Descriptive Statistics and Inferential Statistics in Medical Device Quality Assurance

FDA Requirements and the Transition to QMSR

The FDA Quality System Regulation (QSR), specifically 21 CFR §820.250, clearly stipulates the importance of data analysis in quality assurance for medical devices. This regulatory requirement mandates that manufacturers systematically collect and analyze quality data, and utilize the results to improve their quality systems. This data analysis approach is fundamentally based on two methodological frameworks: descriptive statistics and inferential statistics (sampling statistics).

It is important to note that on February 2, 2026, the new Quality Management System Regulation (QMSR) will become effective, replacing most of the current QSR by incorporating by reference ISO 13485:2016, Medical Devices—Quality Management Systems—Requirements for Regulatory Purposes. However, the fundamental requirements for statistical techniques will continue under the new QMSR framework through ISO 13485:2016, which includes similar requirements for statistical methods throughout various clauses including process validation (7.5.6), design verification (7.3.6), design validation (7.3.7), and data analysis (8.4).

Current QSR Requirements (Effective until February 1, 2026)

§820.250 Statistical Techniques

(a) Where appropriate, each manufacturer shall establish and maintain procedures for identifying valid statistical techniques required for establishing, controlling, and verifying the acceptability of process capability and product characteristics.

(b) Sampling plans, when used, shall be written and based on a valid statistical rationale. Each manufacturer shall establish and maintain procedures to ensure that sampling methods are adequate for their intended use and to ensure that when changes occur the sampling plans are reviewed. These activities shall be documented.

Understanding the Two Types of Statistical Methods

Section §820.250(a) addresses descriptive statistics, while section (b) addresses inferential statistics (sampling statistics). Under the upcoming QMSR, these concepts will be integrated through ISO 13485:2016 requirements, which emphasize the use of appropriate statistical techniques with rationale for sample sizes across multiple quality management system activities.

Descriptive Statistics

Descriptive statistics is a fundamental methodology for objectively understanding the characteristics of collected data and clarifying its features. For example, by calculating statistical measures such as mean, median, and standard deviation from measurement values and inspection results obtained in manufacturing processes, it becomes possible to quantitatively evaluate process stability and the degree of variation.

Furthermore, by utilizing statistical graphs such as histograms and control charts, it is possible to visually understand data distribution and changes over time. These analytical results serve as objective evidence for accurately grasping the current state of manufacturing processes and determining the necessity for improvement.

The application of descriptive statistics enables manufacturers to:

• Monitor process trends and identify patterns in quality data
• Establish baseline process performance metrics
• Visualize data distributions to detect anomalies
• Support objective decision-making for process improvements

Inferential Statistics (Sampling Statistics)

Inferential statistics, on the other hand, is a methodology for estimating the characteristics of an entire population from limited sample data. This becomes particularly important in situations where it is difficult to inspect all products, such as when 100% inspection is not practical or when destructive testing is required.

For example, it becomes possible to determine a statistically appropriate sample size from a manufacturing lot and estimate the overall quality level from the inspection results of that sample. In this process, developing an appropriate sampling plan and evaluating statistical significance are essential to ensure statistical reliability.

ISO 13485:2016, which forms the core of the upcoming QMSR, specifically addresses this through various clauses:

• Clause 7.5.6 (Validation of processes): Requires documentation of procedures for validation including, as appropriate, statistical techniques with rationale for sample sizes
• Clause 7.3.6 (Design and development verification): Requires verification plans to include, as appropriate, statistical techniques with rationale for sample sizes
• Clause 7.3.7 (Design and development validation): Requires validation plans to include, as appropriate, statistical techniques with rationale for sample sizes
• Clause 8.4 (Analysis of data): Requires determination of appropriate methods, including statistical techniques and the extent of their use

Practical Applications in Quality Management Systems

FDA QSR §820.250 (and the equivalent requirements in ISO 13485:2016 under the QMSR) requires effective utilization of these data analysis methodologies within the quality system. Specifically, the following applications are anticipated:

Manufacturing Process Control

In-process inspection data is statistically analyzed to continuously monitor process stability and capability. Early detection of outliers and trends enables preventive responses to quality issues. Statistical process control (SPC) techniques, including control charts and capability indices (Cp, Cpk), play a vital role in maintaining process performance within acceptable limits.

