1

Using Control Charts to Evaluate Process Variability

Daniel Y. Peng, Ph.D. Quality Assessment Lead

Office of Process and Facility (OPF) OPQ/CDER/FDA

PQRI 2015 Annual Meeting North Bethesda, Maryland

October 5, 2015

Walter Andrew Shewhart (1891-1967)

A physicist, engineer and statistician “Father of statistical quality control”

– “Statistical method from the viewpoint of quality control” (1939)

“Creator of PDSA (Plan, Do, Study and Act) cycle” “Creator of control chart” Originator of the “Chance and

Assignable variation” concept 2

“Uncontrolled variation is the enemy of quality”

3

Dr. W. Edwards Deming (1900-1993)

4

Sources of Variation

Variation exists in all processes. Variation can be categorized as either:

– Chance or Common causes of variation • Inherent to a system, random, always present and

hence predictable within statistical limits • Eliminate inherent variability (noise) is difficult

– Assignable or Special causes of variation • Exterior to a system, non-random, not always present

(intermittent) • can cause changes in the output level, such as a spike,

shift, drift, or non-random distribution of the output. • Are usually easier to be detected, controlled or

eliminated

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Control Chart

Definition: a graphical display of a product quality characteristic that has been measured or computed periodically from a process at a defined frequency

Every control chart consists of: – A set of data – A central line (CL) (mean) – Two statistical process control limits (UCL and LCL) (Is the process Stable?)

Upper and Lower Specification Limits (USL and LSL) – Patient’s need ( Safety and Efficacy) (Is the process Capable?)

Quality attribute (unit)

Sample #

4.0

5.0

6.0

30 40 50 60

USL

LSL

CL

UCL

LCL

Potential Applications

To proactively monitor and trend a process To detect the presence of special cause variation To identify continual improvement opportunities To maintain the process in a state of statistical

control – Using science and risk-based approach – Take action in a timely manner

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Key Considerations for Constructing a Control Chart

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Choice of Product Quality Characteristics Critical Quality Attributes (CQA)

– A physical, chemical, biological or microbiological property or characteristic of an output material including finished drug product that should be within an appropriate limit, range, or distribution to ensure the desired product quality (ICH Q8)

– Identification of CQA: primarily based upon the severity of harm to the patient (safety and efficacy)

Critical (input) material attributes and critical process parameters (CMAs/CPPs) Other relevant process characteristics that can

assist in process monitoring and controlling 8

9

Types of Control Chart Variable Control Chart

– Characteristics that can be measured (continuous numeric data) e.g. Assay, Dissolution, % of Impurity…

– The average and variability charts are usually prepared and analyzed in pairs • Average – Range chart (Xbar-R chart, subgroup size 2-10) • Average – Standard Deviation chart (Xbar-S chart, subgroup size >10) • Individual – Moving Range chart (I-MR chart, n=1)

Attribute Control Chart – Characteristics that have discrete values and can be counted, e.g. % defective, #

of failed batches in a month – p chart / np Chart: for fraction of occurrence of an event- Binominal distribution

• e.g. % of unsuccessful batch at a facility every month – c chart / nc Chart: for counts of occurrence in a defined time or space increment

-Poisson distribution • e.g. number of particulate matter in an injection vial

Other types of control chart: – cumulative sum control chart (CUSUM) – exponentially weighted moving average control charts (EWMA)

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Subgroup Size and Sampling Frequency Subgroup: the observations sampled at a particular

time point Subgroup Size and Sampling Frequency (N x K)

– The number of observations in each subgroup: 1 n – the objective of the monitoring (detect large or small shift) – how quickly the output responds to upsets – consequences of not reacting promptly to a process upset – time and cost of an observation

Rational Subgroup: – Minimize the variation of observations within a subgroup – Maximize variation between subgroups

Statistical Process Control Limits UCL and LCL:

– the thresholds at which the process output is considered statistically unlikely

– typically, ±3 SD (Shewhart limits)

Rationale: to balance the two risks: – Failing to signal the presence of a special

cause when one occurs; – False alarm of an out-of-control signal when

the process is actually in a state of statistical control

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How out-of-control points are identified? Rule No.1

– any point falls outside UCL/LCL

Other Rules – certain nonrandom

patterns of the plotted data

– Use it judiciously Risk of “false alarm”

