Highly Precise Anomaly Detection Using Multivariate Statistical Process Control with Appropriate Scaling of Input Variables in Pharmaceutical Continuous Manufacturing

Abstract

Multivariate statistical process control (MSPC) has attracted considerable attention as a monitoring method for pharmaceutical continuous manufacturing. However, there are few examples of its application in pharmaceutical manufacturing, and previous studies have shown high false-positive rates. One of the reasons is the use of inappropriate scaling factors. In pharmaceutical processes, the number of experiments for MSPC modeling tends to be small because the active pharmaceutical ingredients are expensive. Subsequently, the standard deviation, a common scaling factor for some variables, becomes too small, and the model may become sensitive to small variations. In this study, we have proposed methods for determining the appropriate scaling factors. These methods were applied to granulation and drying processes in pharmaceutical continuous manufacturing. The MSPC model can detect changes in the process parameters and raw materials used during continuous wet granulation and fluidized bed drying using the proposed scaling method.

Introduction

Continuous manufacturing (CM) has been actively studied in pharmaceutical manufacturing because it reduces development time, production time, and costs compared to conventional batch manufacturing.^1,2) The U.S. Food and Drug Administration issued draft guidelines in 2019.³⁾ In Japan, a research team, including the regulator, the Pharmaceuticals and Medical Devices Agency, reported a study to demonstrate an approach for establishing a control strategy for the CM of oral solid dosage forms.⁴⁾ Furthermore, the International Council on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH) published “Continuous Manufacturing of Drug Substances and Drug Products Q13⁵⁾,” a guideline for CM, which is expected to stimulate further research and implementation of CM. The ICH Q13 guidelines require real-time process monitoring to ensure that the operating conditions are within the range of the state of control and that products with the desired quality can be produced. If the operating conditions deviate from the normal range due to fluctuations during process operation, it is necessary to prevent products without the desired quality from being shipped to the market.⁶⁾ Traditionally, univariate statistical process control (SPC) has been used to monitor operating conditions.⁷⁾ In SPC, upper and lower limits are set for each variable to be monitored, and when a variable value deviates from its range, the operating condition is regarded as an anomaly. The 3σ method is generally used to set upper and lower limits.^8,9) The normal range set by this method is the range that includes approximately 99.7% of the data under normal conditions. Approximately 0.3% of the data is regarded as anomalous, even under normal conditions. Therefore, as the number of variables increased, the probability of erroneously judging a normal state as an anomaly also increased. SPC monitoring cannot consider the interactions between variables when monitoring multiple variables. This increases the risk of missing an anomaly caused by the breakdown of the correlation when monitoring a process in which there is a correlation between two variables.^10,11)

Multivariate SPC (MSPC) is a monitoring method that can solve this problem. MSPC expresses the operating conditions using Hotelling’s T² and Q residuals and determines whether an anomaly exists based on the values of Hotelling’s T² and Q residuals. Compared with SPC, MSPC requires fewer values to be monitored, thereby reducing the false-positive rates. In addition, MSPC can detect anomalies by considering the interaction among the variables and can detect anomalies that cannot be detected by SPC.^12,13) Because of these characteristics, MSPC is attracting attention as a process monitoring method for pharmaceutical CM, in which many variables are controlled.^14,15)

Although MSPC applications have been reported in various fields,^16–19) only a few examples have been documented in pharmaceutical manufacturing. An example of the application of MSPC to pharmaceutical CM was reported by Silva et al.²⁰⁾ Although Silva et al. concluded that MSPC successfully detected anomalous conditions, the false-positive rate was very high, and the Q residuals always exceeded the control limit under normal operating conditions (NOCs). Furthermore, they considered only the anomalies of the equipment, and raw materials fed to the machine were not considered. In addition to this, two further studies on the same topic have been reported in Japanese.^21,22) In the AMED report,²¹⁾ non-NOCs were detected with high sensitivity, but many data in which Hotelling’s T² and Q residuals exceeded the control limit were observed in NOC. Furthermore, they considered only equipment anomalies and did not consider raw materials fed to the machine. In the report by Oishi et al.,²²⁾ they detected not only equipment anomalies but also changes in the raw material fed to the machine, but as in the other two reports, the false-positive rate at NOC was high.

An example of MSPC application in batch granulation and drying processes using a fluidized bed granulator was reported by Kona et al.²³⁾ In this study, a sensor that measures temperature and humidity was added to a fluidized bed granulator to detect anomalies. However, a study using only the sensor in a normal fluidized bed granulator dryer has not been conducted.

