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Use Process Capability to Ensure Product Quality

Lawrence X. Yu, Ph.D. Director (acting)

Office of Pharmaceutical Science, CDER, FDA

FDA/ PQRI Conference on Evolving Product Quality September 16-17, 2104, Bethesda, MD

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Quality by Testing vs. Quality by Design

Quality by Testing

– Specification acceptance criteria are based on one or more batch data (process capability)

– Testing must be made to release batches

Quality by Design

– Specification acceptance criteria are based on performance

– Testing may not be necessary to release batches

L. X. Yu. Pharm. Res. 25:781-791 (2008)

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ICH Q6A: Test Procedures and Acceptance Criteria…

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Pharmaceutical QbD Objectives

Achieve meaningful product quality specifications that are based on assuring clinical performance

Increase process capability and reduce product variability and defects by enhancing product and process design, understanding, and control

Increase product development and manufacturing efficiencies

Enhance root cause analysis and post-approval change management

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Concept of Process Capability

First introduced in Statistical Quality Control Handbook by the Western Electric Company (1956).

– “process capability” is defined as “the natural or undisturbed performance after extraneous influences are eliminated. This is determined by plotting data on a control chart.”

ISO, AIAG, ASQ, ASTM ….. published their guideline or manual on process capability index calculation

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Four indices:

– Cp: process capability index

– Cpk: minimum process capability index

– Pp: process performance index

– Ppk: minimum process performance index

Nomenclature

ASTM E2281: Standard Practice for Process and Measurement Capability Indices

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Calculation Formula

Cpk= min (Cpkl, Cpku) Ppk= min (Ppkl, Ppku)

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)( LSLUSLCp

SD

LSLUSLPp

6

)(

3

LSLMeanCpkl

3

MeanUSLCpku

SD

LSLMeanPpkl

3

SD

MeanUSLPpku

3

USL: upper specification limit; LSL: lower specification limit;

Mean: grand average of all the data

Sigma hat: estimated inherent variability (noise) of a stable process

SD: overall variability

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A Perfectly Centered Process… USL

LSL

-5 -4 -3 -2 -1 0 1 2 3 4 5

LSL

USL

For this case:

USL= +4σ

LSL = -4σ

USL-LSL= 8σ

Cp= 1.333

Cpku=1.333

Cpkl=1.333

Cpk=1.333

Mean (μ ), Sigma (σ)

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Process Mean is not Centered…

When the process is not centered, or deliberately run off-center for economic

reasons, or only a single specification limit is involved, Cpk should be used.

Similarly, Ppk offsets Pp weakness by introducing process mean in the calculation formula.

For this case: USL= +4σ LSL = -4σ USL-LSL= 8σ Cp= 1.333 Cpkl = 1.667 Cpku = 1.0 Cpk= 1.0

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Cpk, Sigma Value, and PPM

Cpk Value

Sigma Value

Area under normal

distribution curve (%)*

Non conforming parts per million (ppm) Capability Rating**

Unilateral specification Bilateral specification*

0.333 1 68.27 158650 317300 Terrible

0.667 2 95.45 22750 45500 Poor

1.0 3 99.73 1350 2700 Marginally

capable

1.333 4 99.993636 32 64 Capable

1.667 5 99.999942 0.29 0.58 Good

2.0 6 99.9999998 0.001 0.002 Excellent

*Process mean is centered at middle of the specification limits and has normal distribution

**Bothe, D. R., Measuring Process Capability, Cedarburg, W.I., Landmark Publishing Inc., 2001

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Difference between Cpk and Ppk

inherent variability overall variability

N

i

i

N

XXSD

1

2

1

)(

422 c

Sor

d

MRor

d

R

SD: standard deviation of all individual (observed) values, which accounts for both common cause variability (noise) and special cause variability. It is often referred as overall variability.

: the inherent variability (noise) due to common cause of a stable process. It is often estimated by using within subgroup variability which is linked to the use of control charts.

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Difference between Cpk and Ppk

Cpk represents the potential process capability (i.e.

how well a given process could perform when all

special causes have been eliminated).

Ppk addresses how the process has performed

without the demonstration of the process to be

stable.

