PPI Repository

Expected total elapsed time between the earliest event and the earliest instantiation of a specific activity in a case belonging to a group of cases.

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

Minimizing lead time is desirable.

act
actinst
case
time
type

Formula for practitioners

$\displaystyle \frac{\sum_{c \in g} \begin{cases} \mathit{LTtA}(c, \mathit{a}) & \mathit{if \ } \mathit{fi}\mathit{^{c}}(c, \mathit{a}) \neq \emptyset \\ 0 & \mathit{if \ } \mathit{fi}\mathit{^{c}}(c, \mathit{a}) = \emptyset \end{cases}} { \sum_{c \in \mathit{cases}(g)} \begin{cases} 1 & \text{if } \mathit{fi}\mathit{^{c}}(c, \mathit{a}) \neq \emptyset \\ 0 & \text{otherwise} \end{cases} }$

$\mathit{LTtA}(c, \mathit{a})$ returns the lead time from the start of case $c$ to the first completed instance of activity $\mathit{a}$ in case $c$.
$\mathit{fi}\mathit{^{c}}(c, \mathit{a})$ returns the set of first completed instances of activity $\mathit{a}$ in case $c$.
$\left| \{ c \in g \mid \mathit{fi}\mathit{^{c}}(c, \mathit{a}) \neq \emptyset \} \right|$ returns the number of cases in group $g$ where activity $\mathit{a}$ occurs at least once (i.e., cases with a non-empty $\mathit{fi}\mathit{^{c}}(c, \mathit{a})$).