Product Design Verification

Performance data from prototypes is statistically analyzed to objectively evaluate conformance to design specifications. These analytical results serve as evidence for design validation and as a basis for improvement decisions. The use of statistical techniques ensures that design outputs meet design inputs with an appropriate level of confidence.

Risk-Based Sampling Strategies

Under both the current QSR and the upcoming QMSR framework, sampling plans must be based on valid statistical rationale. Organizations should consider:

• The risk associated with the product and its intended use
• Appropriate confidence levels (typically 95% or higher unless justified)
• Statistical tolerance intervals as defined in ISO 16269-6
• Acceptance quality limits (AQL) based on risk assessment
• Operating characteristic (OC) curves for attribute sampling plans

Standards such as ISO 2859-1 (Sampling procedures for inspection by attributes) and ANSI/ASQ Z1.4 provide frameworks for establishing statistically valid acceptance sampling plans.

Complaint and Post-Market Data Analysis

Furthermore, by conducting statistical analysis of complaint data and feedback from the market, it is possible to identify potential quality issues and improvement opportunities. These analytical results are utilized as input to the Corrective and Preventive Action (CAPA) system.

Integration with Risk Management

A critical aspect emphasized in ISO 13485:2016 is the integration of statistical techniques with risk management principles. Clause 4.1.2 requires organizations to apply a risk-based approach to the control of appropriate processes needed for the quality management system. This means that:

• Sample size determination should be based on risk assessment using ISO 14971 principles
• Higher-risk products or critical parameters require more stringent statistical criteria
• The rationale for statistical techniques and sample sizes must be documented and justified based on the severity and probability of potential failures

Preparing for QMSR Implementation

As manufacturers prepare for the February 2, 2026 QMSR effective date, they should:

1. Conduct Gap Analysis: Compare current statistical procedures against ISO 13485:2016 requirements, particularly clauses 7.3.6, 7.3.7, 7.5.6, 8.1, and 8.4
2. Document Statistical Rationale: Ensure all sampling plans include documented statistical rationale based on valid statistical principles and risk assessment
3. Update Procedures: Revise procedures to explicitly reference statistical techniques and their application where appropriate
4. Train Personnel: Provide training on statistical methods, sample size determination, and the risk-based approach required by ISO 13485:2016
5. Review Validation Activities: Ensure process validation, design verification, and design validation activities include appropriate statistical techniques with documented rationale for sample sizes

Essential Principles for Quality Assurance

This data analysis approach is positioned not merely as compliance with regulatory requirements, but as an essential activity in medical device quality assurance. Appropriate data analysis leads to the reduction of quality risks, improvement of product quality, and ultimately to ensuring patient safety.

Manufacturers are required to understand the fundamentals of these statistical methodologies and effectively utilize them within their quality systems. Whether operating under the current QSR or preparing for the QMSR transition, the core principle remains the same: statistical techniques must be valid, appropriate for their intended use, and based on sound statistical and risk-based rationale.

The transition to QMSR represents an opportunity for manufacturers to strengthen their statistical practices by aligning with internationally recognized standards, ultimately contributing to improved patient safety and product quality worldwide.

Key References

• 21 CFR §820.250 Statistical Techniques (Effective until February 1, 2026)
• 21 CFR Part 820 Quality Management System Regulation (QMSR) (Effective February 2, 2026)
• ISO 13485:2016 Medical devices—Quality management systems—Requirements for regulatory purposes
• ISO 14971 Medical devices—Application of risk management to medical devices
• ISO 2859-1 Sampling procedures for inspection by attributes
• ISO 16269-6 Statistical interpretation of data—Part 6: Determination of statistical tolerance intervals
• GHTF SG3 Quality Management System—Process Validation Guidance