ESTIMATION OF PARAMETERS IN STEP-STRESS ACCELERATED LIFE TESTS FOR THE RAYLEIGH DISTRIBUTION UNDER CENSORING SETUP
Keywords:
Step-stress Accelerated Life Tests, Cumulative Exposure Model, Rayleigh Distribution, Maximum Likelihood Estimation, Type-I And Type II Censoring, Fisher Information Matrix, Bootstrap Confidence Interval.Abstract
In this paper, step-stress accelerated life test strategy is considered in obtaining the failure time data of the highly reliable items or units or equipment in a specified period of time. It is assumed that life time data of such items follows a Rayleigh distribution with a scale parameter (θ ) which is the log linear function of the stress levels. The maximum likelihood estimates (MLEs) of the scale parameters (θi) at both the stress levels (s ), i =1, 2 i are obtained under a cumulative exposure model. A simulation study is performed to assess the precision of the MLEs on the basis of mean square error (MSE) and relative absolute bias (RABias). The coverage probabilities of approximate and bootstrap confidence intervals for the parameters involved under both the censoring setup are numerically examined. In addition to this, asymptotic variance and covariance matrix of the estimators are also presented.
Downloads
References
Bagdonavicius, V. and Nikulin, M. (2002.) Accelerated Life Models:
Modeling and Statistical Analysis. Florida: Chapman & Hall/CRC Press.
Bai, D., Kim, M. and Lee, S. (1989). Optimum simple step-stress accelerated
life tests with censoring, IEEE Transactions on Reliability, 38, p. 528-532.
Balakrishnan, N. (2009). A synthesis of exact inferential results for
exponential step-stress models and associated optimal accelerated life-tests,
Metrika, 69, p. 351-396.
Balakrishnan, N. and Xie, Q. (2007). Exact inference for a simple step-stress
model with Type-II hybrid censored data from the exponential distribution,
Journal of Statistical Planning and Inference, 137, p. 2543-2563.
Balakrishnan, N., Kundu, D., Ng, H.K.T. and Kannan, N. (2007). Point and
interval estimation for a simple step-stress model with Type-II censoring,
Journal of Quality Technology, 39, p. 35-47.
Bessler, S., Chernoff, H. and Marshall, A.W. (1962). An optimal Sequential
Accelerated Life Test, Technomenics, 4, p. 367-379.
Chernoff, H. (1962). Optimal Accelerated Life Designs for Estimation,
Technomenics, 4, p. 381-408.
Chandra, N. and Khan, M.A. (2012). A new optimum test plan for simple step-
stress accelerated life testing, Proceeding of Applications of Reliability Theory
and Survival Analysis, edited volume, 57-65, Bonfring Publication,
Coimbatore, India
Gouno, E. and Balakrishnan, N. (2001). Step-stress accelerated life test, In
HandBook of Statistics: Advances in Reliability (Eds., N.Balakrishnan and
C.R.Rao), 20, p. 623-639.
Gouno, E., Sen A. and Balakrishnan, N. (2004). Optimal step-stress test under
progressive Type-I censoring, IEEE Transactions on Reliability, 53, p. 383-
Kateri, M. and Balakrishnan, N. (2008). Inference for a simple step-stress
model withType-II censoring and Weibull distributed lifetimes, IEEE
Transactions on Reliability, 57, p. 616-626.
Meeker, W.Q. and Hahn, G.J. (1985). How to Plan Accelerated Life Tests:
Some Practical techniques. Milwaukee, Wisconsin: American Society for
Quality Control, testing, IEEE Transactions on Reliability, 32, p. 59-65.
Meeker, W.Q. and Escobar, L. A. (1998). Statistical Methods for Reliability
Data. New York, John Wiley & Sons.
Miller, R. and Nelson, W.B (1983). Optimum simple step-stress plans for
accelerated life models and associated optimal accelerated life-tests, Metrika,
, p. 351-396.
Nelson, W.B. (1980). Accelerated life testing: Step-stress models and data
analysis, IEEE Transactions on Reliability, 29, p. 103-108.
Nelson, W.B. (1990). Accelerated Life Testing, Statistical Models, Test Plans,
and Data Analysis, New York, John Wiley & Sons.
Nelson, W.B. and Meeker, W. Q. (1978). Theory of optimum accelerated
censored life tests for Weibull and extreme value distributions, Technometrics,
, p. 171–177.
Xiong, C. (1998). Inferences on a simple step-stress model with type II
censored exponential data, IEEE Transactions on Reliability, 5, p. 67-74.
Xiong, C. and Milliken, G. (2002). Prediction for exponential lifetimes based
on step-stress testing, Communications in Statistics-Simulation and
Computation, 31, p. 539-556.