A novel global health index framework for asset prognostics and health management in the oil and gas industry

Abstract

The oil and gas industry must remain efficient and flexible to navigate shifting market uncertainties in an era of increasing global energy demand. Ensuring the reliability and availability of oil and gas production systems is vital for meeting supply requirements at optimal cost and sustainability. Comprehensive engineering Prognostics and Health Management (PHM) approaches can significantly support these objectives. This paper introduces a novel Global Health Index (GHI) for monitoring and benchmarking production system health, serving as a foundation for big data to advance artificial intelligence and machine learning applications. The proposed GHI captures system-wide health requirements by integrating descriptive, diagnostic, predictive, and prescriptive analytics within the PHM framework. A hierarchical structure organizes sub-indices into units, systems, pillars, elements, and parameters, enabling an explicit decomposition of complex production systems. Six adaptable indicators quantify health and guide proactive management strategies at the parameter level. This comprehensive yet practical benchmark indicator provides real-time health monitoring and data-driven decision-making, enhancing system availability and efficiency. By identifying emerging issues and guiding timely interventions, the GHI improves reliability and supports sustainable growth in the oil and gas sector.

Introduction

Driven by the imperatives of a growing global economy, the energy sector is evolving rapidly, requiring the oil and gas industry to be efficient and agile in the face of market uncertainties. In this environment, the reliability and availability of oil and gas production systems are critical for meeting demand optimally and sustainably. Comprehensive engineering solutions in Prognostics and Health Management (PHM) support achieving these goals.

Recent research highlights a diverse evolution in PHM methodologies across multiple industries. Integrating advanced data analytics, ontological modeling, and digital twin technologies is paving the way for proactive, data-driven strategies that improve reliability and cost-effectiveness in today’s complex industrial settings. For example,¹ propose a technical language processing framework that leverages natural language processing to extract and analyze maintenance work orders, enhancing fault detection and predictive maintenance in aviation. Addressing the challenge of limited data,² review minor data issues in PHM and explore techniques such as data augmentation, transfer learning, and few-shot learning to improve model robustness even when data are scarce, imbalanced, or noisy. Similarly,³ develop an ontological framework that standardizes multi-attribute criticality analysis, enabling consistent asset prioritization and more effective maintenance planning across dispersed facilities. ⁴ further contribute by reviewing PHM methods for induction machines, comparing expert, physics-based, and machine-learning approaches for diagnostics and predicting remaining useful life.

In a complementary effort,⁵ introduce a novel PHM framework that extracts comprehensive system health data, forming a robust foundation for health quantification through indexing, a methodology adopted in this study. This novel PHM framework (See Fig. 1) motivates us to develop a new Global Health Index (GHI), which is inherently dynamic, evolving continuously as real-time data is fed into a monitoring system. The framework pillars offer detailed health indicators, including health requirement extraction, which identify potential failures and the root causes of downtime factors or parameters.

Fig. 1.

Alfahdi et al.⁵ PHM Framework.

Despite the progress made in developing health indices for production systems, existing models exhibit significant limitations when applied to complex, interdependent assets. Many previous approaches fail to provide a comprehensive, interpretable, scalable, and proactive assessment of system health, often focusing solely on component-level sensor data or static measurements. While some methods are quantitative and predictive, they lack the flexibility to capture the full context of system performance, address underlying causes of downtime, or serve as a benchmarkable and customizable tool for management decision-making. Furthermore, the absence of transparent, descriptive, and prescriptive capabilities in most models limits their practical applicability and constrains proactive maintenance planning.

These gaps underscore the need for a hierarchical, multi-level GHI framework that integrates diverse indicators including operational, process, maintenance, and human factors, while remaining dynamic, robust, and actionable. By addressing these deficiencies, the proposed approach enables a comprehensive and practical measurement of system health, supporting predictive, proactive, and data-driven decision-making across complex industrial environments.

Furthermore, the proposed GHI supports predictive operations by forewarning operators about potential failures before they occur. It offers a holistic view at the asset level and a broader perspective on plant, unit, or system health by incorporating both correlational and non-correlational factors. Moreover, the index must be customized to reflect different assets’ unique characteristics and operational demands. However, combining these diverse element types introduces complexity, requiring careful design and ongoing monitoring to ensure efficiency, as demonstrated in this study.

A comprehensive approach to quantifying the GHI involves developing a robust mathematical algorithm that integrates multiple characteristics. This study aims to obtain the GHI that accurately represents the system’s overall health, leveraging reliability and asset management expertise. This process must address issues such as redundancy and skewness by carefully selecting elements, allocating appropriate weights, and applying correlation analysis, normalization, and outlier detection to remove redundancies.

Beyond technical formulation, the proposed GHI also serves as a benchmark for top management reporting. It provides stakeholders with a complete view of plant or system health from the perspective of the PHM framework, which currently has a gap in industrial practices. It establishes a baseline for continuous improvement in efficiency and safety. In addition, the GHI estimation is derived from a detailed analysis of various indicators that support a proactive approach. This approach minimizes failures and reduces downtime while accelerating the digital transformation journey in the industry through enhanced data utilization, which may benefit future Artificial Intelligence (AI) applications.

