Concept Article pubs.acs.org/OPRD
I‑MR Control Chart: A Tool for Judging the Health of the Current Manufacturing Process of an API and for Setting the Trial Control Limits in Phase I of the Process Improvement† K. Mukundam,§ Deepak R. N. Varma,§ Girish R. Deshpande,‡ Vilas Dahanukar,‡ and Amrendra Kumar Roy*,‡ ‡
Custom Pharmaceutical Services, Dr. Reddy’s Laboratories Ltd., Bollaram Road, Miyapur, Hyderabad, Andhra Pradesh, PIN 500 - 049, India § Chemical Technical Operations, Dr. Reddy’s Laboratories Ltd., Unit-II, Plot Nos. 110 and 111, S.V. Co-operative, Industrial Estate, Bollaram, Jinnaram Mandal, Medak District, PIN 502 - 325, India S Supporting Information *
ABSTRACT: It has been observed that the main focus during the process development and manufacturing of an API is to meet the customer’s specifications (LSL and USL) rather than estimating and improving the natural control limits (LCL and UCL) of the process. It results in the overlap of the natural control limit and customer’s specification, which in turn increases the chance of failure with respect to the customer’s specifications. A better approach is to work on decreasing the variability of the process so that natural control limits become much tighter than customer’s specification. The statistical control charts not only help in estimating these internal/natural control limits but also raises an alert when the process goes out of control. These alerts trigger the investigation through root cause analysis leading to the process improvements which in turn lead to the decrease in variability of the process. This process continues till inherent variability of the process is due to common causes only and cannot be attributed to assignable causes. At this point, the natural control limits of the process can be taken as internal specification for an output quality parameter. only variation left in the process is because of common causes.4 Under this condition the process is said to be under control. A given process can only be improved if there are some tools available for timely detection of an abnormality due to assignable causes. This timely and online signal of an abnormality (or an outlier) in the process could be achieved by plotting the process data points on an appropriate statistical control chart. These control charts can only tell that there is a problem in the process but cannot tell anything about its cause. Investigation and identification of the assignable causes associated with the abnormal signal allows timely corrective action which ultimately reduces the variability in the process (Figure 3) and gradually takes the process to the next level of the improvement. This is an iterative process resulting in continuous improvement until abnormalities are no longer observed in the process and whatever variation is observed is due to common causes only. To conclude, the main objective of control charts is to calculate the present status of the process, raise the alerts when the process is going out of control, and finally facilitate the process monitoring (detecting outliers) and improvement (decrease in variability of the process) until the process comes under statistical control.5 The significance of these control charts is evident by the fact that it was discovered in the 1920s by Walter A. Shewhart,6 and since then it has been used extensively across the manufacturing industry and became an intrinsic part of SPC7 and DMAIC
1. INTRODUCTION The research-driven pharmaceutical company aims to produce an API which either meets or exceeds the customer specification on the quality parameter1 although the real challenge is to maintain that consistency from batch to batch.2 Due to certain unavoidable reasons such as wear and tear of machines, a new operator, a new supplier, fluctuation in atmospheric conditions, etc. could disturb the process resulting in a variation in the output attribute of an API (Figure 1).
Figure 1. Causes of variation for an output attribute, A and B are some assignable or special causes, whereas N1 and N2 are noise factors or common causes.
Any chemical process is affected by two types of input variables or factors. Input variables which can be controlled are called assignable or special causes (e.g., person, material, unit operation, and machine), and factors which are uncontrollable are called noise factors or common causes (e.g., fluctuation in environmental factors such as temperature and humidity during the year). Usually, when a process is developed, e.g. using QbD or DoE principles,3 it takes care of the assignable causes, and the © 2013 American Chemical Society
Received: April 24, 2013 Published: July 8, 2013 1002
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methodology of the 6σ8 process. Except for a few, there are not many references available for the API manufacturing.9−13 A control chart also provides an online test of the hypothesis14 if the process is under statistical control.