Forecast future batch failure rate

– Cpk (Yes) ; Ppk (No)

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Control Chart

To evaluate if a process is in a state of statistical control – Western Electric 8 Rules

Two Types of Control Chart – Variable control chart: continuous numeric measurements

(e.g. assay, dissolution, uniformity, impurity level) – Attribute control chart: discrete data (pass or fail, or

counts of defects)

CL: the grand average UCL and LCL:

• Typically: 3SD from CL • Should not be confused with upper and lower specification limits

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Variable Control Chart

The average chart (X-bar chart)

The variability chart – Moving range chart (MR chart, n=1)

– Range chart (R-chart, subgroup size 2-10)

– Standard deviation chart (S-chart, subgroup size >10)

The average and variability charts are usually prepared and analyzed in pairs.

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Example Xbar-R Chart

252321191715131197531

102

100

98

Batch No.

Su

bg

rou

p M

ea

n

__X=100.287

UCL=102.108

LCL=98.466

252321191715131197531

4

2

0

Batch No.

Su

bg

rou

p R

an

ge

_R=1.78

UCL=4.582

LCL=0

252015105

104

102

100

98

96

Batch No.

Assa

y (

%)

1041021009896

LSL USL

LSL 96

USL 104

Specifications

1051029996

Within

Overall

Specs

StDev 1.051

Cp 1.27

Cpk 1.18

PPM 229.14

Within

StDev 1.079

Pp 1.24

Ppk 1.15

Cpm *

PPM 323.15

Overall

Process Capability Analysis of Tablet Assay (first 25 batches, subgroup size =3)

Xbar Chart

R Chart

Run Chart

Capability Histogram

Normal Prob PlotA D: 0.636, P: 0.094

Capability Plot

Data source: Chopra, V., Bairagi, M., Trivedi, P., et al., “A case study: application of statistical process control tool for determining process capability and sigma level,” PDA J Pharm Sci and Tech, 66 (2), 2012, pp. 98-115

Cp: 1.27

Cpk: 1.18

Ppk: 1.15

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Attribute Control Chart

Control chart for fraction occurrence of an event (p chart) – For example: % of unsuccessful batch at Site A every month

– Binominal distribution

Control chart for counts of occurrence in a defined time or space increment (c chart) – For example: number of particulate matter in an injection vial

– Poisson distribution

Other types of control chart: – cumulative sum control chart (CUSUM)

– exponentially weighted moving average control charts (EWMA)

– etc.

ASTM E2587- Standard Practice for Use of Control Charts in Statistical Process Control

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Example P chart

252321191715131197531

0.15

0.10

0.05

0.00

Month

Pro

po

rti

on

_P=0.0437

UC L=0.1809

LC L=0

252015105

6

5

4

3

2

Month

Cu

mu

lati

ve

Un

su

cce

ss R

ate

Upper C I: 1.9123

%Defectiv e: 4.37

Lower C I: 2.79

Upper C I: 6.49

Target: 0.00

PPM Def: 43726

Lower C I: 27917

Upper C I: 64891

Process Z: 1.7090

Lower C I: 1.5150

(95.0% confidence)

Summary Stats

302520

20

10

0

T otal Batch Manufactured/Month

% U

nsu

cce

ss R

ate

129630

10.0

7.5

5.0

2.5

0.0

% Unsuccess Rate

Fre

qu

en

cy

Tar

Binomial Process Capability Analysis of Unsuccess Batch

P Chart

Tests performed w ith unequal sample sizes

Cumulative Unsuccess Rate

Unsuccess Rate

Histogram

Similar principles can be used to evaluate process capability of a single product, a product class, different manufacture sites, or a manufacturer global sites.

Process-Z: 1.709

Binomial process capability index:

0.569 Lower 95%

confidence bound 0.505

% of “unsuccessful batch”/month at Site A (# of lots attempted: 20-30/month)

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Summary: Process Capability Indices

Patient first: clinical relevant specification

Consider not only process mean & variability but also in relation to the specification

Quantitative and action enabling

Applicable for cross sectors (brand, generic, OTC and biotech)

No additional testing is required since batch release data is available per current regulation

A simple and powerful indicator to ensure product quality and process robustness.

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Acknowledgements

Daniel Peng

Alex Viehmann

Karthik Iyer