# A Statistical Approach to Discovering Process Regime Shifts and Their Determinants
## 1 Introduction
Formally, we thus translate our aim in this work to the following three linked research questions:  
1. Are there any regime shifts in the process output? 2. What are the potential determinants that may have affected the regime change? 3. What role do these potential determinants play in forming these regimes? We propose a novel algorithm that addresses the above questions in a stepwise fashion. Before discussing it in detail, we first refer to a common process modeling framework, which allows translating different process views to a commonly agreed model, which is then used in regime shift analysis. This framework, which is theoretically grounded, well-defined and applicable to most process scenarios, is borrowed from the recent process modeling literature [20], and it is briefly discussed in Section 3.1. Once a process is mapped to a model, the algorithm's first step defines its modeling basis, referring to the aspect of the process output being analyzed. For example, in a particular manufacturing process, the production line analyst may be interested in the  
Figure 1: Examples of process regime shifts in (**a**) level and (**b**) trend of the output event log time series data. output _levels_. In contrast, the quality control analyst may look to find any systematic _trend_ (positive or negative) in a quality characteristic. These two distinct aims can be captured via respective _level_ and _trend_ regression modeling bases. Once a statistical modeling basis is agreed upon, it is then used with the output event log time series data to test for any regime changes. Since, at this stage, we are concerned only with discovering all regime shifts, this model basis is kept to its minimal form, i.e., the level model has the intercept term only, and the trend model has an intercept and a proxy _time-index_ term capturing any trend element in the data. Since there are no explicit variables for any determinants in this form, it allows unearthing maximum regime shifts. Once all regime shifts are discovered, the methodology addresses the second question: identifying potential process determinants. This question is mainly dealt with at the modeling stage mentioned earlier, in which a process model is built to identify any related elements. As these determinants are found, relevant time series data from event logs are further gathered. A key aspect to note here is that a track of changes in these determinants on the timeline is needed, which can then be used in the next phase to statistically link any change in the process output to a change in a particular determinant. The rest of the methodology deals with statistically relating changes in determinants to regime shifts in process output data (the third question). The idea is to sequentially introduce determinants as independent variables to the base model, one at a time. The introduction sequence is based on the first appearance of change on the timeline in these determinants. Each time a determinant variable is introduced, the revised model is statistically fitted and tested again for regime shifts. If the statistical tests now fail to recognize a regime shift discovered in the first stage, we deduce that this determinant played a causal role in forming this shift. This step is repeated until all potential determinants are introduced and tested. Finally, the fitted models can then be analyzed for their significance or impact on the process output. It is also easy to see that this approach can be used in conformance analysis when a determinant is intentionally adjusted for a potential enhancement. To demonstrate the merits of our proposed approach, we use three case studies from processes in manufacturing, commodity price generation and road traffic safety analysis. These cases vary significantly in terms of their technical, socio-economic and socio-technical nature and their levels of complexity. The results indicate regime shifts in all cases, with varying relationship structures with their respective determinants.