the mean value of an output parameter is done with the help of a control chart for the mean (X̅ , I-charts), and monitoring of the process variability is done by preparing the control chart for the standard deviation ‘s’ or the range ‘R’ or the moving range ‘MR’. The mean value of an output parameter gives a sense of accuracy, while variability gives an indication of the precision of the process.17 As both accuracy and precision are important (Figure 2) for monitoring, both X̅ - and R-charts are analyzed together for taking any decision on readjusting the running process although they are prepared separately for a given output parameter. In summary, a control chart enables an online scrutiny of the process. Any control chart has the following basic components as shown in Chart 1. Values of USL and LSL are customer defined,
null hypothesis Ho = process under control (observed mean = process mean)
alternate hypothesis Ha = process is out of control (observed mean ≠ process mean)
Chart 1. Typical control chart and the Western Electric Rule for detecting assignable causes
If points on the control charts are between UCL and LCL (natural control limits of the process), it can be concluded that observed mean is equal to process mean. It indicates that the null hypothesis cannot be rejected and the process is said to be under statistical control. On the other hand if points are beyond the control limits, it indicates that the observed mean has drifted from the process mean and now two means are not equal, leading to the rejection of the null hypothesis. In the latter case a readjustment of the process15 is required. The control chart also helps in minimizing the Type-I error (unnecessary adjustment of a stable process) and Type-II error (continuation of an uncontrolled process) associated with the hypothesis testing (Table 1). Table 1. Type-I and Type-II errors associated with a process state of process decision continue the process adjust the process
in control correct decision Type-I error: adjusting an incontrol process
or its values are taken from a pharmacopeia.18 Values of UCL, LCL, σ, and mean are calculated on the basis of the trend data of an output parameter. UCL and LCL represent the natural variability of the process. Any data point (outliers) outside these control limits (red circle, Chart 1) indicates that some assignable cause has resulted in this drift which needs immediate attention and investigation. This would lead to the process improvement (i.e., decreasing the σ of the process), and after some iterative cycle it will bring the process into the state of statistical control (Figure 3). Careful observation of the patterns on the control charts can reveal a lot about the health of the current process and
out of control Type-II error: continuing an outof-control process correct decision
In order to take the correct decision for readjusting an out-ofcontrol chemical process it becomes imperative to monitor not only the mean value of an output parameter (e.g., impurity level, assay, etc.) but also its variability or its spread.16 Monitoring of
Figure 2. In-control and out-of-control processes. 1003
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Figure 3. Association of process improvement with process variability.
gives an indication of an assignable cause when the process goes out of control. These assignable causes can be detected by using established Western Electric Rules as shown19 in Chart 1. It is not necessarily true that all the deviations on control charts are bad (e.g. the trend of an impurity drifting towards LCL, which is good for the process). Regardless of the fact that the deviation is ‘good’ or ‘bad’ for the process, the outlier points must be investigated. Reasons for good deviation then must be incorporated into the process, and reasons for bad deviation need to be eliminated from the process.20 This is an iterative process until the process comes under statistical control. Gradually, it would be observed that the natural control limits become much tighter than the customer’s specification, which is the ultimate aim of the process improvement (Figure 3). The process thus developed would not only be capable of producing an API that always meets customer’s specifications (Figure 3 and eqs 8, 9, and 10) but also would reduce the risk of failure.21 In general UCL and LCL are calculated on the basis of natural variability of the process (σ/R/MR) in such a way that they are ±3σ away from the process mean (eqs 5, 6, and 7) and contain approximately 99.73% of the data points. Often warning control limits at ±2σ are also plotted on the control chart to alert an operator, but this increases the chance of a Type-I error.22 1.1. I-MR Chart: Individual Moving Range Chart. There are various control charts that are available for monitoring purposes. Selection of a control chart for a given process depends on two things, first is the phase23 of the process improvement and second consists of the type of data available and the rational sub grouping.24 There are two phases in statistical process control. Phase I is where control charts are being prepared for the first time and the main focus is on calculating current natural control limits of a process (UCL and LCL). Usually in phase I, the process is not under statistical control, and the main objective is to monitor forthcoming batches for any outliers and assignable causes associated with it, followed by investigation and process improvement by incorporating good deviations and eliminating bad ones from the process. Once all assignable causes are removed from the process, process improvement efforts enter phase II (Figure 4). The type of data available and rational subgrouping are other criteria for the selection of an appropriate control chart.25 In the present case, where the batches of API were coming very slowly from manufacturing and only one sample was provided at a given time, the most appropriate control chart to be used was the ‘I-MR’ control chart, where ‘I’ denotes the individual data of an output attribute of the API and ‘MR’ is the moving range (eq 1) which is the measure of variability of the given output attribute. The I-MR chart is also the most appropriate chart to be used in phase I of the improvement for individual observations,26 and when it is used with Western Electric Rules (Chart 1), it is really a
Figure 4. Flowchart for process improvement and estimation of UCL and LCL.
