*3.6. Data Driven Analysis for Quantitative Data: Risk Profile Analysis*

The risk-profile analysis in facilities management can be defined as the assessment of the inoperability of building equipments. A study conducted the severity analysis of Indian coal mine accidents with the historical data of 100 years with Weibull and Exponential distributions for evaluating hazard rate functions; whereas Poisson and Negative Binomial distributions for risk profiles of mine accidents [38]. To compare which distribution fits best to the data, a recent study analyzed the robustness of different methods of comparing fitted distributions such as AIC (Akaike Information Criterion), BIC (Bayesian Information Criterion), LRT (log-likelihood ration test), etc. [39]. AIC and BIC measure the performance of the models based on their complexity. AIC is a prediction error estimator which prevents overfitting of data whereas BIC penalizes the model more based on the number of parameters. While comparing the AIC and BIC, lower scores are preferred and both information criteria are used for appropriate model selection, and it can also be used for distribution

selection [39]. The Negative Binomial (NB) distribution for a discrete random variable (X) can be calculated based on Equation (2) [40]:

$$P(X=x|r,p) = \binom{x-1}{r-1} p^r.(1-p)^{x-r}.\tag{2}$$

where *x* = *r*, *r* + 1, ... , *p* refers to the independent Bernoulli trials, *r* is a fixed integer. From Equation (1), it can be said that X follows NB distribution at which *r*th success occurs. The parameters of NB fit are denoted by the number of successes (*r*) and event probability (*p*).

In this study, survival function risk profiles were developed to identify the high probability of getting a UPM work order at the subsystem level. Risk-profile consists of three steps: (1) Data mining, (2) Distribution fitting, and (3) Generation of the survival function risk-profiles. The data mining (1) is to select the appropriate data points from the raw data. The distribution fitting (2) is to find appropriate probability distributions by calculating AIC and BIC scores. The last step is generation of the survival function riskprofiles (3) where, the top three systems (HVAC, electrical, and plumbing from Figure 10) with their respective subsystems (e.g., heating, cooling, distribution, etc. for HVAC), identified to distinguish the risks in the UPM. As a result, Table 5 shows the comparison of distribution fits for the systems and subsystems based on AIC & BIC scores. The distribution fitting and comparisons were performed using R-programming.

**Table 5.** Goodness-of-fit of distributions for systems and subsystems.


Table 5 shows that NB distribution fits the data best based on lower AIC & BIC scores. The table also shows the NB fit parameters (*r* and *p*) which were used to generate the risk profiles of the individual systems as well as their subsystems. Figure 11 illustrate the results of the survival function risk profiles for HVAC, plumbing, and electrical systems.

The risk-profiles are presented in Figure 11 where the *x*-axis represents the number of work order occurrences in a year for a building and *y*-axis represents the probability of inoperability. The probability of inoperability refers to all the occurrences which hindered the operation of the building elements. The probabilities for each occurrence were calculated for the *x*-axis ranging from 1 to 100. Each plot represents the probability of all major subsystems of a respective system with 850 data points of the top 25 buildings with most UPM work orders were identified for each of the eight universities for 2 to 5 years. As can

be seen from Figure 11a, the controls & instrumentation resulted in highest inoperability probability as HVAC control panel, airflow and thermostat adjustment requests are very frequent in a building. Distribution systems resulted in the second most work order generating subsystem with repair requests as it is comprised of components like air handlers, fans, filters, ventilation, etc. Terminal & package units and heat generation systems were found to generate moderate number of MR&R requests with cooling generation systems being the lowest probability of generating UPM work orders. In Figure 11b, plumbing fixtures resulted in the highest probability of inoperability in plumbing systems. The key components in fixtures are sink, toilet, shower, bathtub, etc. Domestic water distribution being the second most prone subsystem followed by sanitary waste. Rain water drainage and other plumbing systems resulted in low inoperability probability. Additionally, Figure 11c illustrates that lighting and branch wiring subsystem dominated the system in terms of inoperability in electrical systems. Communications and security being moderate in terms of work order requests followed by electrical service and distributions. Other electrical system was found to be negligible in terms of UPM work order requests.

**Figure 11.** *Cont*.

**Figure 11.** Survival Function Risk Profile for UPM Work Orders: (**a**) HVAC; (**b**) Plumbing; and (**c**) Electrical.