In this study, we verified whether it is possible to monitor the operating conditions and confirm changes in the process parameters and raw materials intentionally generated during the granulation or drying process. In addition, a method is proposed to reduce the false-positive rate and improve the true-negative rate (TNR) and true-positive rate (TPR) by changing the scaling factor when standardizing the data as a preprocessing step. Granulators and dryers were used as examples of equipment used in pharmaceutical CM.

Experimental

Continuous Wet Granulation

The raw materials were mixed at the weight fractions listed in Table 1 using a mixing granulator (FM-VG-100, Powrex Corp., Hyogo, Japan). Two grades of lactose monohydrate were used. Table 2 shows the differences in powder properties between the two grades of lactose monohydrate.

Table 1. Formulations Used in Continuous Wet Granulation Process

Ingredient	Grade	Maker	% (w/w)
Ethenzamide	—	Iwaki Seiyaku Co., Ltd. (Tokyo, Japan)	1
Lactose monohydrate	Pharmatose 200M or Pharmatose 100M	DFE Pharma (Veghel, Netherlands)	60.1
Cornstarch	—	Matsutani Chemical Industry Co., Ltd. (Hyogo, Japan)	25.8
Low-substituted hydroxypropyl cellulose	LH-21	Shin-Etsu Chemical Co., Ltd. (Tokyo, Japan)	10.1
Hydroxypropyl cellulose	HPC-L	Nippon Soda Co., Ltd. (Tokyo, Japan)	3

Table 2. The Powder Properties of the Two Grades of Lactose Monohydrate

	D50 (μm)	Bulk density (g/mL)	Tapped density (g/mL)
Pharmatose 200M	31.44	0.456	0.876
Pharmatose 100M	143.07	0.710	0.869

The mixed raw materials were then fed into a continuous wet granulator (CTS-MG100; Powrex Corp.). The CTS-MG100 uses a center blade (CB) rotating at a high speed in the center of the vessel and a scraper blade rotating at a low speed along the inner wall of the vessel. A loss-in-weight (LIW) feeder (LIW-300-P; Ishida Co., Ltd., Kyoto, Japan) was used to feed the CTS-MG100, and water was added during the feeding process. A peristaltic pump (530S; Watson-Marlow, Falmouth, U.K.) was used to add water. The wet granules were dried in a semi-batch fluidized bed dryer (CTS-FD-01W, Powrex Corp.). An in-line particle size analyzer (Parsum IPP70, Parsum GmbH, Chemnitz, Germany) was installed between the CTS-MG100 outlet and the CTS-FD-01W inlet to monitor the particle size distribution of the wet granules. Figure 1 shows the flow diagram of the process used in this experiment. During granulation, the 15 variables shown in Fig. 1 were recorded every 5 s.

Fig. 1. Process Flow of Continuous Wet Granulation Process

The system was operated at NOC and non-NOC to evaluate the TNR and TPR. NOC was defined as a water addition ratio of 30%, CB rotation speed of 5000 min^–1, and lactose monohydrate grade of Pharmatose 200M. The water addition ratio, CB rotation speed, and grade of lactose monohydrate changed during granulation to produce non-NOCs. These changes are believed to affect granulation.²⁴⁾ In addition, changes in the water addition ratio and CB rotation speed can occur in the actual manufacturing settings due to operation errors in handling the machine or equipment malfunctions. Changes in lactose monohydrate powder properties can occur in the actual manufacturing settings due to a mistake in raw materials by operators or lot differences. In Experiments 1–5, the water addition ratio was changed in the order of 30, 20, 30, 42, and 30%, respectively, and granulation was performed for 30 min under each condition. In Experiments 6–10, the CB rotation speed was changed in the order of 5000, 4000, 5000, 6000, and 5000 min^–1, and granulation was performed for 30 min under each condition. In Experiment 11, the grade of lactose monohydrate was changed to Pharmatose 100M and granulated for 30 min. Experiments 1–5 were conducted on a different day than Experiments 6–11. Experiments 6–11 were conducted on the same day, and the LIW-300-P and CTS-MG100 were washed between Experiments 10 and 11.

The experimental data obtained were divided into 11 datasets for each operating condition. The operating conditions for each dataset are listed in Table 3.

