In a recent article on this blog site we looked at how Ishikawa diagrams can be used to represent the causal drivers or factors for risk. However, these schematics lack the statistical models necessary for quantifying which factors are contributing most to the top event.

Perhaps one of the biggest problems with all causal analysis techniques are the conclusions that risk analysts draw from their assumptions, yet they often fail to test these postulations. In this blog we are going to look at how causal factors in a Bowtie or Ishikawa diagram can be investigated by "adding-in" the relevant statistical models. Our aim here is to identify which factors contribute most to a top event by considering both their frequency of occurrence as a driver but also how each variable intertwines and correlates in a network of factors to spawn an outcome.

Perhaps one of the biggest problems with all causal analysis techniques are the conclusions that risk analysts draw from their assumptions, yet they often fail to test these postulations. In this blog we are going to look at how causal factors in a Bowtie or Ishikawa diagram can be investigated by "adding-in" the relevant statistical models. Our aim here is to identify which factors contribute most to a top event by considering both their frequency of occurrence as a driver but also how each variable intertwines and correlates in a network of factors to spawn an outcome.

**Ishikawa Diagram Recap**

Just to recap on our previous article, let's briefly look at the Ishikawa diagram we originally created and that entire Ishikawa article can be found here [ LINK ].

Example Fire Ishikawa Diagram | Causal Capital - Link

The question which we want to answer is: Which causal factors are the most serious concern for a risk analyst and which drivers are contributing to the majority of fires in warehouses?

Contribution to the top event (our fire) could be measured in many ways but in this case we are trying to identify; When there was a fire was a specific factor present ... That is easy to measure and the recommended ISO 31010 Pareto Analysis is often used to capture the commonalty of factors.

What is more complex to understand is that a factor such as 'combustant' may not actually be a serious hazard if there is a control in use like 'material handling'. So then, just looking at whether factors are present or not when a top event occurs is simply not enough. What we also have to understand is how each factor is adding positively or negatively to the top event and how it is being offset by other variables across the entire causal framework.

**Partial Least Squares Paths**

There are many ways this analysis could be carried out but we are going to select Partial Least Squares Path Dependency or PLS-PM modeling to perform this test. Partial Least Squares Path modelling is a statistical analysis that allows us to investigate the multiple relationships between different sets of variables or risk factors in this case and in a regressive bi-linear manner.

Nature of key risk indicators / factors | Causal Capital

PLS regression is particularly suited when the matrix of predictors has more variables than observations, and when there is multicollinearity among X values. By contrast, standard regression will fail in these cases.

Definition of Partial Least Squares | Wikipedia - Link

Operational risk is one of these risk disciplines that seems to have predictors with more variables than observations. We can also probably guess that our fire example above is going to be a multicollinear event.

Now the good news for us is that R-Project has a special library for PLS-PM modelling which we can use to investigate the properties of our fire event case study.

We have to create an inner model of outcomes to risk events which are the main categories of the Ishikawa diagram. There is also an outer model where the variables linked under each branch of the Ishikawa diagram are connected to the outcomes of the top event. In the end, what we are trying to quantify is how A1, A2, A3 (Hazards) and A4, A5, A6 (Controls) lead to S1, S2, S3, S4 (Measures of fire).

Formative, Reflective and Inner Models | PLS-PM R-Library

Now the good news for us is that R-Project has a special library for PLS-PM modelling which we can use to investigate the properties of our fire event case study.

We have to create an inner model of outcomes to risk events which are the main categories of the Ishikawa diagram. There is also an outer model where the variables linked under each branch of the Ishikawa diagram are connected to the outcomes of the top event. In the end, what we are trying to quantify is how A1, A2, A3 (Hazards) and A4, A5, A6 (Controls) lead to S1, S2, S3, S4 (Measures of fire).

**PLS-PM Fire Example**

There are a few steps we need to progress through to carryout our analysis of the 'A' to the 'S' factors but we start off by rejigging our Ishikawa diagram into a PLS-PM map. This will allow us to interconnect the various factors or variables we are going to end up modeling.

The next step is to load the Key Risk Indicator factor data that we have identified from our original Ishikawa diagram into R-Project. We need to assign this data to the various nodes in the PLS-PM framework that we have just set up and then we can begin modelling.

Now we are ready to run the PLS-PM R-Project library function across all data loadings and against the internal model defined by our Ishikawa diagram. This has been translated into a new PLS-PM map and all the data factors are now loaded.

What the PLS-PM library report function will generate is a set of numbers ranging from -1 to +1 that indicates which factors are most prevalent for causing a fire. This takes in both the presence of a risk factor during a fire event and its 'multi-correlation' effects with other risk variables in the entire Ishikawa model. The larger the number as you move towards -1 or +1, the more implication the risk factor is having on producing the top event and consequently the more attention it should receive from a risk analyst.

The negative factors are shown in red as the effectiveness of a control, while the positive factors that cause an event are displayed in blue on the report. As we would expect, some factors are adding to the event while other factors are preventing it and some factors are combining in a network fashion to create outcomes only when other variables are present. Most importantly, being able to understand how all these causal factors are operating together, furnishes risk analysts with real knowledge on the causative nature of fires and how to treat them.

More information on the R-Project PLS-PM library can be found here at the following [LINK].

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