Interestingly enough, the HVAC work consisted of mostly controls and distribution systems work orders where controls and instrumentation having only 4 components (control panel, thermostat, digital controls, and meters) generated adjustment work orders in majority while distribution system generated more MR&R activities having more diverse components. On the other hand, plumbing work was dominated by plumbing fixtures and electrical work primarily consisted of lighting and branch wiring work orders. Considering the fact that universities spend a great deal of resources doing PPM work in fire protection which benefited the FM in reducing UPM work significantly but failed to do the same for other major systems. Therefore, the proposed diverse analyses, including a statistical analysis and a risk-profile analysis, are necessary to acknowledge the current status of the facility management from different angles.

Additionally, the outlier analysis allowed for understanding which building elements require careful consideration when planning PPM work. Out of the top 25 UPM buildings selected, the outliers from the HVAC system included the exhaust fan, air-conditioner, unit heater, fan, and thermostat (temperature issues). Similarly, the top components having the higher risk for generating electrical work orders involved the light fixtures, circuit breaker, smoke detector, and receptacle. The top outliers for plumbing systems were found to be toilet & stall, sink, urinals, floor drains, and shower. Table 6 presents the components recorded for over 100 number of occurrences generated for a building in a year.

As shown in Table 6, thermostat adjustments and issues recorded the highest number of workorder for a university in a year. This is one of the most requested facility operations in the buildings. For HVAC, air conditioners, air handlers, and radiators also generate high work order numbers. For electrical, light changing requests are frequent and changing of batteries in equipments seems more like routine requests. For Plumbing, sink and toilet repair requests are the most common request followed by the bathtub and shower enclosure. As a result, the outlier analysis helps facility managers (1) recognize the components registering more than 100 work orders in MR&R, and (2) to prepare budget allocation for facility management.


**Table 6.** Outlier components for UPM.

### **4. Discussion and Conclusions**

This study attempted to analyze the current trend and status of Facility Management (FM) practice at higher education institutions by proposing (1) the Facility Management Unified Classification Database (FMUCD), and (2) the systematic data-driven analyses: survey questionnaires and phone interviews, Natural Language Process (NLP) approaches, statistical analysis, risk-profile analysis, and outlier analysis.

The current trends and status of PPM at universities were mainly identified from the survey, phone interview, and statistical comparison analysis. The survey revealed that the progress of the PPM work was mostly monitored based on the Computer Maintenance Management System (CMMS) reports and four factors (work, set-up, clean-up, and documentation) were critical for the PPM estimates. Analyzing interview results suggested that schedule maintenance and PPM were two major organized maintenance plans at universities. At this stage, the application of NLP approaches found that the focus of the interview was on PPM, supported by the positive sentiment scores. From the statistical analysis, it was revealed that although PPM work order count increased over the years, UPM work orders remains consistent. Therefore, such a finding will be applied to be a guideline for facility managers or decision makers to allocate budgets for PPM and UPM; the budget of the UPM can be similar to the last year while, the budget of the PPM can be increased according to the budget flexibility. Additionally, HVAC was identified as the most significant system resulting in the highest number of work orders and labor hours every year in both PPM and UPM.

Findings related to UPM were mostly derived from risk-profile analysis and outlier analysis. At the system level, the main trades were HVAC, electrical, and plumbing which generated higher work orders and labor hours. Especially, while distribution systems and controls & instrumentation in HVAC were found to generate the maximum number of UPM work orders, lighting and branch wirings and communication & security for electrical, and plumbing fixtures in plumbing systems were identified as a major proportion of UPM work. Therefore, the proposed FMUCD and the results of the data-driven analyses will provide guidelines and best practices for the facility management to make an appropriate decision in an uncertain situation at higher education institutions. Moreover, the broader impact of this research is that it would help stakeholders of any campus-sized institution to develop, operate, maintain, upgrade, and disperse their assets in a cost-effective manner.

**Author Contributions:** Conceptualization, S.Y., T.J.W., M.H.; Methodology, A.K.P., S.Y., T.J.W. and J.J.; Software, A.K.P., J.J.; Validation, A.K.P., S.Y., J.J. and M.H.; Formal Analysis, A.K.P., S.Y., J.J. and T.J.W.; Investigation, T.J.W., S.Y., J.J. and M.H.; Resources, S.Y., T.J.W. and M.H.; Data Curation, S.Y. and T.J.W.; Writing—Original Draft Preparation, A.K.P., S.Y., T.J.W. and J.J.; Writing—Review and Editing, A.K.P., S.Y., T.J.W. and J.J.; Visualization, A.K.P., S.Y.; Supervision, S.Y., T.J.W. and M.H.; Project Administration, S.Y., T.J.W. and M.H.; Funding Acquisition, S.Y., T.J.W. and M.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

#### **References**

