<p>In degradation data modeling, parametric stochastic processes such as gamma, inverse Gaussian, and Wiener processes are commonly used as parametric models for the degradation data to estimate the first-passage time distribution. Accurate identification of the underlying stochastic process is crucial to avoid model misspecification errors. Traditional goodness-of-fit testing procedures such as the Kolmogorov–Smirnov, the Cramér–von Mises, or the Anderson-Darling tests are applicable when the degradation measurements are taken at equally spaced time intervals. However, equally spaced degradation measurements are often unavailable due to experiment constraints or missing measurements, making goodness-of-fit testing challenging as degradation differences become non-identical. This study introduces several novel goodness-of-fit test procedures to test the underlying degradation process when degradation data are measured in irregular time intervals. Instead of testing the distribution of the degradation data, the first-passage time distribution is used to derive the test statistics. The empirical distribution of the first-passage time is estimated using the empirical saddlepoint approximation method. Monte Carlo simulation studies are performed to assess the Type-I error rates and statistical power of the proposed statistical testing procedures. Furthermore, the effectiveness and practical applicability of the proposed goodness-of-fit tests are demonstrated using real-world experimental degradation data.</p>