powerful tool for detecting large shifts in the process (more than ±1.5σ). When a process enters phase II, it is characterized by a stable process with inherent variations (due to common causes) in the process. Now the main focus is on monitoring and detecting the small changes (less than ±1.5σ) in the process, and for this, more sensitive control charts such as CUSUM27 and EWMA28 charts are employed.
2. RESULTS AND DISCUSSION Herein we present our endeavor to deploy statistical control charts for the first time (i.e., we were in phase I of the process improvement) to the manufacturing process of an API.29 The main aim was to access the current health of the process, calculating its natural control limits, and on that basis identify the large shifts in the future batches. As the batches were coming out very slowly, providing only one sample per batch at a given point of time, the most simple and appropriate control chart that could be used was the I-MR chart. This article describes the use of the IMR chart for phase I improvement of the process, and UCL and LCL were estimated on the basis of the historical data obtained from the past 53 batches (Table 3) of the API. These limits were 1004
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Each and every data point that goes the beyond control limits in future batches would then be investigated, and subsequently the process would be improved using QbD or DoE, leading to the narrowing of the internal control limits.31 Gradually, these control limits would become much stringent than USP specifications (Figure 3 and Table 5), thereby increasing the process capability. 2.1. Calculation of UCL, LCL, Mean, MR, σMR Required for Generating the I-Chart.32 2.1.1. Normality Test of the Data.33 I-MR charts are very sensitive to the normality of the data, and there are many statistical methods available for testing the normality.34 Subjecting the data set from Table 3 to the Anderson−Darling test35 gave a ‘p value’ of 0.02, indicating that data set was not normally distributed. This was because of the few data that were near the lower and upper ends of the data set which resulted in tailing. As the reason for non-normality was obvious, these outliers were ignored later on (see Table 4 for
then taken as the internal specification (rather than the customer’s specification) and would be used as a baseline for the monitoring of the future batches. The ultimate aim would be to increase the gap between natural control limits and the customer’s specification (Figures 3 and 5).
Figure 5. Interpretation of 6σ for the assay data.
There were many output quality attributes associated with this API as shown in Table 2. As evident from the data, all other
Table 4. Recalculations of various components of I-MR chart
Table 2. Specification of the API USP specifications impurity-1 individual impurity total impurities assay
mean assay std. deviation mean MR std. deviation
observed trend %
USL = NMT 0.2% LSL = 0% USL = NMT 0.1% LSL = 0% USL = NMT 0.5% LSL = 0% USL = NMT 102% LSL = NLT 98%
maximum minimum maximum minimum maximum minimum maximum minimum
0.0405 0 0.06 0.03 0.12 0.07 101.5 98.9
X̅ σ MR σMR Control Limit for Revised I-Chart
UCL centre line LCL
100.59 0.45 0.249 0.221 101.248 100.58 99.91
Control Limit for Revised R-Chart UCL centre line LCL
quality attributes30 were well within the specification limits except for the assay. Although the assay values of all 53 batches produced in the past were well within the USP specifications (NMT 102% and NLT 98%), some of the observed values were too close to the specification limits (Tables 2 and 3) which increases the probability of failure in the future. Hence, it was desired to monitor the assay using the I-MR control chart so that the variation in the assay value could be minimized. As a first step, the historical data of all 53 batches were used to establish the natural control limit of the existing process which would then become the internal benchmark for future batches.