Table 3. Operating Conditions during the Continuous Wet Granulation Process

Experiment	Run type	Operating conditions			Purpose
		Water addition ratio (%)	Center blade rotation speed (min–1)	Pharmatose grade
1	NOC	30	5000	200M	Calibration
2	Non-NOC	20	5000	200M	Test
3	NOC	30	5000	200M	Test
4	Non-NOC	42	5000	200M	Test
5	NOC	30	5000	200M	Test
6	NOC	30	5000	200M	Test
7	Non-NOC	30	4000	200M	Test
8	NOC	30	5000	200M	Test
9	Non-NOC	30	6000	200M	Test
10	NOC	30	5000	200M	Calibration
11	Non-NOC	30	5000	100M	Test

Fluidized Bed Drying

The wet powder was prepared by mixing 1000 g of microcrystalline cellulose (CP-102; Asahi Kasei Corp., Tokyo, Japan) with 200 g of water, using a mixing granulator (FM-VG-01; Powrex Corp.), then dried using an FD-MP-01 (Powrex Corp.). It can be used as a fluidized bed granulator dryer, tumbling fluid bed granulator coater, or Wurster coating machine by replacing the vessel. In this study, it was used as the fluidized bed dryer. The near-IR spectroscopy (NIRS) of the powder during the drying process was performed by installing an optical fiber through a window at the bottom of the vessel. It was performed using a PNIR-F17 (Powrex Corp.) at wavelengths of 900–1700 nm. The moisture content was obtained using a calibration curve for the moisture content prepared in advance.²⁵⁾ The inlet airflow rate, inlet air temperature, exhaust air temperature, product temperature, and NIRS were recorded every 10 s.

Non-NOC data were recorded by changing the inlet airflow rate and inlet air temperature. These changes affect the drying conditions of a fluidized bed dryer²⁶⁾ and can occur in the actual manufacturing settings due to operation errors in handling the machine or equipment malfunctions. The drying process is located downstream of the granulation process, and any anomalies in the raw materials should be detected and eliminated in the granulation process. In addition, it would be difficult to detect any anomalities on the raw materials during the drying process that could not be detected in the granulation process; therefore, no experiments were conducted to change the raw materials in the drying process. Experiments were conducted 14 times, and the inlet air flow rate and the inlet air temperature were changed twice. Experiments 1–10 were conducted on the first day, followed by experiments 11–14 on the second day. The equipment was cleaned with a vacuum cleaner between experiments. The operating conditions for each experiment are listed in Table 4.

Table 4. Operating Conditions during the Fluidized Bed Drying Process

Experiment	Run type	Operating conditions
		Inlet air flow rate (m3/min)	Inlet air temperature (°C)	Exhaust air temperature at end point (°C)
1	NOC	1	75	43
2	NOC	1	75	43
3	NOC	1	75	43
4	NOC	1	75	45
5	NOC	1	75	45
6	NOC	1	75	45
7	NOC	1	75	45
8	NOC	1	75	45
9	Non-NOC	1	65	45
10	Non-NOC	1.5	75	45
11	Non-NOC	1	75	45
12	Non-NOC	1	75	45
13	Non-NOC	1	85	45
14	Non-NOC	0.5	75	45

MSPC Model Development

To develop the MSPC model, the data were standardized according to Eq. (1) as follows:

  

$${\tilde{x}}_m=\frac{x_m-{\overline{x}}_m}{{\sigma }_{x_m}}$$(1)

where x_m is the mth column of the data matrix with N samples and M variables, ${\tilde{x}}_m$ is the standardized mth variable x_m, ${\overline{x}}_m$ is the mean value of the variable x_m in the calibration data, and σ_xm is the scaling factor of x_m. Autoscaling is generally performed, in which the standard deviation of x_m in the calibration data is used as the scaling factor of x_m.¹³⁾ However, when nonrepresentative data were used to calculate the standard deviations and the standard deviation of some variables became too small, and a small change in x_m resulted in a large change in the value of ${\tilde{x}}_m$. Therefore, the model may be sensitive to small variations in x_m that do not need to be detected as anomalies. In soft sensors that predict product quality from real-time measurements, the accuracy of a model can be improved by devising a scaling factor.²⁷⁾ Therefore, this study examined a method for reducing the false-positive rate of MSPC by devising a scaling factor. When MSPC is used for anomaly detection, non-NOC data with intentionally changed operating conditions should be obtained to verify that the model can detect anomalies. In such cases, the standard deviation of x_m in a dataset, including non-NOC and NOC data, can be used as a scaling factor to prevent the scaling factor from becoming too small. In cases where non-NOC data are not available, the scaling factor is defined based on the domain knowledge of the process, that is, knowledge of process characteristics gained from past experience. In this study, we compared the performance of the MSPC models using three types of scaling factors: the standard deviation of NOC data (σ₁), which is generally used as a scaling factor, the standard deviation calculated by the dataset including NOC and non-NOC data (σ₂), which is proposed in this study, and a value set based on domain knowledge (σ₃). In this paper, the models using σ₁, σ₂, and σ₃ are called Models 1, 2, and 3, respectively.

