Cramer-Von Mises Test for Power-Law Process Model

Both the minimal repair process and the AMSAA (Reliability growth) model assume a non-homogeneous Poisson process based on the power-law formula. This model allows for the application of statistical techniques such as the calculation of the maximum likelihood estimators (MLE), confidence intervals, and the Cramer-von-Mises test statistic for goodness of fit. To determine whether the non-homogeneous Poisson process is a more appropriate model than the constant failure rate model (Homogeneous Poisson Process), a trend test on the failure times is performed. For the intensity function,

ρ (t) = abt^{b - 1} and the hypotheses tested are :

H₀ : The intensity function is constant (b = 1).

H₁ : The intensity function is not constant (b ≠ 1). The Test statistic is computed from the expression

                             χ²  = 2n / bˆ     

Where  n = number of failures, and

b = MLE for the growth of deterioration rate.