0.753 0.249 0
revised calculations) for obtaining the more realistic control limits. As a first step, the I-MR chart was prepared deliberately by including all data points from Table 3 as discussed below. 2.1.2. Moving Range (MR). MR is the absolute value of the difference between two consecutive data points as shown by eq 1. MR values are used as a measure of the variability or the spread of the data points. If there is not much variation between the batches, then MR values would remain almost constant, and if there is variation in the process, then there will be a sudden increase in MR values on the MR-chart.
Table 3. Assay data of 53 batches of the API batch assay MRi
1
2
3
4
5
6
7
8
9
10
11
12
13
14
100.8
100.8 0.0
101.5 0.7
101.5 0.0
101.5 0.0
101.3 0.2
100.9 0.4
100.6 0.3
100.6 0.0
100.4 0.2
100.8 0.4
100.1 0.7
100.7 0.6
100.4 0.3
batch assay MRi
15
16
17
18
19
20
21
22
23
24
25
26
27
28
100.4 0.0
100.3 0.1
98.9 1.4
100.3 1.4
100.3 0.0
100.3 0.0
100.3 0.0
100.2 0.1
100.8 0.6
100.8 0.0
99.5 1.3
100.7 1.2
100.4 0.3
100.4 0.0
batch assay MRi
assay MRi
29
30
31
32
33
34
100.8 0.4
100.7 0.1
100.7 0.0
100.4 0.3
100.0 0.4
100.3 0.3
35 100.7 0.4 batch
36
37
38
39
40
41
42
100.7 0.0
100.7 0.0
100.6 0.1
100.0 0.6
100.7 0.9
100.8 0.1
100.3 0.5
43
44
45
46
47
48
49
50
51
52
53
mean
100.3 0.0
100.9 0.6
100.5 0.4
100.5 0.0
101.2 0.7
100.6 0.6
100.7 0.1
100.6 0.1
101.1 0.5
101.0 0.1
101.1 0.1
X̅ = 100.59 MR = 0.333
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Concept Article
Chart 2. (a) I-chart for assay (USL = 102 and LSL = 98 are not shown); (b) MR-chart for assay
(1)
N = number of individual data Xi = measurement of the data
MRi data are captured in row 3, Table 3 2.1.3. Mean Moving Range MR. Average of all range values as shown by eqs 2a and 2b. This value is the basis for calculating the standard deviation of the process. MR =
1 N−1
N
∑ MR i
centre of the MR chart (2a)
i=2
MR = 0.333 (last column of Table 3)
(2b)
2.1.4. Standard Deviation (σMR). Standard deviation of the process is calculated from the average moving range as shown by eq 3 and represents the average variation of the process. Main aim of the control charts is to help in minimizing this variation. σMR would reach its minimum value when all assignable causes from the process are being eliminated and whatever variation left after that would be the inherent variation of the process due to common cause only. This is the fundamental basis of any process improvement strategy. σMR =
MR MR 0.334 = = = 0.295 d2 1.128 1.128
case 2 (hence n = 2) as two subsequent data points is used and corresponding D3 and D4 values are 0 and 3.267, respectively. 2.2.2. MRi Trend (row 3, Table 2). MR (= 0.333) is the centre line given by eq 2a. 2.3. Interpretation. I-chart of the assay (Chart 2a) shows that the third, fourth and fifth data points lie outside the UCL, indicating the rejection of null hypothesis (alternatively we can say that process has gone out of control, Table 1), which in turn indicates a possible assignable cause associated with this shift. This required investigation and corrective action in the process. Similarly, assay of the 17th and 25th were out of LCL indicating a shift in the mean. These sudden drops in the mean value of the assay (Chart 2a) resulted in MR values going beyond the UCL on MR-chart (Chart 2b). This does not mean that both mean and the variability were out of control. In