1. Process Analysis (CEP)

ANVISA guidance requires the various pharmaceutical industries to carry out a statistical evaluation of the results of in-process and finished product control. The methodology presented here is well-founded and follows the requirements of the ANVISA Guide (2012). Action Stat provides a statistical tool that allows the generation of complete product quality analysis reports, containing a statistical methodology that follows the following flow: first, an exploratory analysis of the results is carried out with a descriptive summary and a BoxPlot graph. This is followed by a distribution fit test. Next, the stability of the process is assessed using control charts. This is followed by an assessment of the capacity and performance of the process and, finally, a multiple lots comparison test.

Analysis of CEP

To assess the stability of results over time, analysis using CEP graphs is most often used. However, this technique is only recommended in cases where there are not many subgroups of data. The recommendation is a maximum of 150 subgroups to allow proper interpretation of the control chart. In cases where there are more than 150 subgroups, it would be best to perform time series analysis.

Example 1:

An analyst has measured the content of a substance for 31 production batches of a particular tablet over the course of the year. The aim is to generate a complete statistical report of the process review:

Lots Content
2400001 98.78
2400002 95.53
2400003 98.37
2400004 100.41
2400005 96.54
2400006 94.12
2400007 96.13
2400008 94.96
2400009 98.00
2400010 97.54
2400011 98.74
2400012 92.60
2400013 96.63
2400014 104.64
2400015 97.38
2400016 94.91
2400017 100.44
2400018 92.57
2400019 95.97
2400020 97.06
2400021 95.19
2400022 92.12
2400023 99.06
2400024 104.13
2400025 102.01
2400026 99.13
2400027 96.73
2400028 97.27
2400029 98.19
2400030 98.58
2400031 101.18

We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis.

Then click Calculate we obtain the results. You can also generate the analyses and download them in Word format.

Los resultados son:

Descriptive summary

Statistics
Minimum 92.12
1º Quartile 95.53
Mean 97.5777
Median 97.38
Tri-Mean 97.4736
3º quartile 99.06
Maximum 104.64
Standard Desviation 3.0247
Coefficient of variation (%) 3.0998
Asymmetry 0.3541
Kurtosis -0.1224
Range 12.52
Sample Size 31

Outliers

The Order of Collection Data
1 14 104,64

Automatic Analysis

Process Analysis Situation
1 Normality Test Accept a 0.05 significance level
2 Box-Cox Transformation No Aplicable
3 Johnson Transformation No Aplicable
4 Non-Normal Distribution No Aplicable
5 Non-Parametric Distribution NO Aplicable

Normality test

Statistics P-Value
Anderson Darling 0,2613 0,6836

Specifications

Value
1 Sample 31
2 Lower Limit 90
3 Upper Limit 110

Estimates

Value
Mean 97.5777
Standard Desviation (Short term) 2.8625
Desviación Estándar (Long term) 3.0247

Performance Indices (Long term)

Performance Indexes - Total Variability
PP 1.1020
PPL 0.8351
PPU 1.3690
PPK 0.8351

Capacity Indices (short term)

Capacity Indices - Inherent Variability
CP 1.1645
CPI 0.8824
CPS 1.4465
CPK 0.8824

Observed Indices

Observed Indices
PPM < LIE 0
PPM > LSE 0
PPM Total 0

Observed Indices (Long Term)

Observed Indices (Total Variability)
PPM < LIE 6118.1571
PPM > LSE 20.0514
PPM Total 6138.2086

Expected Indexes (Short term)

Expected Indexes (Inherent Variability)
PPM < LSL 4057.6342
PPM > USL 7.1359
PPM Total 4064.7701

SIGMA LEVEL

SIGMA Level
Zbench (long term) 2.5041
Zbench (short term) 2.6466
Zshift 1.5
Sigma Metrics 4.0041

