Statistical Details for the Repeated Measures Degradation Platform
The repeated measures degradation model can be expressed as follows:
where:
h is the transformation for the Y variable
g is the transformation for the time variable
μ is a function of the parameter vector θ, the time t, and the option explanatory variable X
θ is a vector of parameters
i indicates the unit ID
t indicates the timestamp of the measurement
X is an optional explanatory variable
the error term εit are independent and identically distributed as N( 0, σε ).
Note: Some of the θ parameters are fixed, such that they are unknown but do not vary from unit to unit. Other parameters in θ are random parameters, such that they vary from unit to unit. The random parameters can follow a normal or lognormal distribution.
The residuals are computed on the transformed Y scale: h(Y) - μ.