A principal component analysis (PCA) was performed using standardized data. In the PCA, the principal component score T was calculated according to Eq. (2) as follows:

  

$$T=XP$$(2)

where X is a data matrix with N samples and M variables, P is a loading matrix with M variables and R principal components, and T is a principal component score matrix with N samples and R principal components. Based on the principal component scores, Hotelling’s T² was calculated using Eq. (3), and Q residuals were calculated using Eqs. (4) and (5)^28,29) as follows:

  

$$T^2=\sum _{r=1}^R\frac{t_r^2}{{\sigma }_{t_r}^2}$$(3)

  

$$Q=\sum _{m=1}^M{({\tilde{x}}_m-{\hat{x}}_m)}^2$$(4)

  

$${\hat{x}}_m=\sum _{r=1}^R{t}_r{P}_{r,m}^T$$(5)

where t_r is the rth principal component score, ${\sigma }_{t_r}^2$ is the variance of the rth principal component score of the calibration data, and $P_{r,m}$ is the (r, m) element of the loading matrix P. The number of principal components was the smallest, with a cumulative contribution greater than 80%. The control limits of Hotelling’s T² and Q residuals were calculated using Eqs. (6) and (7)^28,30) as follows:

  

$$C{L}_{T^2}=\frac{R(N+1)(N-1)}{N(N-R)}{F}_{1-\alpha ,R,N-R}$$(6)

  

$$C{L}_Q={\theta }_1{\left[\frac{z_{\alpha }\sqrt{2{\theta }_2{h}_0^2}}{{\theta }_1}+\frac{{\theta }_2{h}_0\left(h_0-1\right)}{{\theta }_1^2}+1\right]}^{\frac{1}{h_0}}$$(7)

where $C{L}_{T^2}$ is the control limit of Hotelling’s T², $C{L}_Q$ is the control limit of Q residuals, n is the number of samples in calibration data, $F_{1-\alpha ,R,N-R}$ is the F-distribution with the level of significance α, and parameters R and N–R, ${\theta }_i=\sum _{j=R+1}^M{\lambda }_j^i$, with i = 1, 2, 3, $h_0=1-\frac{2{\theta }_1{\theta }_3}{3{\theta }_2^2}$, and z_α is the value of the normal deviate cutting off an area of α under the upper tail of the distribution if h₀ is positive and under the lower tail if h₀ is negative. In this study, the level of significance α was set at 0.3%. If Hotelling’s T² and/or Q residuals exceeded the control limits, the data were considered to be non-NOC.

The contribution of each variable to Q residuals was calculated to identify the variables responsible for the anomalies detected by Q residuals. The contributions of mth variable to Q residuals were calculated using Eq. (8)³¹⁾ as follows:

  

$$C_{n,m}^{\left[Q\right]}={({\tilde{x}}_m-{\hat{x}}_m)}^2$$(8)

where $C_{n,m}^{\left[Q\right]}$ is the contribution of the mth variable in the nth sample to Q residuals.

The experimental data from fluidized bed drying are three-dimensional, with variable, time, and batch information. Multiway PCA was used, which created two-dimensional data with variable and batch information for each measurement time and combined them in the row direction to create a two-dimensional data matrix.^32,33) In this study, six measurements (i.e., 1-min measurements) were combined in the row direction to create a two-dimensional data matrix. This data matrix was created at each time point, and the MSPC model was created using it.³⁴⁾ To avoid reducing the number of samples, a data matrix was created until the end of the drying process for the batch with the shortest drying time.

MATLAB R2023a (MathWorks, MA, U.S.A.) was used to create the MSPC model and analyze the manufacturing data.

Results and Discussion

Continuous Wet Granulation

Experimental Results

Some of the data measured during the granulation process are shown in Fig. 2. The green line denotes the raw data, and the black and red lines denote the moving average values of the NOC and non-NOC data with a window size of 12 samples. Data are shown from when the powder flow rate and water addition ratio were stabilized to when water addition was stopped. Figure 2 shows that the raw data fluctuated widely, even for the NOC. To reduce the effect of noise, moving average data were used in the analysis.

