A Combined Approach of a Sequential Life Testing and an Accelerated Life Testing Applied to a Low-Alloy High Strength Steel Component

Authors: D. I. De Souza, D. R. Fonseca, G. P. Azevedo

Abstract:

Sometimes the amount of time available for testing could be considerably less than the expected lifetime of the component. To overcome such a problem, there is the accelerated life-testing alternative aimed at forcing components to fail by testing them at much higher-than-intended application conditions. These models are known as acceleration models. One possible way to translate test results obtained under accelerated conditions to normal using conditions could be through the application of the “Maxwell Distribution Law.” In this paper we will apply a combined approach of a sequential life testing and an accelerated life testing to a low alloy high-strength steel component used in the construction of overpasses in Brazil. The underlying sampling distribution will be three-parameter Inverse Weibull model. To estimate the three parameters of the Inverse Weibull model we will use a maximum likelihood approach for censored failure data. We will be assuming a linear acceleration condition. To evaluate the accuracy (significance) of the parameter values obtained under normal conditions for the underlying Inverse Weibull model we will apply to the expected normal failure times a sequential life testing using a truncation mechanism. An example will illustrate the application of this procedure.

Keywords: Sequential Life Testing, Accelerated Life Testing, Underlying Three-Parameter Weibull Model, Maximum Likelihood Approach, Hypothesis Testing.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1089229

References:

[1] D. I. De Souza, "Sequential Life-Testing with Truncation Mechanisms for Underlying Three-Parameter Weibull and Inverse Weibull Models,” COMADEM 2004 Conference, Cambridge, U.K., pp. 260-271, August 2004.
[2] P. Erto, ". New Practical Bayes Estimators for the 2-Parameter Weibull Distribution”, IEEE Transactions on Reliability, R-31, (2), 194-197, 1982.
[3] D. I. De Souza, D. R. Fonseca and D. Kipper, "Appling Eyring’s Accelerated Life Test Model to Times to Breakdown of Insulating Fluid: A Combined Approach of an Accelerated and a Sequential Life Testing,”, World Academy of Science, Engineering and Technology: Year 6, Issue 7, pp. 77-82, September 2010.
[4] Harter, H. et al., "Maximum Likelihood Estimation of the Parameters of Gamma and Weibull Populations from Complete and from Censored Samples”, Technometrics, No 7, pp. 639-643; 1965, erratum, 15 (1973), pp. 431.
[5] L. J. Bain, "Statistical Analysis of Reliability and Life-Testing Models, Theory and Method”, Marcel Dekker, Inc., New York, NY, USA, 1978.
[6] S. H. Zanakis and J. A. Kyparisis, "Review of Maximum Likelihood Estimation Methods for the Three Parameter Weibull Distribution”, Journal of Statistical Computation and Simulation, 25, 53-73, 1986.
[7] D. N. P. Murthy, M. Xie and R. Hang, "Weibull Models”, Wiley Series in Probability and Statistics, John Wiley & Sons, Inc., New Jersey, 2004.
[8] W. R. Blischke, "On non-regular estimation II. Estimation of the Location Parameter of the Gamma and Weibull Distributions”, Communications in Statistics, 3, 1109-1129, 1974.
[9] A. C. Cohen, B. J. Whitten and Y. Ding, "Modified Moment Estimation for the Three-Parameter Weibull Distribution”, Journal of Quality Technology 16, 159-167, 1984.
[10] K. Kapur and L. R. Lamberson, "Reliability in Engineering Design”, John Willey & Sons, Inc., New York, 1977.
[11] D. I. De Souza, G. P. Azevedo, D. R. Fonseca, " Further Thoughts on a Sequential Life Testing Approach Using an Inverse Weibull Model”, World Academy of Science, Engineering and Technology, Issue 69, pp. 1287-1290, 2012.
[12] A. M. Mood and F. A. Graybill, "Introduction to the Theory of Statistics”, Second Edition, New York: McGraw-Hill., USA, 1963.