PPI Repository

Service Time from activity A to activity B

\mathit{STAB}\mathit{^{\times}}(c, \mathit{a}, \mathit{b})

\mathit{\times} \in \{\mathit{s}, \mathit{c}, \mathit{sc}, \mathit{w}\}

Dimension:

Time

Granularity:

Case

Description

Sum of elapsed time between the start and complete events of all activity instances of a case, which occur between the earliest instantiation of a specific activity, and the earliest instantiation of another specific activity that occurs after the former one, including both.

Potential use

Event log is associated with a process in which the actual time spent executing a specific subprocess is of relevance.

Assumptions

Minimizing service time is desirable.

Desired Value:

MINIMIZE

Required attributes

act
actinst
case
time
type

Equations

Formula for practitioners

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

$\mathit{st}$ returns the service time between activity instance $x$ and activity instance $y$ .
$\mathit{fi}\mathit{^{s}}$ returns the set of first started instances of activity $\mathit{a}$ in case $c$ .
$\mathit{fi}$ returns the set of first instances of activity $\mathit{b}$ that occur after the first instance of $\mathit{a}$ in case $c$ .

Formal Definition

$\begin{cases} \mathit{st}\mathit{^{\times}}(x, y) & \mathit{for~any \ } x \in \mathit{fi}\mathit{^{s}}(c, \mathit{a}) \mathit{\ and \ } y \in \mathit{fi}\mathit{^{sc}}(c, \mathit{a}, \mathit{b}) \\ \bot & \mathit{if \ } \mathit{fi}\mathit{^{sc}}(c, \mathit{a}, \mathit{b}) = \emptyset \end{cases}$
The $\mathit{\times}$ indicates that the PPI can take multiple forms, in this case, $\mathit{\times} \in \{\mathit{s}, \mathit{c}, \mathit{sc}, \mathit{w}\}$ . If $\mathit{\times} = \mathit{s}$ , then the function considers activity instances that were started within the start and end activity instances, i.e., it uses $\mathit{st}\mathit{^{s}}$ ; if $\mathit{\times} = \mathit{c}$ , then the function considers activity instances that were completed within the start and end activity instances, i.e., it uses $\mathit{st}\mathit{^{c}}$ ; if $\mathit{\times} = \mathit{sc}$ , then the function considers activity instances that were either started or completed within the start and end activity instances, i.e., it uses $\mathit{st}\mathit{^{sc}}$ ; if $\mathit{\times} = \mathit{^{w}}$ , then the function considers all activity instances that were active within the start and end activity instances, i.e., it uses $\mathit{st}\mathit{^{w}}$ .

Python implementation

This indicator is implemented in the process_performance_indicators Python library.

process_performance_indicators.indicators.time.cases.service_time_from_activity_a_to_b

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