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API MPMS 13.1 (1985, Errata 2013): Statistical Procedures for Petroleum Measurement Accuracy
Understanding the Statistical Framework for Precision and Bias in Hydrocarbon Measurement
Scope and Purpose
API Manual of Petroleum Measurement Standards (MPMS) Chapter 13.1, originally published in 1985 and updated with an errata in 2013, establishes a uniform statistical framework for evaluating the quality of measurement data in the petroleum industry. The standard focuses on the application of statistical concepts and procedures to detect and correct systematic errors (bias) and random errors (precision), ensuring that measurement results are both accurate and reliable. It covers the entire measurement chain—from laboratory analysis to field meters—and provides methods for calculating repeatability, reproducibility, and overall measurement uncertainty.
Key Purpose: To provide a standardized statistical methodology for assessing and improving the accuracy of petroleum measurements, including crude oil, refined products, and natural gas liquids.
The 2013 errata corrected typographical errors, clarified several formulas, and updated references to later editions of related statistical texts, ensuring that the standard remains technically sound and applicable to modern instrumentation and data analysis software.
Technical Requirements and Statistical Methods
Core Statistical Concepts
API MPMS 13.1 defines and recommends procedures for the following fundamental statistical measures:
- Precision: The closeness of agreement between replicate measurements under specified conditions, quantified by standard deviation, variance, or range.
- Bias (Trueness): The systematic difference between the average of a large number of measurements and a true or accepted reference value.
- Repeatability and Reproducibility: Measures of precision under repeatability (same operator, same equipment) and reproducibility (different operators, laboratories, instruments) conditions.
- Outlier Identification: Statistical tests (e.g., Grubbs’ test, Dixon’s Q-test) to identify and handle anomalous data points that could distort averages and uncertainty estimates.
- Control Charts: Shewhart control charts for monitoring measurement processes over time, detecting trends, shifts, or increased variability.
Outlier Detection Tests
The standard recommends specific outlier tests for different sample sizes and measurement contexts. The table below summarizes the primary tests and their applicable sample size ranges.
| Test | Application | Sample Size Range | Critical Values Source |
|---|---|---|---|
| Grubbs’ Test (Extreme Studentized Deviate) | One or two outliers at either tail of a normally distributed data set. | n = 3 to 30 | Table A-1 of API MPMS 13.1 |
| Dixon’s Q‑Test | Single outlier in small data sets; uses ratio of gaps to range. | n = 3 to 25 | Table A-2 of API MPMS 13.1 |
| Chauvenet’s Criterion | Rejection of outliers based on normal probability; simpler but less powerful. | n ≥ 4 | Referenced standard tables |
Caution: The standard emphasizes that outlier rejection must be based on objective statistical criteria, not subjective judgment. Repeated removal of data without justification can mask real process issues.
Measurement Uncertainty
API MPMS 13.1 aligns with the ISO Guide to the Expression of Uncertainty in Measurement (GUM) for combining random and systematic uncertainties. It provides simplified methods for petroleum-specific applications, such as uncertainty estimation for meter factors and laboratory analyses.
Implementation Highlights for Measurement Assurance
Effective implementation of API MPMS 13.1 requires integration into daily measurement operations and periodic audits. Below are key areas where the standard’s procedures are typically applied.
Laboratory and Field Calibration
When calibrating flow meters, temperature sensors, or density meters, replicate measurements are collected. The standard’s repeatability and reproducibility calculations are used to verify that the calibration process is stable. Control limits are set based on historical data, and any result falling outside the limits triggers an investigation.
Practical Tip: Maintain a rolling database of at least 20 replicate measurements for each device. Use the standard’s control chart templates (Appendix B) to monitor long-term trends.
Meter Proving Operations
During meter proving, a series of proving runs (typically five or more) are completed. API MPMS 13.1 provides criteria for evaluating whether the runs are statistically consistent. If the range of the prove results exceeds a multiple of the standard deviation, additional runs or maintenance is required.
Data Review and Documentation
The standard recommends that all statistical tests, outlier handling decisions, and uncertainty calculations be documented in a log that can be examined during internal or third-party audits. Software used for statistical calculations should be validated against examples in the standard.
Common Non-Compliance: Using spreadsheet functions (e.g., Excel’s STDEV.P instead of STDEV.S) without confirming the correct degrees of freedom. Always verify formulas against API MPMS 13.1 examples.
Compliance and Verification Notes
Auditors evaluating conformance to API MPMS 13.1 typically check the following areas:
- Written Procedure: Does the facility have a documented statistical quality control procedure that references API MPMS 13.1?
- Training Records: Have personnel received training on the statistical methods (especially outlier detection and control charts)?
- Outlier Handling: Are data points rejected only after applying the standard’s tests, and is the rejection recorded with justification?
- Uncertainty Calculations: Are combined uncertainties correctly computed, including contributions from both random and systematic errors?
- Control Charts: Are control charts current and are out-of-control conditions investigated and resolved?
- Software Validation: Has the statistical software been validated against the standard’s examples (provided in Appendix C of the 1985 edition and amended in the 2013 errata)?
Compliance Tip: The 2013 errata includes corrected worked examples. Use these examples as test cases when validating your calculation spreadsheets or software.
Organizations that successfully implement API MPMS 13.1 can demonstrate due diligence in measurement accuracy, which is critical for custody transfer, loss control, and regulatory reporting.
Frequently Asked Questions
Q: Who should use API MPMS 13.1?
A: The standard is intended for laboratory supervisors, quality control engineers, metering specialists, and anyone responsible for collecting and analyzing petroleum measurement data. It is widely used by oil refineries, pipeline companies, and testing laboratories.
A: The standard is intended for laboratory supervisors, quality control engineers, metering specialists, and anyone responsible for collecting and analyzing petroleum measurement data. It is widely used by oil refineries, pipeline companies, and testing laboratories.
Q: Does the 2013 errata change any fundamental statistical methods?
A: No, the fundamental methods remain the same. The errata corrects typographical errors in formulas and tables, updates references to newer versions of statistical textbooks, and clarifies ambiguous wording. Users of the 1985 edition should obtain the errata to ensure calculations are correct.
A: No, the fundamental methods remain the same. The errata corrects typographical errors in formulas and tables, updates references to newer versions of statistical textbooks, and clarifies ambiguous wording. Users of the 1985 edition should obtain the errata to ensure calculations are correct.
Q: Is API MPMS 13.1 consistent with ISO 5725 (Accuracy of measurement methods and results)?
A: Yes, the standard’s definitions of repeatability and reproducibility are aligned with ISO 5725. However, API MPMS 13.1 includes additional guidance specifically tailored to petroleum applications, such as meter proving and sample handling.
A: Yes, the standard’s definitions of repeatability and reproducibility are aligned with ISO 5725. However, API MPMS 13.1 includes additional guidance specifically tailored to petroleum applications, such as meter proving and sample handling.
Q: Can outlier rejection be automated?
A: Yes, but the standard warns that automation must be implemented carefully. A rejected data point should never be deleted permanently; instead, it should be flagged and reviewed by a qualified person before exclusion from the final calculation. The justification must be documented.
A: Yes, but the standard warns that automation must be implemented carefully. A rejected data point should never be deleted permanently; instead, it should be flagged and reviewed by a qualified person before exclusion from the final calculation. The justification must be documented.
© 2026 International Standards Advisory. All rights reserved. This article is for informational purposes and not a substitute for the official standard.