This paper presents a novel GHI for complex production system health monitoring and benchmarking. As foundation data for future AI and Machine Learning (ML) applications, the proposed GHI integrates descriptive, diagnostic, predictive, and prescriptive analytics within a PHM framework to capture system-wide health requirements.

The paper is organized as follows: the Literature Review surveys related work on Health Index (HI) development; the Global Health Index Adaptation section details the method used for index adaptation; the Health Index Comparison section outlines the differences between the proposed GHI and other HI adaptations in similar contexts; and finally, the Conclusion offers suggestions for future research.

Literature review

The literature presents multiple perspectives on health indices across various disciplines⁶ define an HI as a tool that processes data about an asset’s condition. In contrast⁷ relate HI to the health condition of engineering assets to condition monitoring data⁸ describe HI as a pragmatic approach that integrates multiple information sources into a consistent indicator for asset management, and⁹ combine operating observations, field inspections, and laboratory test results into an objective, quantitative index. In each case, extensive data, guidelines, and expert knowledge are compressed into a single value that facilitates decision-making.

The literature also reveals considerable variability in the scales used for HI measurement. Some studies, such as those by⁹, employ scales ranging from 1 to 10 (with 1 indicating good condition and 10 indicating poor), while others use a 0-to-1 scale where higher scores represent better health. Depending on the application, additional scales include ranges from 0 to 100 or other segmented values. This diversity underscores the necessity for careful standardization and justification of the chosen range, as these definitions directly influence the preventive actions taken.

The justification for developing an HI is multifaceted. In a comprehensive PHM context, it is crucial to provide technical and economic justification for engineering decisions and spending plans, prioritize assets with high business risk, and reduce maintenance costs⁹. Furthermore, an effective HI is critical for scheduling in manufacturing facilities¹⁰ and supports a systems approach that integrates technical, organizational, and social aspects¹¹. The maturity of HI adoption is often classified into stages: reactive (no HI used), controlled, proactive (consistent HI application across similar assets), and ultimately predictive, which encompasses descriptive, diagnostic, predictive, and prescriptive analytics.

Despite these advancements, several limitations persist. Many scoring and ranking techniques vary according to expert judgment and facility-specific conditions, leading to discrepancies even when the same equations are applied. Researchers have explored the Analytic Hierarchy Process (AHP), fuzzy logic, Bayesian methods, and decision trees to address these challenges. Discontinuities in HI scores have also been mitigated using smoothing techniques.

Several methods have been employed in the literature to calculate HI.¹² developed an aircraft HI by reconstructing original data, while⁷ employed a linearly weighted summation approach for a planetary gearbox, measuring performance using the Root Mean Squared Error (RMSE).¹³ formulated an inherent safety and HI based on hazard scores.⁸ proposed a probabilistic HI for transformers using logic failure models combined with scoring and weight factors.¹⁴ introduced an ocean HI for marine renewable energy by combining 25 indicators into a weighted sum. Other studies have included quantified scoring and weighting for power transformers¹⁵, fuzzy methods for HI extraction^11,16,17, and an electromechanical behavior analysis approach¹⁸ that calculates HI based on damage signal gradients during tensile testing. ¹⁹ explored statistical measures such as crest factor, kurtosis, skewness, and quadratic mean for bearing degradation, while⁶ recommended calculating HI as an average of standardized parameters weighted by international guidelines. ²⁰ advanced this work by combining a fuzzy analytic hierarchy process with convolutional neural networks to quantify machine degradation. Additional approaches include the arithmetic mean model by²¹, reliability assessments by²², anomaly detection in oil refineries by²³, and an air quality HI proposed by²⁴, which sums excess risks from single-pollutant models.

In addition²⁵ conducted a case study on improving safety and performance in oil refineries by installing an active redundant cooler in a Hydrocracker Unit (HCU) and assessing risks using FMEA to prioritize critical components based on their Risk Priority Number (RPN). ²⁶ developed a methodology using structural modeling, digraph models, and matrix methods to evaluate and analyze failures in mechatronics-based production systems, proposing a failure index to assess reliability and identify weak areas for improvement. ²⁷ proposed a performability index for biogas plants using graph theory and matrix methods, integrating factors like reliability, maintainability, safety, quality, and sustainability. Their study emphasizes interdependencies to ensure dependable and sustainable biogas plant operations throughout its lifecycle.

Each of these studies advances the evolving landscape of HI development by showcasing the diversity of methodologies and the inherent challenges of standardization. Notably, the primary gap identified is the lack of a comprehensive measure of system health within a manufacturing plant using the PHM framework comprehensively, a gap that our study aims to address.

Global health index adaptation

Figure 2 illustrates the GHI concept by breaking it into input, mathematical algorithm, and output. The input is based on the PHM framework proposed by⁵, which comprises 12 pillars and their respective elements. The algorithm quantifies the GHI using traditional methods that advanced AI and ML techniques could eventually enhance. Finally, the output translates the GHI into actionable steps mapped to a specific range, ensuring that preventive measures are prioritized appropriately, given limited resources.