Fig. 2. (a) Powder Flow Rate, (b) Ratio of LIW Feeder Motor Torque to Rated Torque, (c) Water Addition Ratio, (d) Center Blade Current Value, (e) Scraper Blade Current Value, and (f) D₅₀ during the Continuous Wet Granulation Process

The green line denotes the raw data, and the black and red lines denote the moving average values of the NOC and non-NOC data with a window size of 12 samples, respectively.

In Experiment 4, the ratio of the LIW feeder motor torque to rated torque (LMT) increased as the water addition ratio increased. At the beginning of Experiment 5, the LMT was still high, although the water addition ratio returned to its normal value and the LIW feeder temporarily stopped owing to an overload because of the residual effects of the high water addition ratio in Experiment 4. Therefore, the period from the start of Experiment 5 to the resumption of operation after the feeder stopped was treated as Experiment 5-1, classified as non-NOC data.

Process Monitoring Results

The data obtained from Experiments 1 and 10, the first and last NOC experiments, were used as calibration data. Data for the first minute of Experiments 1 and 10 were excluded from the calibration data because the operating conditions were unstable. The values of the three scaling factors are listed in Table 5. σ₃ was set based on past experimental experience to be an acceptable range of variations under the NOC, that is, a range of changes that do not affect product quality. For example, the σ₃ of the powder flow rate was set to 200 g/h because past knowledge has shown that even a change in powder flow rate of about 100 g/h does not affect product quality.

Table 5. Scaling Factors of Variables during the Continuous Wet Granulation Process

	σ1	σ2	σ3
Powder flow rate (g/h)	66.545	374.078	200.000
Ratio of LIW feeder motor torque to rated torque (%)	3.546	26.681	5.000
Water addition ratio (%)	2.401	11.125	2.000
Center blade rotation speed (min–1)	0.295	534.920	10.000
Center blade current value (A)	0.021	0.028	0.020
Scraper blade rotation speed (min–1)	0.408	0.492	0.500
Scraper blade current value (A)	0.012	0.010	0.020
D1 (μm)	6.610	9.837	6.000
D10 (μm)	28.221	38.959	23.000
D25 (μm)	61.207	67.112	50.000
D50 (μm)	101.527	100.453	80.000
D75 (μm)	125.605	129.665	100.000
D90 (μm)	139.006	152.263	110.000
D99 (μm)	160.270	186.336	130.000
Particle concentration at the measuring part (%)	4.118	4.874	4.000

The MSPC model was developed using standardized data for each scaling factor, and Hotelling’s T² and Q residuals were calculated. Table 6 shows the results of anomaly detection using MSPC. The TNR and TPR were calculated as the percentage of data for which Hotelling’s T² and Q residuals do not exceed the control limits in NOC data, and the percentage of data for which Hotelling’s T² or Q residuals exceed the control limits in non-NOC data, respectively. Table 6 shows that the TPR of all models in Experiment 11 was 100%. The MSPC model was able to detect an unexpected anomaly in Experiment 5-1, which was conducted under the same operating conditions as the NOC, at a high TPR of 100% for Models 1 and 3, and 80.9% for Model 2. This indicates that the MSPC can be used to confirm changes in raw materials and anomalies that occur unintentionally by the operator, which has not been confirmed in previous studies.

Table 6. True Negative and Positive Rates of Anomaly Detection Using MSPC during the Continuous Wet Granulation Process

Experiment	Operating conditions	True negative and positive rate (%) (number of correctly samples (–)/number of all samples (–))
		σ1		σ2		σ3
1	NOC (calibration)	98.0	(341/348)	98.0	(341/348)	98.6	(343/348)
2	Water addition ratio low (test)	99.4	(358/360)	9.7	(35/360)	99.2	(357/360)
3	NOC (test)	96.3	(336/349)	99.1	(346/349)	99.4	(347/349)
4	Water addition ratio high (test)	99.2	(357/360)	61.9	(223/360)	98.9	(356/360)
5-1	Non-NOC (test)	100.0	(47/47)	80.9	(38/47)	100.0	(47/47)
5-2	NOC (test)	81.8	(225/308)	99.7	(307/308)	92.2	(284/308)
6	NOC (test)	13.7	(46/335)	83.0	(278/335)	74.6	(250/335)
7	CB rotation speed low (test)	100.0	(360/360)	60.3	(317/360)	100.0	(360/360)
8	NOC (test)	87.1	(304/349)	95.7	(334/349)	93.1	(325/349)
9	CB rotation speed high (test)	100.0	(359/359)	100.0	(359/359)	100.0	(359/359)
10	NOC (calibration)	98.3	(346/352)	99.1	(349/352)	98.9	(348/352)
11	Pharmatose grade 200M (test)	100.0	(360/360)	100.0	(360/360)	100.0	(360/360)

