Degradation analysis on trend gamma process

Manufactures always face a big challenge to obtain the sufficient reliability information for high-quality products when only a relatively short time period is available for an internal life testing. Fortunately, if QCs exists, whose degradation over time can be related to reliability, an approach is suggested to collect sufficient degradation data for estimating the product's lifetime distribution more accurately. In numerical applications, the gamma process (GP) is commonly used when the degradation path is strictly increasing. However, in some circumstances, the GP is not able to successfully capture the degradation path. One resolution to tackle this problem is to consider the random effect into the GP model. In this paper, we propose a trend gamma process (TGP), which integrated the merits of trend function into a GP model, as an alternative approach to overcome this obstacle. The proposed TGP model is a generalized formulation of GP model, and it is attempted to transform a monotonic stochastic process into a GP. The results based on simulation studies and real data examples illustrate that our proposed TGP model is suitable for widely use when the degradation path is monotonically increasing.