Synthetic maintenance data generation for industrial assets based on historic statistical distribution using pseudo-random algorithm Open Access

Technological evolution has transformed maintenance management into a critical function for industrial competitiveness, leading companies to prioritize strategies that maximize asset performance and operational profitability (Mora, 2009). In this context, data has emerged as a pivotal industrial asset, enabling pivotal insights and informed decision-making through diverse analytical strategies (Merkt, 2019; Bekar et al., 2020; Bousdekis et al., 2021; Filz et al., 2021; Sajid et al., 2021; Abbate et al., 2022; Cui et al., 2022). These data-driven approaches facilitate the iterative optimization of maintenance management via continuous feedback mechanisms (Ciliberti et al., 2019; Tarantino, 2021; Diaz et al., 2023).

However, a significant obstacle to implementing these advanced analytics is the frequent scarcity or complete absence of high-quality maintenance data records. This often forces a reliance on established, yet inherently limited, maintenance techniques like TPM, RCM, and FMEA (Mora, 2009; International Organization for Standardization, 2016). While foundational, such approaches fall short of the comprehensive, data-driven engineering analysis required for holistic asset management – which is necessary to optimize strategies without compromising assets, production, or safety (Jones, 1995; SAE, International, 2009). This challenge is critical in high-consequence environments where fault impacts and data integration are vital (Hannam, 1997). A further complication involves ensuring data quality and reliability, which demands a well-planned acquisition process that prioritizes essential assets and protects their integrity (Díaz, 2023; Diaz et al., 2023; International Organization for Standardization, 2016).

To address this, ISO 14224:2016 outlines a structured framework for data acquisition. Figure 1 illustrates the planning procedure, which involves steps such as determining data acquisition processes, verifying and researching data sources, defining the maintenance data to acquire, setting time, population, and operation parameters, ensuring uniformity in failure definition and classification, and training staff. Subsequently, Figure 2 depicts the acquisition procedure, which includes accessing consequential data, interpreting data, transferring data to a database, and evaluating and analyzing gained insights.

The escalating value of data as a convertible asset for business intelligence underscores the need to overcome inherent data issues, which can be categorized into concerns regarding privacy release and sensitivity, data bias and variance, the need for increased data robustness, and limited or zero data availability (Cole et al., 2015; Mannino and Abouzied, 2019; Dankar and Ibrahim, 2021; Jordon et al., 2022). Synthetic data emerges as a viable solution to these challenges, defined as artificially generated data that acquires the statistical and phenomenological properties of a real dataset (Dankar and Ibrahim, 2021; Jordon et al., 2022). Methodological advancements highlight that synthetic datasets vary in fitness for purpose, necessitating tailored evaluation protocols and practical metrics to enhance reproducibility (Lautrup et al., 2024; Giuffrè and Shung, 2023).

Synthetic data offers significant benefits, including privacy protection through the absence of personally identifiable information, improved accessibility by creating larger datasets, flexibility to replicate specific statistical characteristics, and the potential to enhance original data quality (El Emam et al., 2020). Various generation techniques exist, such as those based on Bayesian networks, copulas, parametric fitting (e.g. Monte Carlo methods), and non-parametric trees (Mannino and Abouzied, 2019; Dankar and Ibrahim, 2021; El Emam et al., 2020; Li et al., 2020; Jordon et al., 2022; Okagbue et al., 2020).

Within reliable maintenance engineering, synthetic data generation employs diverse strategies, including machine learning, such as generative adversarial networks (GANs) and mathematical functions, maintaining statistical fidelity (Lakshmanan et al., 2023; Martínez-Heredia and Ventura, 2025).. Contemporary research trends encompass digital twin frameworks for physics-informed data streams and Bayesian methods for uncertainty-aware reliability estimates, providing a context where a parameterized pseudo-random generator offers a reproducible baseline for transparent benchmarking (Zio and Miqueles, 2024; Liu et al., 2024; Pan et al., 2024; Zheng et al., 2024). To address the challenge of absent maintenance records, this work develops a pseudo-random algorithm grounded in the high-quality data attributes prescribed by ISO 14224:2016 (Diaz et al., 2023; Díaz, 2023) and leveraging statistical distributions from the OREDA database (SINTEF, 2009), where failure rates follow a gamma distribution. This methodology ensures the generation of valid and practically useful synthetic maintenance data for industrial assets.