the present case, sudden drops in assay values lead to the large change in the value of the MR.39 It only indicates that the mean was out of control and not an indication that both mean and MR were out of control. This is a very typical behavior of I-MR chart.40 It is important to state once again that, when these control charts are prepared for the first time to estimate the natural control limit of the process (called as estimated or trial control limits), it is done on the basis of the historical data. Hence, it is generally assumed that assignable causes for the outliers were identified and the process was rectified at that point of time.41 On the basis of this assumption control limits were recalculated by ignoring out-of-control points (in the present case, batches 3rd, 4th, 5th, 17th, and 25th) to avoid Type-II error (continuing the out-of-control process, Table 2) during the monitoring of the future batches. Another reason for ignoring these points is to avoid the inflated values42 of the control limits (σMR would be larger, eqs 5a and b) and to have fairly realistic estimate of the trial control limits. It is evident from Chart 2 and Chart 3 that the trial control limits of the process become more stringent after recalculation (eqs 5a and b and Table 4). These trial limits are to be used as a baseline for the monitoring of future batches. 2.4. Recalculation of Trial Control Limits for Assay (ignoring 3rd, 4th, 5th, 17th, and 25th batches). An Anderson−Darling test for the new data set obtained after ignoring outliers gave a ‘p value’ of 0.10,43 indicating that the data is normally distributed and could be used for I-MR chart.
(3)
36
d2 is a control chart constant and depends on individual data used for calculating MR. In the current case as two subsequent data points were used, hence n = 2 and corresponding d2 value is 1.128. 2.1.5. Mean Assay (X̅). Average value of the assay of all the batches as shown by eq 4. This becomes the centre line of the Ichart.37 X̅ =
1 N
N
∑ Xi
centre of the I‐chart (4)
i=1
mean assay = 100.59 (last column of Table 3)
2.1.6. Control Limit for I-Chart. As described earlier, this is the natural control limit of a process. Both UCL and LCL are calculated on the basis of the mean and σMR values obtained from individual data set. Control limits are calculated in such a way that they are ±3σMR away from the process mean X̅ as shown by eq 5. control limits = X̅ ± 3σMR = 100.58 ± 3 × 0.296
(5)
UCL = 100.58 + 0.888 = 101.477
(5a)
LCL = 100.58 − 0.888 = 99.71
(5b)
2.1.7. Generating I-Chart. The I-chart is then prepared by plotting the mean, UCL, LCL, and individual values of the assay as shown in Chart 2. 2.2. MR-Chart for the Assay. MR chart has its own control limits and centre line as calculated below and are plotted as shown in Chart 2b. 2.2.1. Control Limits for MR-Chart. LCL MR = D3MR = 0
(6)
UCL MR = D4 MR = 1.007
(7) 38
D3 and D4 are the control chart constants and depend on the number of individual data used for calculating MR. In the present 1006
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(historical mean), a better way of measuring process capability is by using Ppk (eq 9) which includes the mean (X̅ ) in calculation. In this procedure process performance is calculated with respect to both USL and LSL, and the minimum of the two is taken as the process performance index for a given quality attribute of an API.