A comparison of the performance of the models shows that the TNR for the NOC data, especially in Experiment 6, is lower for Model 1 than that for Models 2 or 3. In Experiment 6, the TNR of Models 2 and 3 were 83.0 and 74.6%, respectively, whereas that of Model 1 was 13.7%. This indicates that Model 1 is sensitive to small changes in the variables in the NOC data. However, Model 2 had a lower TPR for non-NOC data than Models 1 and 3 did. In Experiment 2, the TPR of Models 1 and 3 were 99.4 and 99.2%, respectively, whereas the TPR of Model 2 was 9.7%. To further confirm this trend, the control charts for each model are shown in Fig. 3. Because the difference in Hotelling T² caused by the scaling factor is small, only the control charts for Q residuals are shown. The black, blue, red, and green lines represent the calibration, NOC test, non-NOC test, and control limits, respectively. Model 2 has smaller Q residuals than Models 1 and 3, even when Q residuals exceed the control limit. This indicates that Model 2 is insensitive to changes in the variables.

Fig. 3 The Control Chart for Q Residuals during the Granulation Process

The black, blue, red, and green lines represent the calibration, NOC test, non-NOC test, and control limits, respectively. Model 2 has smaller Q residuals than Models 1 and 3.

To ascertain why Model 1 was more sensitive and Model 2 was insensitive to changes in variables, $C_{n,m}^{\left[Q\right]}$ for each variable was calculated. Figure 4 shows $C_{n,m}^{\left[Q\right]}$ for Experiment 6, where the TNR was particularly low in Model 1. In Fig. 4, $C_{n,m}^{\left[Q\right]}$ for each variable is summed to show the values of Q residuals. $C_{n,m}^{\left[Q\right]}$ of the LMT is particularly large when the Q residuals exceed the control limit in Model 1. Model 3 also showed large values of $C_{n,m}^{\left[Q\right]}$ of LMT, but these were smaller than those of Model 1. In contrast, $C_{n,m}^{\left[Q\right]}$ of the LMT was smaller in Model 2. Table 5 shows that the scaling factors of LMT are large σ₁, σ₃, and σ₂, in this order. This indicates that a small scaling factor value causes the model to be sensitive to changes in the variables.

Fig. 4. $C_{n,m}^{\left[Q\right]}$ for Each Variable in Experiment 6 during the Granulation Process

Figure 5 shows $C_{n,m}^{\left[Q\right]}$ for Experiment 2, where the TPR was particularly low in Model 2. Figure 5 shows that the Q residual exceeds the control limit in Models 1 and 3 because of the large $C_{n,m}^{\left[Q\right]}$ of the water addition rate. In contrast, Model 2 had a small $C_{n,m}^{\left[Q\right]}$ of the water addition ratio, and the Q residuals did not exceed the control limit. Table 5 shows that the scaling factor σ₂ of the water addition ratio is larger than σ₁ and σ₃. This indicates that a large scaling factor value causes the model to be insensitive to changes in the variables.

Fig. 5. $C_{n,m}^{\left[Q\right]}$ for Each Variable in Experiment 2 during the Granulation Process

The green lines represent the control limits.

These results indicate that if the value of the scaling factor is too small, the model becomes sensitive to changes in the variables, and if the value of the scaling factor is too large, the model becomes insensitive to changes in the variables. Therefore, using a scaling factor setting based on domain knowledge, a model that accurately detects non-NOC data while minimizing false positives in the NOC data can be developed.

To determine how strictly the scaling factor needs to be determined using domain knowledge, the TNR and TPR were calculated for the NOC and non-NOC test data, respectively, varying only the scaling factor of the water addition rate from σ₃. The results are shown in Supplementary Fig. S1. These results show that the TNR for the NOC test data did not change significantly when the scaling factor of the water addition ratio was changed from 1 to 50%. The TPR for the non-NOC test data decreased when the value of the scaling factor was more than 7%. This indicates that a model that accurately detects non-NOC data while minimizing false positives in the NOC data can be developed using a scaling factor of water addition ratio up to 6%, that is, three times the value set by σ₃. This indicates that the scaling factor, which is set based on domain knowledge, does not need to be strictly set.

