PPI Repository

Total elapsed time between the earliest instantiation of a specific activity and the earliest instantiation of another specific activity that occurs after the former one in a case.

Event log is associated with a process in which the total elapsed time of a specific subprocess is of relevance.

Minimizing lead time is desirable.

act
actinst
case
time
type

Formula for practitioners

$\begin{cases} \mathit{lt}(x,y) & \mathit{for~any \ } x \in \mathit{fi}\mathit{^{s}}(c, \mathit{a}) \mathit{\ and \ } y \in \mathit{fi}(c, \mathit{a}, \mathit{b}) \\ undefined & \mathit{if \ } \mathit{fi}(c, \mathit{a}, \mathit{b}) = \emptyset \end{cases}$

$\mathit{fi}\mathit{^{s}}(c, \mathit{a})$ returns the set of first started instances of activity $\mathit{a}$ in case $c$.
$\mathit{fi}(c, \mathit{a}, \mathit{b})$ returns the first instance of activity $\mathit{b}$ occurring after the first started instance of activity $\mathit{a}$ in case $c$.
$\mathit{lt}(x,y)$ returns the lead time between activity instances $x$ and $y$.