12 8 Western Electric Rules

Over-Reaction vs. No-Reaction

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“Procedures should describe how trending and calculations are to be performed and should guard against overreaction to individual events as well as against failure to detect unintended process variability” (2011 FDA Process Validation Guidance)

Control chart and process capability analysis often go hand-in-hand

Illustrative Examples

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Within Batch Variability Example

ER coated beads, mixed with extra-granular cushioning excipients and compressed into tablets Compression: ~ 5h, sample frequency: every 8-10 min (total 33 subgroups), subgroup size= 6

16251602153915151452142913561338130912331054

45

40

35

30

25

Time

Sam

ple

Mea

n

__X=29.25UCL=31.75

LCL=26.75

16251602153915151452142913561338130912331054

10.0

7.5

5.0

2.5

0.0

Time

Sam

ple

Ran

ge

_R=5.17

UCL=10.36

LCL=0

1

111111

111

1

1

Xbar-R Chart of Disso@240min

Not Stable &

Not Capable

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Between Batch Variability Example

252321191715131197531

102

100

98

Batch No.

Subg

roup

Mea

n

__X=100.287

UCL=102.108

LCL=98.466

252321191715131197531

4

2

0

Batch No.

Subg

roup

Ran

ge

_R=1.78

UCL=4.582

LCL=0

252015105

104

102

100

98

96

Batch No.

Assa

y (%

)

1041021009896

LSL USL

LSL 96USL 104

Specifications

1051029996

Within

Overall

Specs

StDev 1.051Cp 1.27Cpk 1.18PPM 229.14

WithinStDev 1.079Pp 1.24Ppk 1.15Cpm *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

USP: 90-110

Cpk: 2.95

Stable &

Capable

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Between Batch Variability Example

Tablet content uniformity (AV) of last 30 commercial batches of Tablet X manufactured by Firm Y (subgroup size =1, I-MR chart)

55524946434037343128

5.0

2.5

0.0

Indi

vidu

al V

alue

_X=3.137

UCL=5.558

LCL=0.716

55524946434037343128

3.0

1.5

0.0

Mov

ing

Ran

ge

__MR=0.910

UCL=2.974

LCL=0

55524946434037343128

6

4

2

Batch No.

AV

1412108642

USL

USL 15Specifications

6420

Within

Overall

Specs

StDev 0.8070C p *C pk 4.90PPM 0.00

WithinStDev 0.9460Pp *Ppk 4.18C pm *PPM 0.00

O v erall

1

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Process Capability Analysis of Tablet X Content Uniformity (AV)I Chart

Moving Range Chart

Last 30 Observations

Capability Histogram

Normal Prob PlotAD: 0.637, P: 0.088

Capability Plot

Not Stable but

Capable

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Site Performance Monitoring Example

252321191715131197531

0.15

0.10

0.05

0.00

Month

Pro

po

rtio

n

_P=0.0437

UC L=0.1809

LC L=0

252015105

6

5

4

3

2

Month

Cu

mu

lati

ve

Un

succ

ess

Ra

te

Upper C I: 1.9123

%Defectiv e: 4.37Lower C I: 2.79Upper C I: 6.49Target: 0.00PPM Def: 43726Lower C I: 27917Upper C I: 64891Process Z: 1.7090Lower 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 BatchP Chart

Tests performed w ith unequal sample sizes

Cumulative Unsuccess Rate

Unsuccess Rate

Histogram

Binomial process capability index: 0.569

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

Stable but

Not Capable

Paradigm Shift – “Culture of Quality” Manufacturers take full responsibility for

quality of their products – Focus on meeting patients’ expectations – Regulators’ expectations considered minimal

approach Strive for continual improvement Management and organizational commitment

to prioritizing quality Each person in organization understands and

embraces their role in quality 19

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Summary Brief introduction of control chart: history, definition, types Key considerations for constructing a control chart:

– Choice of drug product quality characteristics – Subgroup size and sampling frequency – Statistical process control limits (UCL and LCL)

Illustrative examples for process monitoring and control: – Within batch variability – Between batch variability – Site performance monitoring

Control Chart can be a valuable tool to: – Proactively monitor and trend a process – Detect the presence of special cause variation – Identify continual improvement opportunities – Maintain the process in a state of statistical control

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Acknowledgements

Dr. Christine Moore Dr. Naiqi Ya Dr. Ubrani Venkataram