Remaining useful life estimation based on gamma process considered with measurement error

For high reliability and long life components and systems, remaining useful life (RUL) estimation is the key of the prognostics and health management (PHM). RUL is important to verify reliability of components, and set a condition-based maintenance policy. With degradation data, RUL is able to be computed. For most products, degradation theoretically is a monotonically decreasing process. Because degrading process is an irreversible process for most components that they can only cumulate damage but not cure themselves. However, the actual degrading process described by the online monitoring data is usually not strictly monotonie. In most cases, the performance parameters are detected degrading with fluctuation in a little interval. Base on these facts, this paper proposes the monitored degrading process with fluctuation be made of a gamma process combined with random measurement error. A gamma process is utilized to model degrading process for its monotonicity. The measurement error is an inevitable error that no matter how accurate the measuring equipment is, the measurement result always deviates from the true value. In most cases, the measurement error fits normal distribution, whose mean and variance are related to the accuracy of the measuring equipment. With the approach proposed in this paper, the gamma process is able to fit the real degrading process and prognosticate life without measurement error. The method of moments is utilized to estimate model parameters. At last, a numerical example is used to illustrate the modeling method of utilizing a gamma process combined with random measurement error. The prognosticating result shows that the approach considered measurement error can give a shorter interval of prognosticating lifetime than the classical gamma process.