Statistical properties of maximum likelihood estimates for accelerated lifetime data under the Weibull model
Date of Award
Doctor of Philosophy (PhD)
Computational Analysis and Modeling
Pipe rehabilitation liners are often installed in host pipes that lie below the water table. As such, they are subjected to external hydrostatic pressure. The external pressure leads to early deformation in the liners, which could ultimately lead to its failing or buckling before its expected service lifetime is achieved. Experiments involving long term buckling behavior of liners are typically accelerated lifetime testing procedures. In an accelerated testing procedure a liner is subjected to a constant external hydrostatic pressure and observed until it fails or for a certain time, t whichever occurs first. Liners that do not fail at time t are deemed censored observations. While a constant pressure is convenient to use in experimental situations, in reality pressure fluctuates under soil conditions over time depending on the water table.
In this study, constant and variable pressures using the Weibull model for time till buckling under different sample sizes and different levels of censoring were investigated. Data were generated through computer simulation and estimates of parameters in the Weibull model were obtained using the Maximum Likelihood and Newton-Raphson methods.
It was concluded that the maximum likelihood estimates under fixed or variable pressure, and for different sample sizes with different levels of censoring, are unbiased. However, the estimates for sample sizes as large as 100 are not normally distributed, especially when the parameter value being estimated is small. It was seen that the lack of normality was manifested in lack of agreement between the observed variance-covariance matrix and the theoretical variance-covariance matrix. These results cast doubt on the use of normal theory for inference concerning certain parameters.
Yousef, Mahmoud A., "" (2001). Dissertation. 714.