Chart 3. (a) Revised I-chart for assay; (b) revised MR-chart for MR of assay
⎡ USL − X̅ X̅ − LSL ⎤ Ppk = minimum⎢ , ⎥ 3×σ ⎦ ⎣ 3 × σMR = [Ppk upper , Ppk lower]
It is important to note that in some cases both Ppk upper and Ppk lower are important because the process would be out of control if the data points cross either of the limits, for example ‘assay’ and ‘purity’ of an API. However, in certain conditions only one of them is important; for example Ppk lower does not have any significance for ‘impurities’, because even if it goes below the LSL, it is only good for the process. Hence, in such cases only Ppk upper should be calculated. Process performance can also be expressed in terms of σ level47 as shown below or by using the conversion table.47
Applying Western Electric Rules to Chart 3, it is evident that there was one data point on the I-chart (batch 6, Chart 3a) that was beyond UCL, but this time it was not ignored once again as it would not inflate the control limit values significantly on recalculation. Ignoring this outlier may result in further narrowing of the control limits which increase the Type-I risk.44 Also these control limits are just a baseline for the future batches for the identification of new outliers and hence assignable causes associated with it. The reasons for new assignable causes would then be identified and rectified till there are no more assignable causes and the process is said to be under statistical control. This marks the termination of phase I of the process control. Further monitoring of the process in phase II would then be taken up by more sensitive CUSUM or EWMA control charts. The main purpose of the present exercise was to obtain working or trial control limits for the existing process so that we could start phase I of the process improvement by using these control limits for monitoring of forthcoming batches. Process Performance Indices:45 Pp and Ppk. Process performance index is a dimensionless number that is used to represent the ability of the process to meet the customer specification for a given quality attribute. Process performance indices are being calculated out of curiosity to assess the overall ‘σ level’ of the process for the assay. This will make more sense when the process comes under statistical control. Two most commonly used process capability index are Pp and Ppk. The process performance index was preferred over process capability ratio (Cp and Cpk) in the present case because of following reasons:(1) Since no rational subgrouping was possible hence compulsion of using overall ‘σ’ (standard deviation) for calculating indices (2) The current process was not under statistical control as the process was in phase 1 improvement. (3) Pp and Ppk gives more conservative estimate than Cp and Cpk. (4) Pp index describes the process performance wrt customer’s specification or tolerance limit (eq 8). Pp =
USL − LSL = 2.24, σ = 0.45 (Table 4) 6×σ
(9)
σ level of the process = 3 × Ppk
(10)
For example, Ppk for the assay was 1.5 (Table 5), which when converted to 6σ gives a value of 4.72σ. This means that the USL of the assay is 4.72σ distance away from the centre (Figure 5) Table 5. Calculating process capability ratios for the API process performance indicator
formula
USL − LSL 6×σ
Pp
process performance data for assay 2.26
⎡ USL − X̅ X̅ − LSL ⎤ min[1.57, 2.90] min⎢ , ⎥ Ppk = 1.50 ⎣ 3×σ 3×σ ⎦
Ppk σ level of process failure rate
3 × Ppk
4.72 0.064% or 640 ppm
whereas the internal control limits (UCL) is 3σ away from the centre. Thus, there is a safety margin of 4.72 − 3 = 1.72σ which means that there is 0.064% probability that the value of the assay will cross the USL. One can guess the significance of the value of 4.72σ by the fact that the much talked-about “6σ” is equivalent to 3.4 failures per million and in the present case it corresponds to 640 per million batches; hence, higher values of Ppk are desirable. A Ppk value of 1.33 (i.e., 4σ) is generally seen as sufficient and corresponds to a 99.99% success rate. The above conclusion can also be drawn by looking at the numerator part of the eq 9. The greater the difference between the specification limit and the process mean, the greater is the process capability. Hence, it can be concluded that, even if the current process fails, it is most likely that it will fail towards USL, and the corresponding failure rate is 0.064% or 640 ppm.48 As APIs are qualified on many output attributes, we propose that the process performance of an API must be calculated on the basis of the same rationale that is used for the calculation of Ppk (eq 11). Hence:
(8)
Pp value ≥ 1.33 is desirable which is equivalent to the 4σ process, whereas Pp = 2 represents a 6σ performance.46 As Pp calculated above does not reveal anything about the deviation of the process mean with respect to the centre line
Ppk of an API = min × [impurity − 1, impurity − 2, ..., assay, yield, etc.] (11) 1007
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On the basis of eq 11 Ppk values, the quality attribute that is the minimum Ppk should be taken for the improvement program.