Análisis Gráfico

Estabilidad del Proceso

Gráfico de Valores Individuales y Amplitudes móviles

Individual Values ​​Chart

Valor
Lower Control Limit 88.9902
Center line 97.5777
Upper Control Limit 106.1653

Moving Range Chart

Value
Lower Control Limit 0
Center Line 3.23
Upper Control Limit 10.5524

Example 2:

An analyst measured the weight in mg/pill of a substance for 30 lots divided into subgroups of size 3. The specifications LEL = 173 mg and LSE = 187 mg have been defined. The aim is to generate a complete statistical report to review the process:

Lots Weight
2024001 174.8
2024001 176.7
2024001 176.6
2024002 177.7
2024002 181.2
2024002 181.9
2024003 180.3
2024003 179.8
2024003 179
2024004 176.3
2024004 178.5
2024004 180.1
2024005 179.6
2024005 180.6
2024005 178.8
2024006 174.4
2024006 177.4
2024006 178.8
2024007 176.3
2024007 178
2024007 179.6
2024008 180
2024008 179.2
2024008 177.4
2024009 178.1
2024009 178.1
2024009 179.3
2024010 179.3
2024010 181.5
2024010 178.4
2024011 180.9
2024011 180.6
2024011 179.5
2024012 178.7
2024012 178.6
2024012 179.8
2024013 175.3
2024013 180.0
2024013 178.0
2024014 179.8
2024014 180.7
2024014 181.2
2024015 181.0
2024015 178.2
2024015 176.5
2024016 176.4
2024016 176.5
2024016 178.4
2024017 184.8
2024017 183.2
2024017 177.6
2024018 176.9
2024018 176.0
2024018 177.0
2024019 176.9
2024019 178.5
2024019 178.9
2024020 177.4
2024020 177.7
2024020 178.6
2024021 180.3
2024021 179.4
2024021 179.1
2024022 178.3
2024022 176.1
2024022 175.0
2024023 176.2
2024023 179.9
2024023 181.1
2024024 178.2
2024024 179.4
2024024 178.5
2024025 178.3
2024025 176.9
2024025 178.0
2024026 180.6
2024026 177.0
2024026 176.8
2024027 178.0
2024027 178.6
2024027 179.8
2024028 178.5
2024028 180.6
2024028 179.2
2024029 179.1
2024029 176.9
2024029 177.6
2024030 177.5
2024030 178.0
2024030 178.5

We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis.

Then click Calculate we obtain the results. You can also generate the analyses and download them in Word format.

The results are:

Descriptive summary

Statistics
Minimum 174.4
1º Quartile 177.4
Meana 178.5856
Median 178.5
Tri-Mean 178.5486
3º Quartile 179.8
Maximum 184.8
Standard Desviation 1.8197
Coefficient of Variation (%) 1.0189
Asymmetry 0.3461
Kurtosis 0.6338
Range 10.4
Sample Size 90

Outliers

The Order of Collection Data
1 17 184.8

Automatic Analysis

Process Analysis Situation
1 Normality Test Accept a 0.05 significance level
2 Box-Cox Transformation No Aplicable
3 Johnson Transformation No Aplicable
4 Non-Normal Distribution No Aplicable
5 Non-Parametric No Aplicable

Normality tests

Estatistics P-values
Anderson Darling 0.2273 0.8093

Specifications

Value
1 Sample 90
2 Lower Limit 173
3 Upper Limit 187

Estimates

Value
Mean 178.5856
Standard Desviation (Short term) 1.5184
Standard Desviation (Long term) 1.8197

Performance Indexes (Long term)

Performance Indexes (Total Variability)
PP 1.2823
PPL 1.0232
PPU 1.5414
PPK 1.0232

Capacity Indexes (Short term)

Capacity Indexes (Inherent Variability)
CP 1.5367
CPI 1.2262
CPS 1.8472
CPK 1.2262

Observed Indices

Observed Indices
PPM < LSL 0
PPM > USL 0
PPM Total 0

Expected Indexes (Long term)

