Figure 3: Control chart showing batch tablet weight produced using two presses (A and B). UCL is upper control limit and LCL
is lower control limit.
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Figure 3 shows a control chart for a total weight of 10 tablets manufactured by two tablet presses. The graphic demonstrates
that both presses are stable and in control and producing tablets with the same average weight and variation.
Figure 4: Control chart showing assay values of batches produced over three years. UCL is upper control limit and LCL is lower
control limit.
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Figure 4 shows a control chart for assay values for batches produced over a 3-year period. The process is stable through the
middle of Year 2 and begins to decrease in Year 3. When a process adjustment is made, the batch assay values return close
to the values observed in Year 1. This example is interesting because a process shift is shown, but none of the batch assay
values are close to the assay specifications of 90–110%.
Out-of-specification (OOS) and out-of-control (OOC) values require investigation. These values are not always caused by manufacturing
problems, and may be caused by sampling errors, testing errors, or human administration errors such as recording or data keying.
The causes of OOS and OOC measurements should be carefully considered when interpreting the OOC and OOS values and deciding
on appropriate action.
Process-capability analysis.
A process-capability analysis is conducted to determine the ability of the process to meet product specifications. The Ppk
value represents the ratio of the difference between the process average and the nearest specification divided by three times
the process SD (see Equation 2).
Table I: Summary of process performance index (Ppk value) interpretation.
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Where A is the upper specification minus the process average and B is the process average minus the lower specification. Two
main statistics are used to measure process capability: percent of the measurements OOS and the process Ppk value. The interpretation
of the Ppk value is summarized in Table I.
Figure 5: Process capability for a tablet weight of Ppk = 1.91. LSL is lower specification limit and USL is upper specification
limit.
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Process capability indices of Ppk of 2.0 and higher are consistent with high-performance processes or robust processes. Figure
4 shows an example of process capability for tablet weight. In this case, the Ppk value is 1.91 (an excellent category) which
is based on the distribution of tablet weights being a considerable distance from the lower and upper specifications for tablet
weight.
When a process is robust, small process upsets will not create OOS product. Accordingly, small OOC signals do not result in
OSS product. A process is said to be "robust" if its performance is not significantly uninfluenced by variations in process
inputs (e.g., raw material lot), process variables (e.g., press force and speed), and environmental variables (e.g., ambient
temperature and humidity).
Figure 6: Boxplots showing tablet hardness for two tablet presses (X and Y).
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Variance analysis.
Another way to assess process stability is to study the variation in process performance that is caused by potential special-cause
variation (e.g., tablet presses, raw-material lots, process operating teams). Analysis of variance (ANOVA) enables one to
identify variables that can increase variation in tablet parameters and that may produce OOS product (see Figure 6).
The boxplot in Figure 6 shows the distribution of tablet hardness values for a batch of tablets produced by two different
tablet presses (X and Y). Press X has a wider hardness distribution than Press Y, yet none of the hardness values are outside
the hardness specification of 1–6 kp. With this data in mind, the process operators can determine whether to make process
adjustments.
After statistical significance of a comparison (e.g., average of Tablet Press X versus average of Tablet Press Y) is established,
the practical significance of the difference in average values must be considered. This assessment is frequently carried out
by expressing the observed difference in average values as a percentage of the overall process average. Subject-matter expertise
is used to evaluate the practical importance of the observed percent difference.
Nested analysis of variance is another form of ANOVA used to assess process stability. Nested ANOVA can estimate the portion
of the total variation in the data attributed to various sources of variation. Typically, the larger the percent of the total
variation attributed to a source of variation, the more important is the source of variation. Low amounts (< 30%) of long-term
variation as determined by a nested ANOVA indicate a stable process.
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