Fig. 2.

The Three Components of the GHI Concept.

The proposed adaptation delivers the GHI, comprehensively reflecting a production plant’s overall condition and the health of its individual systems. GHI enables proactive measures to minimize failures, reduce unplanned downtime, and support root cause monitoring within the PHM framework. Figure 2 illustrates the three components of the GHI concept we follow: the input, based on the PHM framework, and the algorithm that supports the output stage, which involves quantifying health by indexing, monitoring, and making decisions. However, developing a robust GHI requires careful consideration of several key properties, as detailed in Table 1, which lists 22 descriptive attributes of the proposed index.

Table 1.

Properties of GHI Development.

Properties	Description
Comprehensive	Using the PHM framework, we encapsulate multiple parameters contributing to the manufacturing system’s health, providing a holistic view of its condition
Practical	Entire proposed methodology to extract the parameter to be considered in PHM is bringing the GHI practical to be applied, at least in the oil and gas sector
Quantitative	The GHI provides a numerical value or score with different level breakdowns, enabling quantitative comparisons and trend analyses over time. A scale from 1 to 0, where heading to 1 means good health and heading to 0 bad health
Normalized	The GHI is normalized to a standard scale (0 to 1) to facilitate comparisons across different pillars/systems/units
Dynamic	The GHI is responsive to changes in the parameters it monitors, reflecting the real-time or near-real-time health of the manufacturing facility
Objective	While expert judgment is used in its design (from a pillar point of view), the index operates objectively from the elements level, relying on measurable and real status data rather than subjective assessments
Reproducible	Proposed GHI is consistent. The GHI produces consistent results when given the same input conditions and data set
Interpretable	Proposed index is designed so end-users can easily interpret the GHI’s value or score. A clear understanding of what constitutes a “good” or “bad” score is clear. Monotonic: A worse GHI condition means an urgent condition
Scalable	Proposed methodology of the GHI is scalable to different assets or systems, allowing for broad applicability
Predictive	Proposed GHI is well-designed to have predictive capabilities, helping end-users anticipate potential issues before they are apparent. The predictive is applicable only specifically to the pillars that use associated time series data of sensors, where the feature can be extracted from correlated elements and be part of the GHI
Customizable	Because of the nature of the oil and gas sector asset and the industry’s demands, proposed GHI has room for customization in design
Reliable	Proposed GHI is reliable and consistently accurately represents the system’s health
Transparent	The methodology and algorithm used to calculate the GHI are transparent, allowing for validation, verification, and trust
Sensitive	Proposed GHI is sensitive enough to detect even minor changes in the system condition, allowing for early interventions if needed with six levels of sub-indices
Benchmarkable	Proposed comprehensive GHI allows comparisons against industry standards, enabling organizations to assess how their assets fare against competitors or best practices. We can consider this as a new benchmarked scale
Matured	Proposed GHI advances PHM maturity
Proactive	Support end-users to be more proactive to prevent failures and downtime
Descriptive	The analytics procedure is descriptive when extracting the parameters from PHM framework elements
Diagnostic	The analytics procedure is diagnostic when extracting the parameters from PHM framework elements
Prescriptive	The analytics procedure is prescriptive when extracting the parameters from PHM framework elements
Auditable	GHI tracks back to Level 6 elements input related tags/equipment using sub-indices
Robust	Proposed GHI is influential in optimizing resources in decisions and planning through recommended actions

The GHI is comprehensive, employing the PHM framework to integrate multiple parameters that provide a holistic view of the system’s condition. It is practical, offering a complete methodology for extracting PHM parameters and applying the GHI, particularly in the oil and gas sector. The GHI is quantitative, expressed as a numerical score that can be broken down into various levels to facilitate trend analysis and comparisons over time, based on a scale from 0 (poor health) to 1 (good health). Additionally, it is normalized to a standard scale (0 to 1), ensuring consistent comparisons across different pillars, systems, or units. The GHI is also dynamic and responsive, updating in real-time (or near-real-time) to reflect changes in the monitored parameters. Although expert judgment informs its design at a higher, pillar-based level, the GHI operates objectively at the element level, relying on measurable, real-world data rather than subjective assessments.

Additionally, the GHI is reproducible and consistent, reliably producing the same results when provided with identical input conditions and data sets. Its design emphasizes interpretability, ensuring end-users can easily understand the score’s meaning and distinguish between “good” and “bad” conditions. The index is monotonic, so a declining GHI directly signals a more urgent situation. Its scalable methodology allows for application across various assets or systems, ensuring broad applicability. Moreover, the GHI is engineered with predictive capabilities, particularly for pillars that utilize time-series sensor data, enabling the extraction of features from correlated elements to foresee potential issues before they become evident. It is also customizable, catering to oil and gas assets’ unique nature and demands. Also, the GHI is reliable, consistently providing accurate and transparent representations of system health; the methodology and algorithms underpinning its calculation are fully transparent, facilitating rigorous validation, verification, and trust.