Applied to centrifugal pumps in an operational chemical engineering setting —specifically, the ethanol-water separation process at the University of Pamplona — our approach generated two distinct datasets (⁠$X1$ and $X2$⁠). Dataset $X2$ demonstrated strong alignment with OREDA's mean failure rate (exhibiting only a 1.96% error), validating its statistical fidelity. Despite higher deviations in standard deviation and maximum values, both datasets yield realistic maintenance records suitable for engineering analysis and decision-making without jeopardizing actual assets or operations.

The generation of synthetic maintenance data requires a robust statistical foundation and a structured methodology. This study utilizes the OREDA database as its primary source for failure mode distributions, providing historically validated reliability data from major petrochemical companies (SINTEF, 2009). OREDA's structure organizes failure data by asset taxonomy, with statistical distributions categorized by failure mode severity (critical, degraded and incipient) and including key metrics such as failure rates, active repair hours, and man-hours.

For this research, the critical risk state was selected, with failure rates following a gamma distribution as confirmed by Kolmogorov-Smirnov and χ² goodness-of-fit tests (ibid.). The probability density function is given by:

and its cumulative distribution function by:

where θ* represents the mean failure rate and $σˆ$ the standard deviation.

The methodology also incorporates probability distributions for failure modes relative to non-maintainable components, ensuring the total probability sums to 100% as expressed by:

where j denotes failure modes, i non-maintainable components, and X_ji the occurrence probability.

The synthetic data generation workflow, depicted in Figure 3, is implemented through Algorithm 1. This algorithm details the modular steps from statistical initialization to dataset cleaning, ensuring reproducibility and transparency.

• 1: Function SyntheticDataGeneration()

• 2: Input: Failure rate distribution parameters, component costs, maintenance parameters

• 3: Output: Synthetic maintenance dataset including Failure Mode, Component, TBF, Maintenance Cost, etc.

• 4: # Step 1: Initialization

• 5: Define constants and distributions (e.g. mean and standard deviation for failure rates)

• 6: Initialize data structures for storing generated records

• 7: # Step 2: Data Sampling

• 8: Generate random values [r₁, r₂, r₃, r₄, r₅] from N(0, 1)

• 9: # Step 3: Failure Mode and Component Selection

• 10: Sample Failure Mode and Component using probabilistic sampling with r₁

• 11: Sample Failure Description using probabilistic sampling with r₂

• 12: # Step 4: Failure Rate and TBF

• 13: Compute parameters $β=μσ$ and α = β ⋅ μ based on failure rate distributions

• 14: Calculate Failure Rate $λ=FX−1(r3,β,α)$

• 15: Calculate $TBF=−lnr4λ$

• 16: # Step 5: Dataset Filtering and Adjustments

• 17: while $1λmax≤TBF≤λmin$ do

• 18: Filter dataset records based on TBF constraints

• 19: end while

• 20: Select subset n₂ from n₁ records

• 21: # Step 6: Calculate Maintenance Costs

• 22: Calculate Failure Date = Start Operation Date + TBF

• 23: Sort the dataset by Failure Date in ascending order

• 24: Calculate ManHours = $FX−1(r5,μ,σ)$ based on manhour distribution

• 25: Compute Maintenance Cost = Component Cost[Component] + (ManHours × ManHour Cost)

• 26: Update TBF = Current Failure Date - Last Failure Date (in hours)

• 27: Calculate Downtime = ManHours + (1 + Average Administrative Time Percentage)

• 28: # Step 7: Repeat and Clean Dataset

• 29: while Additional Filtering Needed do

• 30: Reapply filters to the dataset

• 31: end while

• 32: Clean dataset to finalize output

• 33: Return Synthetic maintenance dataset

Initialization: The process begins with defining the key statistical distributions and parameters, such as the mean and variance for failure rates and component costs. These parameters will shape the random variables generated later in the process. Next, data structures are initialized to store records that will eventually contain attributes such as failure modes, components, Time Between Failures (TBF), and maintenance costs.

