C.; Goh, T. N.; Sun, Y. S.; Ong, T. L., Planning accelerated life tests for censored two-parameter exponential distributions, Nav. Res. Log., 46, 169-186. (1999) · Zbl 0918.90079 [20] Bagdonavicius, V.; Cheminade, O.; Nikulin, M., Statistical planning and inference in accelerated life testing using the CHSS model, J. Stat. Plan. Infer., 126, 535-551 (2004) · Zbl 1076.62101 [21] Balakrishnan, N.; Aggarwala, R., Progressive Censoring: Theory, Methods, and Applications (2000), Boston: Birkhauser [22] Lawless, J. L., Statistical Models and Methods for Life time Data. 2nd ed (2003), New York: Wiley [23] Stephens, M., Tests for the exponential distribution, Goodness-of-Fit Techniques, pp421-459 (1986), New York: Marcel Dekker [24] Weerahandi, S., Generalized confidence intervals, J. Am. Stat. Assoc., 88(423), 899-905 (1993) · Zbl 0785.62029 [25] Efron, B., The Jackknife, the bootstrap and other re-sampling plans, Proceedings of the CBMS/NSF Regional Conference Series in Applied Mathematics, vol. 38 (1982), SIAM, Philadelphia, PA [26] Hall, P., Theoretical comparison of bootstrap confidence intervals, Ann. Stat., 16, 927-953 (1988) · Zbl 0663.62046 [27] Balakrishnan, N., Progressive censoring methodology: an appraisal, Test, 16(2), 211-259 (2007) · Zbl 1121.62052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.