Furthermore, the proposed GHI is finely tuned to detect even subtle changes in system conditions, facilitated by six levels of sub-indices that enable early intervention. It is both benchmarkable and comprehensive, allowing organizations to compare their assets against industry standards and best practices, effectively establishing a new benchmark scale. By advancing PHM maturity, the GHI empowers end-users to take proactive steps to prevent failures and reduce downtime. Its analytics process incorporates descriptive, diagnostic, and prescriptive elements when extracting parameters from PHM framework components. Additionally, the GHI is fully auditable, with sub-indices tracing back to Level 6 inputs related to specific tags and equipment. Ultimately, it offers a robust framework for optimizing resource allocation in decision-making and planning.

So, the top GHI is an overall plant GHI, and to reach the highest hierarchy level of the plant, we need to have sub-indices that help us to deep dive into the individual health condition of each unit and its systems with their pillars and elements to components in the entire plant as follows, from bottom to top (Fig. 3):

• Level 1: Plant health, , obtained by aggregating the health indices of its units.

• Level 2: Unit health for unit , , obtained from the health indices of its systems.

• Level 3: System health for system within unit m, , obtained from its constituent pillars.

• Level 4: Pillar health for system , , obtained from its elements, where

  

• Level 5: Element health for element in system , , obtained from its multiple parameters.

• Level 6: Parameter health for parameter , , representing the normalized and standardized health condition of a single indicator.

Fig. 3.

Bottom-Up GHI.

presents a normalized value of the health condition of the parameter for the element and system at a time . Furthermore, is the number of units in a manufacturing plant . Figure 3 also shows the adaptation of Level 6 equations to estimate a parameter health index as an indicator, where presents the input value as the indicator input, and presents a reference to either the target or health boundary value.

Level 1 and 2 health indices

We aim to derive an overall plant GHI by aggregating sub-indices from individual plant units and systems. Fault Tree Analysis (FTA) is widely used for this purpose and has been successfully implemented in manufacturing, oil and gas, healthcare, aviation, and other industries. For instance⁸ employed FTA to estimate a plant’s HI, while²³ used it to determine the HI of power transformers. FTA is a systematic, deductive methodology that evaluates the potential causes of specific failure events within a system. Constructing a “fault tree” visually represents the logical combinations of healthy conditions that, in our case, highlight potential failure causes leading to downtime. Essentially, FTA works backward from a top-level HI that covers the overall plant, underperforming units, and systems to identify all possible contributing factors, as described in the PHM framework for each system.

Consequently, a lower level in FTA from the top is the system’s health indices , which are estimated to obtain the upper index of unit m , and ultimately a single value for the plant . Since FTA relies on multiplication, applying the product of health sub-indices to calculate the overall GHI is justified by several factors:

• Systematic Evaluation: Plants, units, and systems are assessed in a structured and deductive manner.

• Combined Influence: Multiplying variables mathematically captures their collective impact.

• Impact Representation: This approach illustrates how unhealthy conditions in individual units affect the entire plant.

• Logical Redundancy: The use of AND/OR gates models series and parallel relationships in engineering systems.

• Interdependent Indices: Multiplying sub-health indices expresses their interdependence.

• Sensitivity to Changes: The overall GHI is highly responsive to sub-individual variations.

The FTA-based aggregation was selected for its transparency, interpretability, and consistency with standard reliability block diagram logic. Compared with fuzzy inference systems or Bayesian belief networks, it offers a simpler and more scalable framework that requires fewer assumptions, minimal parameterization, and is directly aligned with real-world engineering reasoning.

Therefore, the estimate of a plant as a scale of health degradation/growth at a time mathematically, using FTA is an extension of Boolean algebra to calculate the GHI of the top system. Considering normalized values (0–1), the following equations are used to obtain :

“And” relation is given by

1

“Or” relation is given by

2

where is the health Index for the unit , and is the number of units in the plant . The same is used to estimate the units’ health indices using the systems’ health indices, using FTA.

“And” relation is given by

3

“Or” relation is given by

4

where is the health index of the system and the number of systems within the unit .

Level 3 and level 4 health indices

When analyzing Level 3, the health of system within unit , the objective is to estimate the system health, at a specific time () based on the PHM framework pillars. Each pillar represents a distinct aspect of the system’s health condition. Therefore, the goal is to evaluate the health status of the system pillars (Level 4) in order to derive the overall system health. The pillar health indices for the system , , describe the condition of each pillar at time . A pillar in a fully healthy state has a GHI value of 1, while a GHI value below 1 indicates degradation or an unhealthy condition:

5

where is the system GHI at time . is the value of the pillar GHI at time . The for each pillar, at a time can be presented as:

6

where represents the health index of element within a given pillar of the system . Accordingly, , representing the health index of each of the twelve pillars in system (as shown in Table 2) can be estimated using the FTA method as follows:

Table 2.

Weighting Pillars by AHP.