Sampling Random Values: Once initialization is complete, random values are generated to simulate various aspects of the maintenance process. Values such as r₁, r₂, r₃, r₄, and r₅ are drawn from a standard normal distribution, N(0, 1), which will later be used in probabilistic sampling.

Failure Mode and Component Selection: Using the generated random values, failure modes and components are selected for each record. The value r₁ is applied within cumulative probability distributions for failure modes and components, allowing for probabilistic sampling. Similarly, r₂ is used to choose a failure description based on the cumulative probabilities associated with each failure mode.

Compute Failure Rate and TBF: After selecting the failure mode and component, the next step is to compute the failure rate (λ) and TBF for each record. Parameters β and α are calculated based on the mean and variance of the failure rate distributions. Using these parameters along with r₃, the failure rate λ is determined by inverting the cumulative distribution function, $FX−1(r3,β,α)$⁠. The TBF is then calculated as $TBF=−lnr4λ$⁠.

Dataset Filtering and Adjustments: With preliminary data generated, the dataset undergoes filtering based on the TBF values to ensure that records meet realistic operational limits. Only TBF values that fall within a specified range (between $1λmax$ and λ_min) are kept. This step ensures that the synthetic data aligns with practical operational expectations.

Calculate Maintenance Costs and Downtime: The maintenance cost and downtime associated with each failure are then calculated. The failure date is determined by adding TBF to the start operation date. Man-hours are computed using distribution-based calculations. Maintenance cost is calculated by combining the component cost with the product of man-hours and the man-hour cost rate. Downtime is calculated by adding man-hours and an additional administrative time percentage.

Final Filtering and Dataset Cleaning: After calculating costs and downtime, the dataset undergoes a final filtering and cleaning stage. Additional filters are reapplied if necessary to ensure that all records meet the predefined conditions. The dataset is then organized and prepared for output.

This structured process yields a synthetic maintenance dataset with realistic attributes, including varied failure modes, components, times between failures, costs, and downtimes, based on statistically grounded parameters and distributions.

The selected study field for the research was the chemical engineering laboratory at the University of Pamplona, whereby the ethanol-water mixture separation subprocess was selected, focusing on a plate column with liquid feed, direct steam injection, and the possibility of having the top product as vapor or liquid through a condenser that can be used as total or partial condenser. The column feed can come from a feed tank or the rectification column (see Figure 4).

Based on an analysis conducted during the research, the assets with high criticality involved in the subprocess are the centrifugal pumps P − 400 and P − 405, located in the P&ID of Figure 4.

Similarly, four failure modes were determined for the study that are common in the mentioned assets: External Leak (ELU), Abnormal Instrument Reading (AIR), Vibration (VIB), and Breakdown (BRD) ^[1].

For this reason, a dataset of synthetic maintenance data for centrifugal pumps with four failure modes was generated based on the methodology for generating synthetic maintenance data and the constructed programming algorithms.

The OREDA provided statistical information based on statistical and percentage distributions per failure mode and non-maintainable components (SINTEF, 2009, pp.138-145).

To satisfy (2) so that the data resembles actual behavior, it is determined, from the statistical distribution of the overall failure rate found in the OREDA during critical phases of the asset, (4). It is worth noting that the values found are failure rates per million hours (10⁶ h).

Under the table structure, these distributions were characterized, allowing for the definition of the data structures proposed in the algorithms presented in this article.

In Table 1, the statistical distribution of failure rates about the selected failure modes for the asset is observed.

Table 2 shows the probability of a failure mode caused by a non-maintainable asset component.

