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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
5
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
6
Key Considerations for Constructing a Control Chart
7
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)
10
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
11
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
13
“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
14
15
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
16
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
17
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
11
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
18
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
20
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
21
Acknowledgements
Dr. Christine Moore Dr. Naiqi Ya Dr. Ubrani Venkataram