	Pillar	Pillar GHI	Weighting by AHP	System GHI
1	Asset Reliability (AR)		0.21
2	Continuous Improvement (CI)		0.13
3	Operating Condition (OC)		0.15
4	Weather & Environmental (EN)		0.09
5	Maintenance Management (MN)		0.08
6	Condition Monitoring Management (CM)		0.08
7	Asset Mechanical Integrity (MI)		0.07
8	Leadership Management (LS)		0.05
9	Physical Asset Management (AM)		0.04
10	Financial Factors (FI)		0.03
11	Process Safety Management (PS)		0.04
12	Human Reliability (HR)		0.03

“And” relation is given by

7

“Or” relation is given by

8

However, for certain pillars, the GHI relationship can alternatively be evaluated using a simple arithmetic mean, assuming equal weights (), as expressed by the following equation:

9

The overall health of system within unit , , is obtained by aggregating the pillar-level health indices. Although a simple average may be applied, certain pillars may have a higher influence on system performance. Therefore, a weighted aggregation is recommended. In the weighted average, some values contribute more than others based on their assigned weights. Hence, each pillar in a system can be considered with a non-equal contribution . These pillar weights can be determined through either data-driven or expert-based methods. Data-driven techniques, such as the Entropy Weight Method (EWM) or Principal Component Analysis (PCA), can objectively capture indicator variability and information content. In contrast, expert-based approaches, such as the Analytic Hierarchy Process (AHP), allow for the inclusion of domain knowledge when validated data are scarce. In this study, the AHP method is adopted as a demonstrative example to reflect expert insight and to illustrate the integration of weighting mechanisms within the GHI framework.

The weight ( coefficient) were obtained using AHP, which captures expert judgment through systematic pairwise comparisons of criteria. In this study, experts were asked to compare pairs of pillars and indicate which is more significant and to what extent, using a 9-point Likert scale ranging from (extreme importance of B over A) to (extreme importance of A over B). The twelve proposed pillars, representing potential root causes of failures and downtime, were thus evaluated in all possible pairs. A total of 11 field experts participated in the assessment. These experts were carefully selected as senior engineers and managers in the oil and gas sector, each with substantial experience in reliability, maintenance, and asset management. Their domain expertise ensured that the pairwise judgments were informed by practical and technical knowledge relevant to the intended application. Given the experts’ strong domain knowledge and shared contextual understanding of the industry, a panel of 11 experts is deemed sufficient for the AHP analysis for demonstration purposes.

To assess the consistency of expert judgments, both individual and group-level reliability measures were examined. At the group level, Kendall’s coefficient of concordance (W) was calculated to evaluate agreement among the eleven experts. The result indicates moderate agreement, and a chi-square test (with df = 11) confirms that this level of concordance is statistically significant at the 5% level . This demonstrates that the observed agreement among experts is unlikely to have occurred by chance.

At the individual level, the AHP pairwise comparison matrix yielded a Consistency Ratio (CR) of 0.144, indicating that expert judgments were largely coherent and within an acceptable range, though slightly above Saaty’s ideal threshold. This value represents a tolerable level of inconsistency, suggesting that the derived weights are reliable. Minor improvements in logical coherence could be achieved through a larger expert pool or iterative consensus refinement.

The weighted average equation can be denoted as follows:

10

where is the pillar number for the system .

Level 5 and level 6 health indices

The last two lower levels of these sub-indices are the elements extracted from the PHM framework analysis, including all parameters, and in general:

11

where presents a value of the health condition of the parameter in the pillar, and the element , for the system .

We suggest classifying the indicators of adaptation as sub-indices , which provides the flexibility to develop the GHI for each element based on the input data and the nature of the health condition we want to monitor or achieve. We divide the adaptation into six types as follows:

• Positive Direct Indicator (PDI)

• Negative Direct Indicator (NDI)

• Positive Compliance Indicator with target (PCI)

• Negative Compliance indicator with target (NCI)

• Resources Indicator with availability (REI)

• Range Indicator with and (RAI)

Figure 3 shows the equations used to obtain the indicator values as health indices. For the PDI indicator, the following equation is used to quantify the indicator from this type:

12

where is the actual input value. For the negative direct indicator NDI:

13

where is the actual compliance in percentage as an input value. For the positive compliance indicator PCI:

14

where is the target of the indicator, and is the actual input value. For the Negative Compliance indicator NCI:

15

where is the target of the indicator, and is the actual input value. For the Resources Indicator REI:

16

where is the total available resources, and is the total required resources as input. For the Range Indicators RAI:

17

where are the healthy condition boundaries, and is the actual input value of the indicator. However, the indexing presentation generally depends on the exact parameter condition scale. For example, if the actual value of the element is within the healthy condition limits (i.e., Design/Normal/Accepted conditions) , so the = 1 where is the lower limit and is the upper limit. Otherwise, it is considered unhealthy, then a drift value (scale) from the healthy condition is calculated as a parameter health index . If we have multiple parameters K in an element , , within a pillar, we need to normalize and standardize them (0–1).