Based on a market analysis, the cost associated with replacing each non-maintainable component of the asset has been defined in Colombian pesos (COP). The prices of the components are expressed in monetary units (see Table 3).

Finally, Table 4 defines statistical information regarding the active maintenance hours required per failure mode of the asset.

Two synthetic maintenance datasets were generated for the centrifugal pump under study based on the four identified failure modes and the provided statistical information. The datasets include maintenance records with relevant and non-redundant maintenance data, as required by ISO 14224:2016. These two data sets will be called $X1$ and $X2$⁠, respectively. The online Supplementary Material includes Dataset $X1$ and Dataset $X2$⁠.

These two data sets were generated with different statistical properties. Data set $X1$ behaves in such a way that it satisfies the ranges of the observed set in (4), while data set $X2$ follows the behavior observed in (5). Despite the latter, data set $X2$ retains statistical characteristics that can be considered as actual for synthetic data, considering that it also complies with (4).

During the code execution, technological limitations were encountered that made it impossible to increase the expected number of maintenance records (K) without affecting the expected statistical properties, thus obtaining the data sets described by (6) and (7).

When the variable filtering process is applied to the maintenance data sets as seen in (6) and (7), the synthetic maintenance data sets with similar statistical and business characteristics are obtained (see 2, 4, 8, and 9).

Table 5 presents a representative subset of the records generated for the dataset $X1$⁠. This subset illustrates different maintenance records, whether corrective or preventive, with all the corresponding data for each record.

One hundred and seventeen (117) filtered maintenance synthetic data records were obtained for dataset $X1$⁠. Meanwhile, twenty-six (26) filtered maintenance synthetic data records were obtained for dataset $X2$⁠.

The statistical comparison between the synthetic datasets and the OREDA benchmark is summarized in Table 6, which presents key failure rate metrics. Subsequently, the Time Between Failures (TBF) distributions are visualized in Figures 5–7.

Figure 5 depicts the gamma distribution of TBF derived from OREDA data, serving as the reference for synthetic data generation. Figure 6 shows the TBF distribution for dataset $X1$⁠, which exhibits a higher mean failure rate and distinct spread compared to OREDA. Figure 7 presents the TBF distribution for dataset $X2$⁠, which aligns closely with OREDA's mean.

As observed in Table 6, dataset $X2$ demonstrates better alignment with OREDA's mean failure rate. The percentage errors for the mean (%_μ), standard deviation (%_σ), and maximum value (%_max) are calculated as follows (Montgomery, 2004):

This paper established a methodology and developed pseudo-code algorithms to generate synthetic maintenance data for industrial assets. By implementing pseudo-random functions within statistical, probabilistic, and exponential-variate distributions based on the OREDA, the approach successfully produces realistic maintenance records.

The results demonstrate the method's practical value. As evidenced in Table 6, the $X2$ dataset shows a notably strong performance, with its mean value exhibiting a minimal error of just 1.96% compared to the OREDA distribution (10). This high degree of accuracy in replicating the central tendency underscores the model's effectiveness. While larger errors were observed for the standard deviation (75.91%) and the maximum global failure rate (292.66%), these are not inherently unfavorable. Instead, they reflect the stochastic nature of the pseudo-random generation across multiple failure modes, which imbues each synthetic dataset with a unique variability from which valuable maintenance engineering insights can be extracted.

Ultimately, this work provides a robust, low-risk tool for simulation and decision-making in asset management. The generated datasets, exemplified by the centrifugal pump category in Table 5, possess statistical and behavioral fidelity to real-world data. This enables organizations to test maintenance strategies, train models, and plan asset lifecycles efficiently and safely—without jeopardizing operational integrity, production, safety, or the environment. Thus, the research bridges a critical gap between theory and practice by leveraging synthetic maintenance data generation as a foundational seed for advanced applications, such as digital twins and machine learning models, which facilitates the incorporation of these and other data-driven tools into decision-making processes to continuously improve maintenance management.

This work is supported by University of Pamplona and University of the Andes, Colombia.

The supplementary material for this article can be found online.