Statistics in the Service of Quality

Published on: 
Pharmaceutical Technology, Pharmaceutical Technology-06-02-2011, Volume 35, Issue 6

Ensuring compliance though increased statistical knowledge and resources.

The application of statistics as a major tool in assuring product quality is usually dated to May 16, 1924, when Dr. Walter A. Shewhart of Bell Laboratories wrote his famous internal memorandum describing for the first time a control chart. It was then used at the Western Electric Hawthorne Works manufacturing plant in Cicero, Illinois, to study fuses and heat controls. The rest, as they say, is history.

Lynn D. Torbeck

During and since World War II, the use of statistics blossomed in American industry. By the mid-1970s, Japan had caught up and then expanded the use of data and analysis for product quality. Following Dr. W. Edwards Deming's philosophy, great progress was made in minimizing variability and waste.

However, statistics have not been used consistently by the pharmaceutical industry. Historically, large firms such as Abbott, Baxter, Smith Kline and French, and others had staff formally trained in statistical quality and process control. But often, small to mid-sized firms did not have anyone on staff with statistical training. These companies frequently received FDA 483 citations and warning letters for not meeting the statistical requirements of cGMPs.

The situation has changed little today. Many companies do not have anyone on staff who can implement a control chart correctly or explain the concepts behind sampling plans. This is true even though cGMPs require that staff "... shall have education, training, and experience, or any combination thereof, to enable that person to perform the assigned functions" (1).

There are indications that this may be changing in the future. FDA's guidance for industry on process validation and the International Committee for Harmonization's (ICH) guidelines for product development and risk management have attracted the attention of influential people in the industry as well as other departments in FDA (2). FDA has been training its staff in statistics for some time and apparently expects to continue. Questions concerning the application of statistics to product quality may be coming to a 483 near you soon.

In the meantime, what should personnel working in pharmaceutical quality know about applied statistics? At a minimum, the quality department should have a team with at least one person who is a certified quality engineer (CQE), as recognized by the American Society for Quality (ASQ), or who has a Bachelor's degree with a major in statistics. The person should also have a background in engineering or a physical science.

In addition to the necessary training in applied statistics for quality, the team should be acquainted with the statistical issues in the following industry documents:

  • 21 CFR 210 and 211 cGMP in Manufacturing, Processing, Packing, or Holding of Drugs and Finished Pharmaceuticals

  • 21 CFR 600 Biological Products: General

  • 21 CFR 820 Quality Systems Regulations

  • Guidance for Industry: Investigating Out-of-Specification Test Results for Pharmaceutical Production (FDA, Oct. 2006)

  • Guidance for Industry: Process Validation: General Principles and Practices (FDA, Jan. 2011).

The quality team also should have access to the current edition of the United States Pharmacopeia (USP) and the Pharmaceutical Forum. The following chapters are the minimum that should be reviewed for their statistical content:

  • General Notices and Requirements

  • USP, Guide to General Chapters:

<616> Bulk Density and Tapped Density

<701> Disintegration

<711> Dissolution

<788> Particulate Matter in Injections

<905> Uniformity of Dosage Units

<1010> Analytical Data–Interpretation and Treatment

<1150> Pharmaceutical Stability

<1223> Validation of Alternative Microbiological Methods

<1225> Validation of Compendial Procedures

<1226> Verification of Compendial Procedures

<1227> Validation of Microbial Recover


Every member of the quality team must be acquainted with the ICH documents as well. One or more of the team must be expert in the statistics contained in the following ICH harmonized quality guidelines (available online at

  • Q1A(R2) Stability Testing of New Drug Substances and Products

  • Q1B Stability Testing: Photostability Testing of New Substances and Products

  • Q1C Stability of New Drug Products

  • Q1D Bracketing and Matrixing for Stability Testing of New Drug Substances and Products

  • Q1E Evaluation of Stability Data

  • Q1F Stability Data Package for Registration Applications in Climatic Zones III and IV

  • Q2(R1) Validation of Analytical Procedures: Text and Methodology

  • Q5C Stability Testing of Biotechnology/Biological Products

  • Q6A Specifications: Test Procedures and Acceptance Criteria for New Drug Substances and New Drug Products: Chemical Substances

  • Q6B Specifications: Test Procedures and Acceptance Criteria for Biotechnology/Biological Products

  • Q7 Good Manufacturing Practice Guide for Active Pharmaceutical Ingredients

  • Q8(R2) Pharmaceutical Development

  • Q9 Quality Risk Management.

Sampling plans are the weakest area in pharmaceutical quality. The team must be trained and competent. Not to do so is to expose the company to great risk of material and product failures.

The team must have copies of the following documents for immediate reference when questions arise.

  • American National Standard/American Society for Quality, Z1.9 Sampling Procedures and Tables for Inspection by Variables for Percent Nonconforming (ASQ, 1993)

  • American National Standard/American Society for Quality, Z1.4 Sampling Procedures and Tables for Inspection by Attributes (ASQ, 2003)

  • International Organization for Standardization, International Standard 2859/2 Sampling Procedures for Inspection by Attributes (Part 2: Sampling Plans Indexed by Limiting Quality for Isolated Lot Inspection) (ISO, 1985)

  • US Department of Defense, DOD Preferred Methods for Acceptance of Product, MIL-STD-1916 (DOD, 1996)

  • L. D. Torbeck, "Square Root of (N) +1 Sampling Plans," Pharm. Technol. (October 2009).

There are 30 ASTM International standards for statistics; far too many to list here. Readers are encouraged to consider them all for application. One new standard of particular note though is E2709, Standard Practice for Demonstrating Capability to Comply with a Lot Acceptance Procedure.

Other quality experts and statisticians will have additional topics they consider important but the material mentioned here is an excellent start. Not everyone needs be an expert in everything, but the quality team must be able to defend their performance in these complex topics with authority, competence, and confidence.

Statistics in the service of quality is not for the unqualified. All clinical trials are designed and analyzed by professional statisticians. We can do no less in the quality department—patients' lives depend upon it.

Lynn D. Torbeck is a statistician at Torbeck and Assoc., 2000 Dempster Plaza, Evanston, IL 60202, tel. 847.424.1314,,


1. Code of Federal Regulations, Title 21, Food and Drugs (Government Printing Office, Washington, DC), Part 211.25.

2. FDA, Guidance for Industry: Process Validation: General Principles and Practices (CDER, Silver Spring, MD, Jan. 2011).