## Description

ISBN 978-0-9635122-9-1, 8.5 x 11, 592 pages

By: Dr. Wayne A. Taylor

Provides statistical procedures designed to ensure that all statistical regulatory requirements for medical devices are met. These regulatory requirements can be found in:

- Code of Federal Regulation 21CFR, Part 820 Quality System Regulations
- ISO 13485:2016, Medical devices – Quality management systems – Requirements for regulatory purposes

This book is designed for engineers and scientists in the medical device industry. However, it is also useful for any engineer or scientists involved in product design, process development or manufacturing.

## Aids and References:

**Tables:** The procedures include extensive tables of sampling plans for both validation and manufacturing.

**Spreadsheets:** On the spreadsheet tab.

**Technical Briefs:** While the procedures provide rationales and justifications supporting the recommended approaches. They also reference the following technical briefs:

**Books:** Further details about the statistical techniques covered by the procedures are available in the following books:

**Courses**: Training on all the procedures is available.

## List of Procedures

**Policy and General:** STAT-01 is the general policy procedure and STAT-02 provides definitions used by the procedures.

STAT-01 Statistical Policy

STAT-02 Glossary of Statistical Terms

**Areas of Application:** STAT-03 to STAT-11 describe the statistical requirements for each area of application. They may also provide statistical techniques that are specific to that area of application or reference a supporting statistical technique procedure.

STAT-03 Statistical Techniques for Process Validation

STAT-04 Statistical Techniques for Design Verification

STAT-05 Statistical Techniques for Component/Material Qualifications

STAT-06 Statistical Techniques for Design Validation

STAT-07 Statistical Techniques for Audits and Effectiveness Checks

STAT-08 Statistical Techniques for Test Method Validation

STAT-09 Manufacturing Acceptance Sampling Plans and Inspections

STAT-10 Statistical Techniques for Trending Data

STAT-11 Statistical Techniques for Setting Specifications

**Supporting Statistical Techniques:** STAT-12 to STAT-19 describe specific statistical techniques. They do not specify any additional requirements beyond those in the policy and application procedures.

STAT-12 Verification/Validation Sampling Plans for Proportion Nonconforming

STAT-13 Verification/Validation Sampling Plans for Rate of Nonconformities

STAT-14 Verification/Validation Sampling Plans for Average

STAT-15 Verification/Validation Sampling Plans for Standard Deviation and RSD

STAT-16 Statistical Techniques for Equivalence Testing

STAT-17 Statistical Techniques for Reliability Life Testing

STAT-18 Statistical Techniques for Normality Testing and Transformations

STAT-19 Rounding of Data

## Statistical Techniques

This book includes step-by-step instruction for executing the 43 statistical techniques included below. For many of the procedures validated spreadsheets are provided. For selecting sampling plans, extensive tables are provided. Otherwise, instructions are provided for executing the procedure in Minitab, Distribution Analyzer, Change-Point Analyzer, Sampling Plan Analyzer and VarTran® software packages.

Area/Statistical Technique | Where to Find |

**Confidence Intervals – 1 Group** | |

Upper Confidence Limit for Percent Conforming – Attribute Data | STAT-12, Appendix D |

Upper Confidence Limit for Percent Conforming – Variables Data | STAT-12, Appendix E |

Upper Confidence Limit for Rate of Nonconformities | STAT-13, Appendix D |

Confidence Limits for the Average | STAT-14, Appendix A |

Upper Confidence Limit for Standard Deviations | STAT-15, Appendix I |

Upper Confidence Limit for Relative Standard Deviations | STAT-15, Appendix J |

**Confidence Intervals – 2 Groups** | |

Confidence Limits for the Difference between Two Averages | STAT-16, Appendix A |

Confidence Limits for the Difference between Two Averages – Paired Data | STAT-16, Appendix C |

Confidence Limits for the Ratio of Two Standard Deviations | STAT-16, Appendix D |

**Equivalence Tests** | |

Equivalence Test for the Average | STAT-14, Appendix B |

Equivalence Test for Two Averages | STAT-16, Appendix B |

Equivalence Test for Two Averages – Paired Data | STAT-16, Appendix D |

Equivalence Test for Two Standard Deviations | STAT-16, Appendix F |

**General Techniques** | |

Regression Analysis – Correlation Study for Substitute Measurement Methods | STAT-08, Appendix I |

