Statistical Analysis

Effective analysis combines univariate statistical process control with structured modelling.

Control charts establish whether a process operates with predictable behavior and identify consistent operating periods. This prevents analysis of drift, mixed conditions, or structural changes as if they represent stable performance.

Once statistical control is established, modelling quantifies the drivers of performance and evaluates relationships between variables. Decisions then rely on evidence derived from stable conditions rather than uncontrolled variation.

Analysis performed without first establishing statistical control produces misleading results. Models fit unstable data and describe instability rather than cause and effect. Decisions then address symptoms rather than the underlying process behavior.


Where this analysis is applied

This analytical approach forms the basis of all Verto Pharma assessments. Historical manufacturing and quality data provide the primary evidence used to evaluate operational performance, regulatory exposure, and manufacturing predictability across the product lifecycle.

• Auditing
Assessment of manufacturing performance, quality systems, and inspection readiness through analysis of historical operational data.

• Business due diligence
Evaluation of operational predictability, manufacturing maturity, and regulatory exposure for investors or partners.

• Development
Analysis of formulation and process development data to understand variability and guide process design.

• Process validation
Assessment of whether the manufacturing process operates with predictable behavior.

• Process investigation
Structured analysis of unexpected shifts, deviations, or performance changes.

• Stability
Evaluation of stability data to assess product behavior over time and detect emerging trends.

• CMC documentation
Statistical review and interpretation of manufacturing and stability data used within regulatory submissions.

• Post market surveillance and pharmacovigilance
Evaluation of field performance data to detect signals and assess whether product behavior remains consistent with historical manufacturing performance.

Recognized standards exist, including those from the International Organization for Standardization and ASTM International. Despite these standards, control charts face frequent misunderstanding and misuse within many organizations.

Statistical Methodology: Statistical Process Control (SPC)

  • The Xbar-R chart was developed by Walter A. Shewhart in the 1920s for fast moving manufacturing environments. The chart performs well when subgroups used to calculate each average are homogeneous and represent short term process conditions. Units produced in rapid succession usually meet this requirement, which explains its suitability in these environments.

    In the 1940s, W. J. Jennett introduced the use of successive differences to estimate routine variation when subgrouping was not available. This approach created the Individuals and Moving Range (IMR) chart.

    The IMR chart saw limited industrial adoption for several decades. Its practical application and modern use gained strong support from Donald J. Wheeler, who demonstrated its effectiveness for sequential data streams common in industrial processes. Wheeler later discussed and demonstrated the Individuals chart to W. Edwards Deming during the 1980s.

    Wheeler had major influence on modern SPC practice. His work translated statistical theory into practical methods used daily by engineers, scientists, and managers. His teaching and publications showed how simple charts, applied correctly, guide sound operational decisions while preserving the principles established by Shewhart.

    Our approach follows Wheeler’s teachings. The focus rests on practical interpretation of process data and disciplined operational decision making. We provide a direct link to Wheeler’s website, which contains extensive material on correct SPC practice.

    Wheeler later referred to control charts as Process Behavior Charts. The wording reflects intent. The term control chart often leads organizations to focus on compliance or limits alone. Process behavior directs attention to how a process performs through time and when management action is required.

    Process Behavior Charts, used together with Process Capability, provide the basis to verify whether equipment, processes, or products are achieving a State of Control. Industry application of this concept varies widely, with frequent misuse and inconsistent interpretation. When applied correctly, this combined approach provides a clear and defensible assessment of true process performance and control.

    With the correct information in place, this supports you to make informed decisions.

    • Decide whether to change the process or leave it unchanged

    • Present the true level of quality to your organization

    • Confirm the product is consistent and meets specification

    • Support continual improvement by maintaining performance on target with minimal variation

    • Ensure regulators are informed with an accurate and evidence based position on process performance

    • Apply multivariate modelling and acceptance sampling at the correct stage and on stable data, ensuring results reflect true process behavior

Statistical Methodology: Process Behavior and Modelling

Statistical modelling supports evaluation of multiple factors that influence process performance. Methods such as regression, multivariate analysis, and designed experiments allow simultaneous assessment of material attributes, process conditions, and operational variables.

Statistical models assume stable underlying behavior. Data used for modelling must represent consistent operating conditions. When a process drifts or combines multiple structural states, parameter estimates become unreliable and interpretation becomes misleading. For this reason, modelling strategies examine the process timeline and identify periods of consistent behavior before evaluating relationships between variables.

  • Our modelling approach uses structured multivariate tools, including but not limited to the following methods.

    Typical analysis includes:

    • Principal Component Analysis (PCA) to understand multivariate structure and relationships across variables. PCA highlights correlated behavior and identifies patterns influencing overall system performance.

    • Fit model procedures to quantify relationships between response variables and candidate factors. These models support structured hypothesis testing and effect estimation.

    • Bootstrap tree methods which repeatedly resample the data and refit models to identify variables that consistently influence the response while filtering unstable or spurious relationships.

    These methods support simultaneous evaluation of formulation variables, material attributes, and process conditions while maintaining statistical discipline.

    This modelling strategy also reflects a principle often attributed to Aristotle. The most informative place to search for causes within a system occurs where the system changes. Analysis therefore focuses on factors associated with transitions in system behavior rather than routine background variation.