Regression analysis method for linear process

The definition and regression analysis method for linear process are put forward, based on which the regression model, regression equation and confidence limit curves with high confidence level and reliability are established. The linear process is an independent increment process with linear mean function and quadratic variance function. Most stochastic processes in engineering, such as creep, stress relaxation, stiffness reduction, crack propagation and performance degradation can be transformed into linear processes. The proposed method extends the traditional regression analysis which is only suitable to data points to stochastic processes. By the presented method, the linear process is analyzed as an integration and the lengthwise information among different test times is applied, therefore this method not only has higher precision but also solves the problem of reliability assessment with very small sample.