Analysis of accelerated failure times of rehabilitation liners subjected to a constant or variable pressure

Abstract

Abstract 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 involving type I censoring a liner is often 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. It is, therefore, desirable to study and compare accelerated life testing models under variable and constant pressure. Statistical analysis of data on accelerated time till buckling is based on the maximum likelihood procedure for censored or uncensored observations. It is known that maximum likelihood estimates of model parameters are asymptotically (for very large samples) unbiased and normally distributed. In practice, however, it is important to determine the applicability of these asymptotic assumptions for relatively small samples with censored observations under constant and variable pressure. In this study, the accelerated Weibull model for time till buckling under constant pressure is extended to variable pressure and the applicability of the model is investigated by simulation for different sample sizes and different levels of censoring. Data were generated through computer simulation and estimates of parameters were obtained using the maximum likelihood and Newton–Raphson methods. Results on the statistical properties (concerning distribution and bias) of model parameter estimates were used to make inference about the applicability of the accelerated life testing procedure for relatively small censored samples encountered in practice. Expressions from the model are given for computing the probability of survival until a given time or the survival time for a given probability of survival.