Expected Indexes (Total Variability)
PPM < LSL 1071.8298
PPM > USL 1.8802
PPM Total 1073.7100

Expected Indexes (Short term)

Expected Indexes (Inherent Variability)
PPM < LSL 117.2693
PPM > USL 0.0150
PPM Total 117.2843

SIGMA LEVEL

SIGMA Level
Zbench (long term) 3.069
Zbench (short term) 3.6785
Zshift 1.5
Sigma Metrics 4.569

Análisis Gráfico

Process Stability - Mean and Range Graphs

Xbar Graph

Value
Lower Control Limit 175.9564
Center Line 178.5856
Upper Control Limit 181.2147

Range Chart

Value
Lower Control Limit 0
Center Line 2.57
Upper Control Limit 6.6152

Example 3:

An analyst has measured the weight in mg/pill of a substance for 10 lots, divided into subgroups of size 10. The specifications LSL = 13 and USL = 15 have been defined. The aim is to generate a complete statistical report to review the process:

Lot Hardness Lot Hardness
2024001 13.06 2024009 13.61
2024001 13.12 2024009 13.71
2024001 13.20 2024009 13.79
2024001 13.21 2024009 13.82
2024001 13.28 2024009 14.18
2024001 13.37 2024009 14.25
2024001 13.39 2024009 14.26
2024001 13.41 2024009 14.29
2024001 13.43 2024009 14.53
2024001 13.48 2024009 13.12
2024002 13.58 2024010 13.20
2024002 13.61 2024010 13.21
2024002 13.71 2024010 13.30
2024002 13.79 2024010 13.37
2024002 13.82 2024010 13.41
2024002 14.18 2024010 13.45
2024002 14.25 2024010 13.53
2024002 14.26 2024010 13.57
2024002 14.29 2024010 13.80
2024002 14.53 2024010 13.81
2024003 13.12 2024011 13.82
2024003 13.20 2024011 14.09
2024003 13.21 2024011 13.06
2024003 13.30 2024011 13.12
2024003 13.37 2024011 13.20
2024003 13.41 2024011 13.21
2024003 13.45 2024011 13.28
2024003 13.53 2024011 13.37
2024003 13.57 2024011 13.39
2024003 13.80 2024011 13.41
2024004 13.81 2024012 13.43
2024004 13.82 2024012 13.48
2024004 14.09 2024012 13.58
2024004 14.13 2024012 13.61
2024004 14.18 2024012 13.71
2024004 14.35 2024012 13.79
2024004 13.06 2024012 13.82
2024004 13.12 2024012 14.18
2024004 13.20 2024012 14.25
2024004 13.21 2024012 14.26
2024005 13.37 2024013 14.29
2024005 13.39 2024013 14.53
2024005 13.41 2024013 13.12
2024005 13.43 2024013 13.20
2024005 13.48 2024013 13.21
2024005 13.58 2024013 13.3
2024005 13.61 2024013 13.37
2024005 13.71 2024013 13.41
2024005 13.79 2024013 13.45
2024005 13.82 2024013 13.53
2024006 14.18 2024014 13.57
2024006 14.25 2024014 13.80
2024006 14.26 2024014 13.81
2024006 14.29 2024014 13.82
2024006 14.53 2024014 14.09
2024006 13.12 2024014 14.13
2024006 13.20 2024014 14.18
2024006 13.21 2024014 14.35
2024006 13.30 2024014 13.06
2024006 13.37 2024014 13.12
2024007 13.41 2024015 13.20
2024007 13.45 2024015 13.21
2024007 13.53 2024015 13.28
2024007 13.57 2024015 13.06
2024007 13.80 2024015 13.12
2024007 13.81 2024015 13.20
2024007 13.82 2024015 13.21
2024007 14.09 2024015 13.28
2024007 14.13 2024015 13.37
2024007 13.06 2024015 13.39
2024008 13.12 2024016 13.41
2024008 13.20 2024016 13.43
2024008 13.21 2024016 13.48
2024008 13.28 2024016 13.58
2024008 13.37 2024016 13.61
2024008 13.39 2024016 13.71
2024008 13.41 2024016 13.79
2024008 13.43 2024016 13.82
2024008 13.48 2024016 14.18
2024008 13.58 2024016 13.28

We will upload the data to the system.

