PPI Repository

Expected 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 belonging to a group of cases.

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

$$\frac{ \sum_{c \in \mathit{cases}(g)} \begin{cases} \mathit{LTAB}(c, a, b) & \text{if } \mathit{fi}(c, \mathit{a}, \mathit{b}) \neq \emptyset \\ 0 & \text{otherwise} \end{cases} }{ \sum_{c \in \mathit{cases}(g)} \begin{cases} 1 & \text{if } \mathit{fi}(c, \mathit{a}, \mathit{b}) \neq \emptyset \\ 0 & \text{otherwise} \end{cases} }$$ $\mathit{cases}(g)$: Set of all cases belonging to group $g$.

$\mathit{LTAB}(c, a, b)$: Lead time between activity $a$ and activity $b$ within case $c$.
$\mathit{fi}(c, \mathit{a}, \mathit{b})$: Function that returns the flow instance between $a$ and $b$ in case $c$. If empty, the pair $(a, b)$ does not occur in $c$.