MRi N n NLT NMT OOS OOT Pp Ppk QbD s,σ
3. CONCLUSION The whole process of process monitoring and improvement of an API starts with the selection of a quality attribute that requires the most attention. Data from the manufacturing process are then collected, and the natural control limits of the process are calculated, followed by plotting the preliminary control chart. If there are few outliers, then the control limits are calculated once again by ignoring those outliers. This final control chart is then used for the hypothesis testing under which the process is controlled for the future batches (for detecting any out-of-control points). If the deviations are good, then the reason for the same is to be incorporated in the process, whereas reasons for bad deviations are to be eliminated. Thus, the process of monitoring and improvement must be continued until the process comes under SPC. At that point (end of phase I) the internal or the natural control limits of the process become new internal specifications for the API for the manufacturer which are much tighter than the customer’s specification, and the failure rates would be extremely low. This way of setting the internal specification would not only benefit the customer and manufacturer but would also avoid many unwanted OOS and OOT investigations and change control requests during manufacturing.
■
SPC UCL UCLMR USL USP VOC VOP Xi wrt σMR μ, X̅
■
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ASSOCIATED CONTENT
S Supporting Information *
Crude data of 53 batches, Excel sheet used for calculating UCL, LCL, mean, Cp, CPk, and σ level of the process. This material is available free of charge via the Internet at http://pubs.acs.org.
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Moving range of a data point Sample size Number of sample taken to calculate control limits Not less than Not more than Out of specification Out of trend Process performance index Process performance index with respect to mean Quality by design Standard deviation/variation/spread of a set of data points Statistical process control Upper control limit Upper control limit for MR-chart Upper specification limit United states pharmacopeia Voice of customer Voice of process Individual data point With respect to Standard deviation of moving range Mean
AUTHOR INFORMATION
Corresponding Author
*Telephone: +91-40-44658520. Fax: +91-40-44658699. E-mail:
[email protected],
[email protected]. Notes †
DRL Communication Number IPDO-IPM 00366. The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the DRL management for supporting this initiative and providing the required data that are being used for the statistical analysis. We are also grateful to Dr. Rakeshwar Bandichhor for his comments and suggestion while preparing this manuscript.
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LIST OF ABBREVIATIONS API Active pharmaceutical ingredient Cp Process capability ratio, does not include mean Cpk Process capability ratio that takes mean into account D3, D4, d2 Statistical constants DMAIC Define, measure, analyze, improve and control phases of 6σ DoE Design of experiments EP European Pharmacopeia HPLC High pressure liquid chromatography I-Chart Individual variable chart LCL Lower control limit LCLMR Lower control limit for MR-chart LSL Lower specification limits MR Moving range MR Moving range mean 1008
dx.doi.org/10.1021/op4001093 | Org. Process Res. Dev. 2013, 17, 1002−1009
Organic Process Research & Development
Concept Article
(13) Carson, P. K.; Yeh, A. B. Ind. Eng. Chem. Res. 2008, 47, 405. (14) Efficient way of learning applied statistics for nonstatisticians is to read statistics books used in business schools. These books can be understood easily as it focuses on the application of statistics rather than on pure statistics. (a) Anderson, D. R.; Sweeney, D. J.; Williams, T. A. Statistics for Business and Economics; South-Western College Publication: 2008. (15) Woodall, W. H. J. Qual. Technol. 2000, 20, 515. (16) Reducing the variability is the main focus of 6σ quality improvement programme. As decrease in variability leads to the improvement of the process (Figure 3) (17) (a) JCGM 200 International Vocabulary of Metrology Basic and General Concepts and Associated Terms (VIM); 2008; http://www.bipm. org/utils/common/documents/jcgm/JCGM_200_2008.pdf. (b) Taylor, J. R. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements; University Science Books: Mill Valley, CA, 1999. (18) Usually these are not plotted on control charts. (19) Western Electric Company. Statistical Quality Control Handbook; Indianapolis: IN, 1956. (20) See ref 8, p 389. (21) As customer’s specification and process’s natural control limits are far apart. (22) See ref 5, p 189. (23) See ref 5, p 198. (24) See ref 5, p 193. (25) See ref 5, p 193 and ref 9, p 357. (26) (a) Wheeler, D. J. Understanding Variation: The Key to Managing Chaos; SPC Press, Inc.: Knoxville, TN, 2000. (b) Wise, S. A.; Fair, D. C. Innovative Control Charting: Practical SPC Solutions for Today’s Manufacturing Environment; ASQ Quality Press: Milwaukee, WI, 1998. (27) (a) Page, E. S. Biometrika 1954, 41, 100. (b) NIST/SEMATECH e-Handbook of Statistical Methods; http://www.itl.nist.gov/div898/ handbook. (28) Roberts, S. V. Technometrics 1959, 37, 83. (29) The name of the API could not be disclosed due to confidentiality reasons. (30) All output quality attributes of an API are to be monitored separately. In the present case other quality attributes were not considered for an additional reason that the data set was not normally distributed. I-MR could not be applied to them because these charts are very sensitive towards the normality assumption and could lead to false control limits. Hence, CUSUM and EMWA charts which are insensitive to normality would be used for these, and it will be a topic of discussion in a forthcoming article. (31) This article does not cover the improvement efforts for elimination of the assignable causes. This article is all about estimating the current health of the process before starting any improvement program. (32) All calculations and control chart preparation were done using a Microsoft Excel sheet, see Supporting Information. (33) (a) Borror, C. M.; Montgomery, D. C.; Runger, G. C. J. Qual. Technol. 1999, 31, 309. (b) Willemain, T. R.; Runger, G. C. J. Qual. Technol. 1996, 28, 31. (34) For a normality test, the hypothesis is constructed in the following way H0: the given distribution is normal. Ha: the given distribution is not normal; p > 0.05 results in acceptance of a null hypothesis, meaning it is a normal distribution. In the present case, p = 0.02 indicates that the null hypothesis is false; hence, the data are not normally distributed. Various tests for normality are the Anderson−Darling test, Kolmogorov− Smirnov test, Shapiro−Wilk test. The template for the Anderson− Darling test is given in an Excel sheet in Supporting Information and could be calculated by using software such as JMP and minitab (a) Anderson, T. W.; Darling, D. A. Ann. Math. Stat. 1952, 23, 193. (b) Stephens, M. A. J. Am. Stat. Assoc. 1974, 69, 730. (c) Smirnov, N. V. Ann. Math. Stat. 1948, 19, 279. (d) Shapiro, S. S.; Wilk, M. B. Biometrika 1965, 52 (3−4), 591−611. (e) The underlying assumption of normality is much more critical when there are no subgroups. Burr, I. W. Engineering Statistics and Quality Control; McGraw-HilI: New York, 1953.
(35) Template used for calculating the AD test: http://www.kevinotto. com/rss/templates/anderson-darlingnormality test calculator.xls. (36) Value for a given number of sample could be found in any statistical process control book (37) Sometimes a target value is taken in place of the mean as a centre point, e.g. when one wants to target an assay value of 100%. (38) Values for a given number of samples could be found in any statistical process control book. (39) As absolute value of the difference is considered for drawing the MR chart. (40) See ref 5, p 261. (41) Since the calculation done in this article was based on the historical data, it was assumed that those outliers were taken care of in order to have a realistic value of control limits so that it can be used to monitor the upcoming batches. (42) Inflated because of the higher value of σ which, in turn, is because of the outliers. (43) Reference 34; values greater than 0.05 indicate that the null hypothesis is true (44) Ignoring another point will lead to tighter control limits, and any point near or above this limit could be considered an outlier and would result in investigation; i.e. it might result in a false alarm even though the process is running between its natural control limits (Type-I error). (45) (a) Breyfogle, F. W. Implementing Six Sigma: Smarter Solutions Using Statistical Methods; Wiley & Sons: New York, 1999. (b) Reference 5, p 363; ref 8, p 171. (46) Conversion table:
(47) Calculation of 6σ can be done with Excel sheet templates available on the Internet or by using software such as minitab. (48) These σ values were obtained after a few outliers were ignored from the calculation. The real value would be obtained once the process comes under statistical control.
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