Fluidized Bed Drying

Experimental Results

The data measured during the drying process are presented in Fig. 6. As shown in Fig. 6f, the moisture content was higher in Experiments 11–14 at the endpoint of drying than in Experiments 1–10. Experiments 11 and 12 were conducted under the same operating conditions as Experiments 4–8, which were NOCs. Furthermore, the exhaust air and product temperatures during drying showed the same behavior in Experiments 4–8 and 11–12. Therefore, the moisture content at the end of drying is expected to be the same if no anomalies occur. Therefore, Experiments 11 and 12 were treated as non-NOC, although the operating conditions were the same as those for the NOC. A possible reason for the difference in moisture content in Experiments 11–14 compared to those in Experiments 1–10 is the changes in the humidity in the room. Because the FD-MP-01 used in this experiment was conducted in room air without humidity adjustment, changes in room humidity would also change the inhaled air humidity and thus the moisture content at the drying endpoint. Experiments 1–3 were treated as NOC because the moisture content at the end of drying was similar to that of the other batches under NOC, although the conditions at the end of drying were different from Experiments 4–14.

Fig. 6. (a) Inlet Air Flow Rate, (b) Inlet Air Temperature, (c) Exhaust Air Temperature, (d) Product Temperature, (e) Moisture Content Change over Time during the Drying Process, and (f) Moisture Content at the Endpoint of Drying

Process Monitoring Results

One of the eight batches operated at the NOC was used as the test data, and the rest were used as calibration data because the number of data points per batch was small. Experiment 4 was used for the test data. The values of the three scaling factors used to standardize the data are shown in Fig. 7. The values of σ₁ and σ₂ differ from time to time because the data matrix was created at each time point. The value of σ₃ was set within an acceptable range of variation under NOC, referring to the standard deviation calculated by all NOC data.

Fig. 7. Scaling Factors of Each Variable during the Fluidized Bed Drying Process

The MSPC model was developed using standardized data for each scaling factor, and Hotelling’s T² and Q residuals were calculated. Table 7 shows the results of anomaly detection using MSPC. Table 7 shows that 100% of the anomalies were correctly detected in Experiments 10 and 12–14. In Experiments 9 and 11, Model 1 was able to detect all anomalies, whereas Models 2 and 3 were unable to detect some anomalies.

Table 7. True Negative and Positive Rates of Anomaly Detection Using MSPC during the Fluidized Bed Drying Process

Experiment	Operating conditions	True negative and positive rate (%) (number of correctly samples (–)/number of all samples (–))
		σ1		σ2		σ3
1	NOC (calibration)	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)
2	NOC (calibration)	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)
3	NOC (calibration)	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)
4	NOC (test)	34.2	(26/76)	100.0	(76/76)	90.8	(69/76)
5	NOC (calibration)	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)
6	NOC (calibration)	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)
7	NOC (calibration)	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)
8	NOC (calibration)	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)
9	Inlet air temperature low	100.0	(76/76)	96.1	(73/76)	96.1	(73/76)
10	Inlet air flow rate high	100.0	(57/57)	100.0	(57/57)	100.0	(57/57)
11	Water content high	100.0	(76/76)	98.7	(75/76)	93.4	(71/76)
12	Water content high	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)
13	Inlet air temperature high	100.0	(72/72)	100.0	(72/72)	100.0	(72/72)
14	Inlet air flow rate low	100.0	(76/76)	100.0	(76/76)	100.0	(76/76)

A comparison of the performance of the models showed that the TNR for the NOC test data was lower for Model 1 than for Models 2 and 3. The TNR of Models 2 and 3 were 100 and 90.8%, respectively, whereas that of Model 1 was 34.2% in Experiment 4. This indicates that Model 1 is sensitive to small changes in the variables in the NOC data. For the non-NOC data, almost all anomalies were detected by the model using any scaling factor.

To confirm the performance of the model further, the control charts for each model are shown in Fig. 8. Because the difference in the Hotelling T² owing to the scaling factor is small, only the control charts for Q residuals are shown. The black, blue, red, and green lines in Fig. 8 represent the calibration, NOC test, non-NOC test, and control limits, respectively. The NOC and non-NOC test data are close to the Q residual value for Model 1, and the Q residuals of the NOC test data are sometimes higher than those of the non-NOC data. However, the Q residuals of Models 2 and 3 for the non-NOC test data were always higher than the control limit, and those of the NOC test data were lower than the control limit. Therefore, Models 2 and 3 were able to distinguish between NOC and non-NOC data more accurately by changing the setting method of the control limits, whereas Model 1 was not able to distinguish between NOC and non-NOC data accurately, even if the setting method of the control limits was changed.