Configuring as shown in the figure below to perform the analysis.

Then click Calculate we obtain the results. You can also generate the analyses and download them in Word format.

The results are:

Descriptive summary

Statistics
Minimum 13.06
1º Quartile 13.28
Mean 13.5972
Median 13.48
Tri-Mean 13.5662
3º Quartile 13.82
Maximum 14.53
Standard Desviation 0.3933
Coefficient of Variation (%) 2.8924
Asymmetry 0.6638
Kurtosis -0.6347
Range 1.47
Sample Size 160

Automatic Analysis

Process Analysis Situation
1 Normality Test Normality hypothesis rejected at 5% significance level
2 Box-Cox Transformation Could not use Box-cox transformation
3 Johnson Transformation Could not use Johnson transformation
4 Non-Normal Distribution It was not possible to use other parametric distribution
5 Non-Parametric Distribution The Kernel nonparametric method was used for the adjustment of the them.

Anderson-Darling

Distribution Statistics P-value
Normal($\mu$ = 13.6, $\sigma$ = 0.39) 4.3496 0.0000
Log-Normal(log($\mu$) = 2.60946, log($\sigma$) = 0.0285766) 4.0776 0.0000
Exponencial(Tasa = 0.0735443) 69.3914 0.0000
Logística(Posición = 13.56, Escala = 0.23) 3.8440 0.0050
Gamma(Shape = 1217.62, Rate = 89.5491) 4.1954 0.0050
Weibull(Shape = 33.1981, Scale = 13.7979) 7.0015 0.0100
Gumbel(Location = 13.416, Scale = 0.301584) 2.0802 0.0100

Process stability

Specification

Value
1 Sample 160
2 Lower Limit 13
3 Upper Limit 15

Estimates

Parameters Value
1 Mean 13.59725
2 Standard Desviation 0.393291144736697

Performance Indexes

Performance Indexes
1 PP 1.0353
2 PPL 0.7232
3 PPU 1.2156
4 PPK 0.7232

Observed Indices

Observed Indices
1 PPM > USL 0
2 PPM < LSL 0

Expected Indexes

Expected Indexes
1 PPM > USL 0
2 PPM < LSL 30774.1006085405
3 PPM Total 30774.1006085405

Fit Quality (Non-Parametric (Core): Method gaussian)

Method Statistic P-value
Cramér-von Mises gaussian 0.0929 0.7652
Kolmogorov-Smirnov gaussian 0.0750 0.7591

Normality Test (Outliers)