Analysis of Variance (ANOVA) | STAT-18, Appendix E |

Kruskal-Wallis Test | STAT-18, Appendix F |

Capability Study | STAT-11, Appendix F |

Screening Experiment – Design of Experiment | STAT-11, Appendix D |

Response Surface Study – Design of Experiments | STAT-11, Appendix E |

**Normality Test** | |

General Normality Tests (Anderson-Darling, Shapiro-Wilk and Skewness-Kurtosis All) | STAT-18, Appendix A |

Skewness-Kurtosis Specific Normality Test | STAT-18, Appendix C |

**Sampling Plans (Also see Equivalence Tests)** | |

Attribute Single and Double Sampling Plans for Proportion Nonconforming | STAT-07, Appendix A
STAT-09, Appendix A
STAT-12, Appendix A |

Variables Single and Double Sampling Plans for Proportion Nonconforming | STAT-09, Appendix A
STAT-12, Appendix B |

Narrow Limit Gauging Single and Double Sampling Plans for Proportion Nonconforming | STAT-09, Appendix A |

Single and Double Sampling Plans for Rate of Nonconformities | STAT-07, Appendix B
STAT-13, Appendix A |

Single and Double Sampling Plans for Standard Deviations | STAT-15, Appendix A |

Single and Double Sampling Plans for Relative Standard Deviations | STAT-15, Appendix B |

Product Life Sampling Plans – Parametric with Specified Test Time | STAT-17, Appendix A |

Product Life Sampling Plans – Censored Failure Time Plans | STAT-17, Appendix B |

**Specification Setting** | |

Tolerance Analysis | STAT-11, Appendix A |

Tolerance Sensitivity Analysis | STAT-11, Appendix B |

Robust Design using Tolerance Analysis | STAT-11, Appendix C |

**Test Method Validations** | |

Gauge R&R Study | STAT-08, Appendix B |

Gauge Reproducibility Study (Variance Components Analysis) | STAT-08, Appendix C |

**Trending Tools** | |

Pareto Chart | STAT-10, Appendix A |

or Average-Standard Deviation Control Chart | STAT-10, Appendix B |

Normalized I_{N} Chart for Individual Values | STAT-10, Appendix C |

Box-Cox I Chart | STAT-10, Appendix D |

U Chart for Counts with Independent Events | STAT-10, Appendix E |

P Chart for Pass/Fail Proportions with Independent Events | STAT-10, Appendix F |

Laney U’ Chart for Counts with Dependent Events | STAT-10, Appendix G |

Laney P’ Chart for Pass/Fail Proportions with Dependent Events | STAT-10, Appendix H |

Change-Point Analysis | STAT-10, Appendix I |

## Spreadsheets

The spreadsheets below are provided as part of purchasing or licensing the book Statistical Procedures for the Medical Device Industry. Permission is granted to purchasers of the book to use and modify the spreadsheets for their personal use. Permission is granted to companies licensing one of the procedures in the title of the Excel file to use and modify the spreadsheet for use within the company per the book’s licensing agreement.

There are two versions of each spreadsheet. The first is protected. Only cells required to enter data and select options can be altered. This is the version used for the validation as this ensures the formulas cannot be changed. However, tabs can be deleted and copied to customize the layout of the spreadsheet. The second version is unprotected. This allows access to the formulas and allows the spreadsheets to be customized.

The protected versions have been validated as required in the medical device industry. The validation package can also be downloaded below.

## STAT-10 – Control Charts.xlsx

**Download STAT-10 - Control Charts - Protected**

**Download STAT-10 - Control Charts - Unprotected**

**Download STAT-10 - Control Charts - Validation Report PDF**

## STAT-12 to 16 – Confidence Intervals and Equivalence Tests.xlsx

**Download STAT-12 to 16 - Confidence Intervals and Equivalence Tests - Protected**

**Download STAT-12 to 16 - Confidence Intervals and Equivalence Tests - Unprotected**

**Download STAT-12 to 16 - Confidence Intervals and Equivalence Tests - Validation PDF**

## STAT-18 – Skewness Kurtosis Normality Tests.xlsx

**Download STAT-18 - Skewness Kurtosis Normality Tests - Protected**

**Download STAT-18 - Skewness Kurtosis Normality Tests - Unprotected**

**Download STAT-18 - Skewness Kurtosis Normality Tests - Validation Report PDF**

## Errata

**Errata for Second and First Printing**

Multiple occurrences of the word gage should be replaced with gauge.