Fig. 8. The Control Chart for Q Residuals during the Fluidized Bed Drying Process

To ascertain why Model 1 was more sensitive to changes in the variables, we calculated $C_{n,m}^{\left[Q\right]}$ for each variable. Figure 9 shows $C_{n,m}^{\left[Q\right]}$ for Experiment 4, which was the NOC test data. In Fig. 9, the values of $C_{n,m}^{\left[Q\right]}$ for each variable are summed to show the values of Q residuals. Figure 9 shows that $C_{n,m}^{\left[Q\right]}$ of the inlet air flow rate and inlet air temperature were particularly high when the Q residuals exceeded the control limit in Model 1. Model 3 also showed large values of $C_{n,m}^{\left[Q\right]}$ for the inlet air flow rate; however, these values were smaller than those for Model 1. In contrast, $C_{n,m}^{\left[Q\right]}$ of the inlet air flow rate was smaller for Model 2. Figure 7 shows that the scaling factors for the inlet air flow rate are large σ₁, σ₃, and σ₂, in this order. The scaling factor for inlet air temperature is smaller for σ₁ than that for σ₂ and σ₃. This indicates that a small scaling factor value causes the model to be sensitive to changes in the variables.

Fig. 9 $C_{n,m}^{\left[Q\right]}$ for Each Variable in Experiment 4 during the Fluidized Bed Drying Process

Conclusion and Future Work

In this study, we verified whether MSPC can be used for anomaly detection in continuous wet granulation and fluidized bed drying processes. In addition, to improve the TNR and TPR, a method was proposed that uses a standard deviation calculated from a dataset combining calibration and non-NOC data as a scaling factor for standardizing data, and another method uses a value set within an acceptable range of variation under NOC, based on domain knowledge, as a scaling factor was proposed.

In the continuous wet granulation process, the water addition ratio and CB rotation speed were changed as variables used in model development. The grade of lactose, a raw material, was changed as a variable not used for model development, and it was verified whether these anomalies could be detected. In the fluidized bed drying process, the inlet air flow rate and inlet air temperature were changed as variables used in model development; the drying conditions were changed as variables not used in model development, and it was verified whether these anomalies could be detected. Thus, the MSPC can detect all anomalies. This indicates that the MSPC can detect raw-material-related anomalies in the continuous wet granulation process, in addition to equipment-related anomalies in the continuous wet granulation and fluidized bed drying processes.

The false-positive rate in NOC could be reduced by using the standard deviation, calculated by the dataset combining calibration and non-NOC data, as a scaling factor to standardize the data as a preprocessing step for MSPC. However, the detection rate of non-NOC would be lowered if data significantly different from the NOC data were used as non-NOC data. The TNR and TPR could be improved with the minimum number of experiments by setting a scaling factor based on domain knowledge.

To apply the proposed method to practical manufacturing settings, software is required that obtains the parameters to be monitored from the equipment and calculates Hotelling’s T² and Q residuals in real time. We have developed and marketed the software called MSPC Production Monitoring System P-i² for the proposed method's application to the manufacturing process. However, it does not support multiway-MSPC, and we would like to improve it so that multiway-MSPC can be implemented in the future.

In the continuous wet granulation process, the proposed method using a scaling factor based on domain knowledge was the most accurate. Still, this method requires an operator with experience and knowledge of the equipment. Therefore, when applying this method to newly introduced equipment, sufficient domain knowledge may not be accumulated, and the scaling factors may not be appropriately determined. To solve this problem, we would like to improve the proposed method so that scaling factors can be automatically and reproducibly optimized without relying on domain knowledge.

Nomenclature

Symbol 

Description

C_LQ

Control limit of Q residuals

$C{L}_{T^2}$

Control limit of Hotelling’s T²

$C_{n,m}^{\left[Q\right]}$

Contribution of the mth variable in the nth sample to Q residuals

$F_{1-\alpha ,R,N-R}$

F-distribution with the level of significance α, and parameters R and N

N

Number of samples

P

Loading matrix

Q

Vector of Q residuals

R

Number of principal components

T

Principal component score matrix

T²

Vector of Hotelling’s T²

t_r

Score vector of the rth principal component

X

Data matrix

x_m

mth column vector of data matrix X

${\overline{x}}_m$

Mean value of x_m

${\tilde{x}}_m$

Vector of standardized x_m

$z_{\alpha }$

Value of the normal deviate cutting off an area of α under the upper tail of the distribution if h₀ is positive and under the lower tail if h₀ is negative

λ_j

Variance of the jth principal component

${\sigma }_{x_m}$

Scaling factor of x_m

σ_tr

Variance of the rth principal component score

Conflict of Interest

The authors declare no conflict of interest.

Supplementary Materials

This article contains supplementary materials.

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