Moreover, the health effects of the tags must be considered to obtain a combined GHI for that element. Hence, again, FTA is suitable for determining the relationship. It is considered an element with multiple tags that are systematically and functionally organized, providing a deductive approach from a health perspective. It presents the effect of such unhealthy conditions on the element from each tag to others. Mathematically, the result of multiplying variables indicates their combined influence. It can be presented as follows:

“And” relation is given by

18

“Or” relation is given by

19

where is a parameter health index, and is the number of parameters.

The algorithm updates each index as new data arrives, performing a fixed amount of computation at each update. For a plant containing units, each unit comprising at most systems, each system containing at most 12 pillars (as in the proposed framework), each pillar having at most elements, and each element containing at most parameters, the plant-level GHI at a single time instance can be calculated by performing a constant-time operation () for each parameter to compute its corresponding health index from monitored data. The resulting values are then aggregated up the hierarchy. In the worst case, the total number of calculations is proportional to , giving an overall time complexity of . Regarding space complexity, if only the current health indices are stored at each level, memory usage is proportional to the total number of parameters, i.e., . If historical values are retained for trend analysis or sensitivity studies, memory usage grows linearly with the number of time points ​, resulting in a space complexity of .

The computational novelty of the proposed GHI lies in its modular and recursive formulation, which enables the consistent aggregation of heterogeneous indicators across multiple hierarchical levels. The same computational logic can be applied regardless of the number of levels or indicator types, allowing both expert- and data-driven weighting approaches to be implemented without modifying the underlying structure. Furthermore, the framework preserves intermediate subsystem indices before final aggregation, enhancing interpretability and transparency.

The proposed GHI framework is designed to be modular and scalable for industrial applications. Although it includes six hierarchical levels and multiple indicator types, this structure allows flexibility rather than imposing complexity. Users can implement only the levels necessary for their objectives. Specifically, Levels 5 and 6, which incorporate additional contextual and managerial information, may be excluded when a simpler or faster calculation is preferred for real-time monitoring.

The multi-level design enables the integration of non-sensor information such as maintenance performance, inspection compliance, and human or process factors, which are often overlooked in conventional health indices. This comprehensive approach ensures that the GHI provides a realistic, actionable assessment of system health while remaining fully applicable in most industrial settings.

Health index comparison

The comparison between the proposed GHI and three other HIs in the same context of asset management demonstrates the novelty of the suggested GHI based on the PHM framework. Table 3 shows the comparison criteria: application, objective, dimension, input parameters, adoption method, equation, output, and properties. We compare the proposed GHI with the HI’s obtained by^8,12,23.

Table 3.

Comparison of Key Features of the Proposed GHI and Three Health Indices from Literature.

HI	Al-Anzi et al.23	Liu et al.12	Aizpurua et al.,8	Proposed GHI
Application	Oil and Gas (Refinery)	Aircraft	Power transformer	Oil and Gas Facilities or any Facility
Objective/ Dimension	Close monitoring and anomaly detection are vital for avoiding significant accidents and losses and enable intervention before failure occurrence	develop several HI extraction methods and contrast them to choose a better one for ACS performance monitoring of commercial aircraft subjected to an airline’s actual use environment	The HI formulation is a pragmatic approach to combine multiple information sources and generate a consistent health state indicator for asset management planning	Comprehensive plant GHI, considering backward potential root causes of inefficiency, failures, and downtime for proactive actions to avoid the impact on safety and production loss
Input Parameters	Process data (170 tags)	a set of raw sensor reading unobserved degradation state of a system	Multiple parameters: solid insulation, DGA, oil quality, and subsystem failure conditions	12 Pillars and their elements Indicators of potential leading root causes of failures and downtime on a system
HI Adoption Method	Deviation, averaging, and success tree	X is the original input, and X* is the output (Drift)	FTA	Hybrid—data-driven and expert knowledge models (FTA and Scoring and weight factors)
HI Equation	,	)		Multiple approaches, Fig. (3) shows them
Output	Index from 0 to 100% only indicates indicators and maintenance actions	Index from 0 to 1	Index from 0 to 1, Maintenance planning Decision-making under uncertainty and risk monitoring	GHI value is based on six levels (tags, element, pillar, system, units, plant) and includes operation, maintenance, organization, and process recommendations
Properties
Comprehensive	×	×	×	✔
Practical	×	×	✔	✔
Quantitative	✔	✔	✔	✔
Dynamic	✔	×	×	✔
Objective	✔	✔	✔	✔
Interpretable	×	×	×	✔
Scalable	✔	×	×	✔
Predictive	✔	✔	✔	✔
Customizable	✔	×	×	✔
Transparent	✔	✔	✔	✔
Benchmarkable	×	×	×	✔
Proactive	×	×	×	✔
Descriptive	×	×	×	✔
Diagnostic	✔	✔	✔	✔
Prescriptive	×	×	×	✔
Auditable	✔	✔	✔	✔
Robust	×	×	×	✔

The proposed GHI is deterministic, meaning it consistently produces the same output for a given set of inputs, ensuring repeatability. Unlike probabilistic methods that provide a range of values to account for uncertainty, deterministic indices offer clarity, consistency, and computational efficiency, making them preferable for PHM pillar indicators where straightforward interpretation and reliable trend monitoring are critical. Although probabilistic approaches capture uncertainty, deterministic models are more practical when clarity, efficiency, and traceable reasoning are required.