** STAT-02 Glossary of Statistical Terms **

Page 24, under definition for Distribution function, “average of 7” should be “average of 10.”

**STAT-03 Statistical Techniques for Process Validation**

Pages 35, 38 and 48, “OC characterization” should be “OQ characterization”

**STAT-08 Statistical Techniques for Test Method Validation**

Page 119, the guardband equations are in error and should read as shown below.

Lower guardband limit = LSL + Max_{bias} + K x UCL_{σ-guardband}

Upper guardband limit = USL + Min_{bias} – K x UCL_{σ-guardband}

** STAT-12 Verification/Validation Sampling Plans for Proportion Nonconforming**

Page 360, for 95/90 Variables—One-Sided Specification the P_{pk} acceptance criterion for n=15 can be reduced from 0.70 to 0.69.

** STAT-18 Statistical Techniques for Normality Testing and Transformations**

Page 570, Section 6.1 should say: “For a single normality test, the test is

considered to pass if the p-value is > 0.05.”

##### Errata for First Printing

They have been corrected in the current second printing.

** Table of Content and elsewhere**

STAT-10 title has “tending” rather than “trending”.

** Introduction**

Table 1 of page 3. RNP should be RPN.

** STAT-02 Glossary**

Page 25, kurtosis, as defined here, is sometimes referred to as the excess kurtosis and is the statistical kurtosis minus 3.

** STAT-08 Statistical Techniques for Test Method Validation**

Page 101, the reference in Section 6.3.2 to Section 6.3 should be a reference to Section 6.3.1.

** STAT-09 Manufacturing Acceptance Sampling Plans and Inspections**

Page 142, Example box should give n=80, a=2 as the “also use” sampling plan rather than n=80, a=3.

Page 162, the AQL=10%, L-3, Variables Single, σ unknown plan is in error. Change MSD to 333.3%.

Page 173 the AQL=1%, L-8, Variables Single, σ unknown plan is in error. Change MSD to 22.5%.

** STAT-10 Statistical Techniques for Trending**

Page 200, the last sentence should reference Appendix I and not Appendix J.

Page 214 the equations for the control limit should be as shown below.

Page 233 the equations for the control limits of the I_{N} chart should be as shown below.

Page 247, bottom right, 0.000502 should be 0.000557.

** STAT-13 Verification/Validation Sampling Plans for Rate of Nonconformities**

Page 424 makes reference to the Beta distribution. It should have referenced the Gamma distribution. There are also some formatting issues.

** STAT-15 Verification/Validation Sampling Plans for Standard Deviation and RSD**

Page 471 shows screenshots for 95% confidence rather than the 90% confidence stated in the text. The confidence statements given in the text are correct but do not align with the graphic.

Page 472 shows formulas for the confidence intervals for the standard deviation. These formulas use the CHIINV function in Excel, which returns the inverse of the right-tailed chi-squared distribution function. These are the formulas used in the spreadsheet. For the more common inverse of the left-tailed chi-squared distribution function, reverse the formulas for the upper and lower confidence limits.

** STAT-17 Statistical Techniques for Reliability Life Testing**

Page 530, the last two paragraphs of the example should read:

To select a plan, use Appendix B of STAT-13. The ratio RQL/AQL = 4. The

resulting single sampling plan is n = 11.8424/RQL, a = 6. Plugging 2 in for the RQL

results in n = 5.9212. This can be rounded up to n = 6 years.

It is desired to complete the testing within 6 months. This requires testing 12 pumps

for half a year to produce 6 years of test time. If 6 or fewer service events occur,

the sampling plan passes, and it can be stated with 95% confidence that the rate of

service events is below 2 per year.

Page 531, the same changes should be made to the last two paragraphs of the example.

** STAT-18 Statistical Techniques for Normality Test and Transformations**

Page 565 if states Z_{k} is valid for n≥20. Simulations demonstrate it is valid for n≥15.