Obs. Normal Quantiles Data Criterion
1 1 -2.73 13.06 Envelope (Confidence Level=95%)
2 43 -2.35 13.06 Envelope (Confidence Level=95%)
3 63 -2.15 13.06 Envelope (Confidence Level=95%)
4 100 -2.02 13.06 Envelope (Confidence Level=95%)
5 142 -1.91 13.06 Envelope (Confidence Level=95%)
6 151 -1.82 13.06 Envelope (Confidence Level=95%)
7 3 -1.74 13.12 Envelope (Confidence Level=95%)
8 8 -1.68 13.12 Envelope (Confidence Level=95%)
9 17 -1.62 13.12 Envelope (Confidence Level=95%)
10 45 -1.56 13.12 Envelope (Confidence Level=95%)
11 59 -1.51 13.12 Envelope (Confidence Level=95%)
12 79 -1.46 13.12 Envelope (Confidence Level=95%)
13 86 -1.42 13.12 Envelope (Confidence Level=95%)
14 116 -1.38 13.12 Envelope (Confidence Level=95%)
15 10 -1.26 13.2 Envelope (Confidence Level=95%)
16 15 -1.23 13.2 Envelope (Confidence Level=95%)
17 19 -1.20 13.2 Envelope (Confidence Level=95%)
18 24 -1.17 13.2 Envelope (Confidence Level=95%)
19 33 -1.14 13.2 Envelope (Confidence Level=95%)
20 27 0.85 14.09 Envelope (Confidence Level=95%)
21 36 0.88 14.09 Envelope (Confidence Level=95%)
22 78 0.90 14.09 Envelope (Confidence Level=95%)
23 119 0.92 14.09 Envelope (Confidence Level=95%)
24 52 0.95 14.13 Envelope (Confidence Level=95%)
25 94 0.97 14.13 Envelope (Confidence Level=95%)
26 135 1.00 14.13 Envelope (Confidence Level=95%)
27 6 1.02 14.18 Envelope (Confidence Level=95%)
28 68 1.05 14.18 Envelope (Confidence Level=95%)
29 73 1.08 14.18 Envelope (Confidence Level=95%)
30 82 1.11 14.18 Envelope (Confidence Level=95%)
31 110 1.14 14.18 Envelope (Confidence Level=95%)
32 124 1.17 14.18 Envelope (Confidence Level=95%)
33 144 1.20 14.18 Envelope (Confidence Level=95%)
34 22 1.23 14.25 Envelope (Confidence Level=95%)
35 89 1.26 14.25 Envelope (Confidence Level=95%)
36 98 1.30 14.25 Envelope (Confidence Level=95%)
37 140 1.34 14.25 Envelope (Confidence Level=95%)
38 38 1.38 14.26 Envelope (Confidence Level=95%)
39 105 1.42 14.26 Envelope (Confidence Level=95%)
40 114 1.46 14.26 Envelope (Confidence Level=95%)
41 129 -0.10 13.43 Envelope (Confidence Level=95%)
42 99 -0.05 13.45 Envelope (Confidence Level=95%)
43 141 -0.04 13.45 Envelope (Confidence Level=95%)
44 136 0.02 13.48 Envelope (Confidence Level=95%)
45 145 0.04 13.48 Envelope (Confidence Level=95%)

Process stability

Xbar Graph

Value
Lower Control Limit 13.2961
Center Line 13.5972
Upper control Limit 13.8984

Standard Deviation graph

Value
Lower Control Limit 0.0876
Center Line 0.3088
Upper Control Limit 0.53

Kruskal-Wallis test

Value
Statistics 54.2338
Degrees of Freedom 15
P-value 0

Table of Grouped comparison of Groups (Kruskal Wallis)

Factor Mean Median Mean ofyhe Ranks Groups
2024002 14.0020 14.0000 127.3000 a
2024009 13.9560 14.0000 119.0500 ab
2024012 13.8110 13.7500 111.5000 ab
2024014 13.7930 13.8150 101.8500 abc
2024007 13.6670 13.6850 93.9500 abc
2024016 13.6290 13.5950 92.6500 abcd
2024006 13.7710 13.7750 90.3000 bcd
2024004 13.6970 13.8150 86.8500 bcde
2024005 13.5590 13.5300 85.7000 bcde
2024013 13.5410 13.3900 69.8000 cdef
2024010 13.4650 13.4300 69.6000 cdef
2024003 13.3960 13.3900 59.0000 defg
2024011 13.3950 13.3250 53.6000 efg
2024008 13.3470 13.3800 52.5000 efg
2024001 13.2950 13.3250 43.4500 fg
2024015 13.2320 13.2100 30.9000 g

Table Proportion of Total Groups Formed by the Total of Lots

Valores
Number of groups Formed 11
Total Frequency 16
Proportion of Groups by the Total of Lots 68.75