In the literature, although numerous studies have proposed health indices (HIs), only a few are closely related to our research. The others differ significantly in terms of health indexing objectives and methods. Our comparison covers criteria such as application, objective, dimension, input parameters, adoption method, equation, output, and properties analysis, highlighting the key strengths and unique features of the proposed GHI.

The comprehensiveness of the proposed GHI is evident in the total number of pillars considered. Earlier studies examined only a few pillars, overlooking important aspects. For example²³ considered only two pillars, omitting system management and human factors. ^8,12 rely solely on condition monitoring and neglect other system-level factors. In contrast, the proposed GHI integrates multiple PHM parameters to provide a holistic assessment of complex production systems.

While²³, ¹² provide dynamic HIs that respond to parameter changes, the HI proposed by⁸ is less dynamic because it does not include long-term monitoring, such as oil condition. The indices in these studies are difficult to interpret. In contrast, the proposed GHI is user-friendly, with clear criteria for good or bad scores, indicating that a lower GHI signals urgent issues. ^8,12 lack scalability and customization, unlike our methodology, which is suitable for diverse systems. Additionally, their indices are not benchmarkable, proactive, or descriptive. In contrast, the proposed GHI allows comparisons against industry standards and enables organizations to assess performance relative to competitors or best practices, effectively establishing a new benchmarked scale.

Furthermore, the proposed GHI is proactive, assisting end-users in preventing failures and downtime. Its analytics procedure is descriptive when extracting parameters from PHM elements. Unlike previous studies, which are not auditable or robust, the proposed GHI tracks back to Level 6 elements and input-related tags/equipment through sub-indices, supporting resource optimization and informed decision-making. The methodology is practical, facilitating the extraction of relevant PHM parameters for direct industrial applicability. The GHI is quantitative, providing a normalized score between 0 (poor health) and 1 (optimal health), enabling clear comparisons across pillars, subsystems, and units for effective trend monitoring.

While quantitative performance metrics, such as robustness to noise, response to input variations, and sensitivity analysis, are important, the current study focuses on developing and proposing the global HI framework. Nevertheless, the hierarchical FTA-based aggregation ensures transparency, interpretability, reliability, and robustness by construction: it preserves monotonicity, series–parallel logic, and explicit weighting of component criticality, allowing intuitive reasoning and traceability of contributions from individual elements to the system-level health index.

On the other hand, Table 4 shows examples of 37 possible elements of health extraction from a system, which gives insight into the comprehensive indexing using the PHM framework with multiple pillars, focusing widely on health aspects, not only the sensor data of a single component. Consequently, it cannot consider, for example, a healthy machine if normal vibration (healthy condition) records, if its lube oil is unhealthy, or if a critical spare part item is not in stock. The single parameter is used to determine the element and then . Later, both are used to get the upper-level indices of , , and .

Table 4.

Parameters Health Indices for System .

Pillar	n) Element	Level 6 GHI	Condition (End-user decision)	Indicator Type (Equation no.)
Asset Reliability (AR)	1) Asset Reliability Growth		Poor (Action is required) Good (No action required)	NDI (13)
	2) System Reliability Growth		Poor (Action is required) Good (No action required)	NDI (13)
Continuous Improvement (CI)	1) Number of tasks recommended		GHI < 1 Poor (Action is required) = 1 Good (No action)	PCI (14)
	2) Number of tasks overdue		< 1 Poor (Action is required) = 1 Good (No action)	NCI (15)
Operating Condition (OC)	1) Pressure Transmitter reading		< = 0.975 Alarm (Action not required) 0.85 = >  > 0.97 Poor (action required) > 0.850 Urgent (action required)	RAI (17)
	2) Pressure Gauge reading			RAI (17)
	3) Temperature Transmitter reading			RAI (17)
	4) Electrical Current			RAI (17)
	5) Fluid properties API degree			RAI (17)
	6) Emergency Valve Position		= > 0.99 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	PCI (14)
	7) Equipment selector Status			PCI (14)
Weather & Environment (EN)	1) Weather Temp		< = 0.975 Alarm (Action not required) 0.850 = >  > 0.975 Poor (action required) > 0.850 Urgent (action required)	RAI (17)
	2) Weather Humidity			RAI (17)
	3) Weather Rain perception			RAI (17)
	4) Emission NOx		< = 0.975 Alarm (Action not required) 0.85 = >  > 0.97 Poor (action required) > 0.850 Urgent (action required)	RAI (17)
	5) Emission H2S			RAI (17)
Maintenance management (MN)	1) Preventive Maintenance Compliance %		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	PDI (12)
	2) Work order waiting for the materials %		= > 0.95 Alarm (Action not required) 0.50 <  < 0.95 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
	3) Work order Waiting for Shutdown %		= > 0.95 Alarm (Action not required) 0.50 <  < 0.95 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
Condition Monitoring (CM)	1) Operator round Compliance		< 1 Poor (Action is required) = 1 Good (No action)	PDI (12)
	2) Operator round Alert		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
	3) Vibration Alert			NCI (15)
	4) Lube oil condition Alert			NCI (15)
Asset Mechanical Integrity (MI)	1) Useful Remaining life (URL)		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	PCI (14)
	2) Integrity inspection status		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required	NCI (15)
	3) Inspection compliance		< 1 Poor (Action is required) = 1 Good (No action)	PDI (12)
Leadership Management (LS)	1) Supervisor existing		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
	2) Leadership Engagement		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	PCI (14)
Physical asset management (AM)	1) Documents Control		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
	2) Spare parts Out of Stock		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
	3) Training Competency		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
Economic Factors (EF)	1) Production Loss value		= > 0.99 Alarm (Action not required) 0.90 <  < 0.99 Poor (action required) = < 0.90 Urgent (action required)	PCI (14)
	2) Preventive Maintenance Cost		= > 0.90 Alarm (Action not required) 0.30 <  < 0.90 Poor (action required) = < 0.30 Urgent (action required)	NCI (15)
	3) Corrective Maintenance Cost			NCI (15)
Process Safety Management (PS)	1) Process Hazard Analysis (PHA) Compliance		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
	2) Pre-Startup Safety Review (PSSR) Overdue		= > 0.85 Alarm (Action not required) 0.50 <  < 0.85 Poor (action required) = < 0.50 Urgent (action required)	NCI (15)
Human Reliability (HR)	1) Probability of Human Error for a task		= < 0.97 Alarm (Action required) > 0.97 Good (Action not required)	PDI (12)

Conclusion

In summary, this study builds on the innovative PHM framework introduced by⁵ by developing a dynamic GHI that evolves continuously with real-time data. The key contribution of our research is that the proposed GHI not only supports predictive operations by preemptively alerting operators to potential failures but also provides a comprehensive view of system health, from individual assets to entire plants or units, by integrating the root causes of potential failures and downtime, as well as correlational and non-correlational factors. To address the inherent complexity of merging diverse data elements, we have designed a robust mathematical algorithm that carefully selects indicators, allocates appropriate weights, and applies correlation analysis, normalization, and outlier detection to mitigate redundancy and skewness.

Furthermore, this study offers significant value for industrial practitioners by establishing the GHI as a critical benchmark for management reporting and stakeholder communication, thereby creating a baseline for continuous improvements in efficiency and safety. Ultimately, our work presents GHI for complex production system monitoring, laying the foundation for future AI and ML applications within a comprehensive PHM framework. Its hierarchical structure supports descriptive, diagnostic, predictive, and prescriptive analytics, ensuring proactive decision-making to maintain high reliability, availability, and efficiency. This approach enhances sustainability, cost-effectiveness, and responsiveness in a rapidly evolving energy sector by focusing on well-defined sub-indices and parameter-level indicators.

Looking ahead, implementing the proposed GHI framework in practice may face several challenges. These include handling rare failure events, ensuring compatibility with digitally mature but heterogeneous industrial systems, and integrating with existing monitoring infrastructure. While many indicators can be collected automatically via sensors, some data may still require manual entry, which could introduce errors or inconsistencies and affect the applicability of the GHI. We recommend applying this new adaptation of the GHI in practical use cases, such as production plants in the oil and gas industry or other high-demand sectors, to validate and further refine the framework. Conducting case studies would provide insights into practical applicability, scalability, and challenges associated with real-world deployment, particularly in mature, digitally asset-intensive facilities and in contexts with rare failure events. Comparing AHP-derived and data-driven weights in the calculation of system health, along with performing sensitivity analyses, constitutes another valuable direction for future research. Another future research direction is the quantitative validation of characteristics outlined in Table 3, such as transparency, reliability, and robustness, which could involve simulated noise injection, sensitivity analyses, and comparisons against labeled failure events in operational plants. Additionally, leveraging the PHM framework to generate extensive input data for ML applications may enable the prediction of both component-level and overall plant health, advancing proactive measures to prevent failures and minimize downtime.

Author contributions

Dr. Khalid Alfahdi conceived and designed the study, conducted the experimental work, analyzed the data, and prepared the manuscript draft. Dr. Hakan Gultekin supervised the research and reviewed the manuscript. Dr. Emad Summad co-supervised the study and contributed to the manuscript review.

Data availability

The data presented in Fig. 1 is summarized and available at 10.36001/IJPHM.2024.V15I2.3933. Data supporting Fig. 2, Fig. 3, Table 1, and Table 4 originated from the authors and are available from the corresponding author by request. Table 2 data of AHP, including experts’ matter survey and detailed questionnaire, calculations, validation, and results, are available from the corresponding author upon request. Table 3 data with the first three columns have been cited and summarized from the following DOIs: 10.1038/s41598-022-18824-2, 10.1016/J.MEASUREMENT.2020.107890 and 10.1016/J.ASOC.2019.105530.

Declarations

Competing interests

The authors declare no competing interests.