Quality Engineering, 4(4), 649-657 (1992)
`
`STATISTICAL QUALITY CONTROL IN
`THE MANUFACTURE OF
`
`PHARMACEUTICALS
`
`R. H. NOEL
`Bristol Laboratories Incorporated
`
`Purpose
`
`There have been many attempts to define briefly the phrase “quality control by
`statistical methods.” Most brief definitions do not indicate much more information
`
`than the phrase itself, and as the literature on the industrial applications of statisti-
`cal methodology becomes more voluminous,
`it
`is increasingly apparent that a
`definition that will be broad enough to include the entire area of application and at
`the same time specific enough to give adequate meaning, has little chance of ever
`being written.
`The absence of an adequate definition for a subject, however, does not preclude
`a description of some of its salient features and a discussion of what it can and has
`accomplished when applied to industrial problems. Therefore, the purpose of this
`paper is to present some basic concepts of statistical quality control and to
`enumerate some of the things that can be expected from it when it is applied in
`the right proportion with other technology to some of the problems of the pharma-
`ceutical industry, and to give illustrative examples as space permits.
`
`649
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`650
`
`NOEL
`
`SQC and Pharmaceutical Practice
`
`The fundamental concept of statistical quality control and the fundamental con-
`cept, “good pharmaceutical practice,” are one and the same thing. It is the basic
`idea of building quality into a product by maintaining a rigid set of manufacturing
`controls on every step of the production process. Our industry has developed this
`idea by employing manufacturing control systems that, by and large, are far more
`comprehensive than the systems utilized by most other industries. In fact,
`the
`basic philosophy of statistical quality control
`is so like that of pharmaceutical
`quality control that it is surprising that our industry was not the first to adopt it.
`To build quality into a product may well be the sincere desire of every worker
`in the plant but how to accomplish this economically is still another matter. It
`must be obvious that one of the necessary tools for accomplishing this feat is one
`which will provide a factual basis for evaluating a production process and which
`will enable specifications to be set in a scientific manner. Statistical quality control
`is a tool which meets these requirements. It does so by applying the relatively
`simple mathematics of nature to problems in which there is a strong tendency
`toward arbitrary decisions and thus it eliminates the errors arising from guess
`work.
`‘
`
`Statistical quality control recognizes one principle that is at times difficult for
`the pharmaceutical manufacturer to digest. This is the principle of variation. Sta-
`tistical quality control accepts the fact
`that no two manufactured products are
`exactly alike regardless of the refinements made in the production process. It also
`recognizes that there usually is a large number of causes which contribute to the
`total variation between individual units of the same product, but, unlike other
`methods, it provides factual evidence which will discriminate between those varia-
`tions that can be identified with an assignable cause and those which are naturally
`inherent in the specific process. In addition, the
`1ndamental techniques of the
`method are practical enough to be applied routinely by operating personnel
`without any excessive additional supervision.
`The common practice in setting quality levels in the pharmaceutical industry
`seems to follow a pattern of establishing, as a minimum, the standards of the
`official compendia and then adding a certain “plus value” which represents the
`quality standards of the individual management. There is nothing wrong with such
`a practice but it should be pointed out that the administration of this policy is
`beset with pitfalls which must be avoided if the enterprise is to be successful.
`There is always the danger of allowing such a practice to give birth to noncom-
`petitive quality standards. This can happen in one of two ways both of which pro-
`duce equally serious consequences. First, quality levels can be raised to heights
`that will quickly destroy the competitive cost structure. Secondly,
`they can be
`lowered to levels that will involve the producer in excessive risks from both the
`
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`QUALITY CONTROL IN THE MANUFACTURE OF PHARMACEUTICALS
`
`651
`
`market and legal standpoints. Clearly then, some middle of the road policy must
`be adopted and this is no easy task for the road is, most generally, a narrow one
`and expert driving will be required.
`
`How SQC Can Help
`
`What can statistical quality control do to help solve this problem? Before this
`question is answered, it should be emphasized that the method has been referred
`to elsewhere in this paper as only a tool and it should be understood that it is not a
`panacea for all of the problems of the industry. Nevertheless, some of the things
`we can expect of it in helping to solve the problem at hand can be enumerated.
`First, we can expect its use to affect economies in the use of raw materials by
`providing a basis for more realistic specifications for purchased goods and better
`scientific sampling methods for incoming materials. Economics in raw materials
`are also indirectly effected through a more efficient utilization of them as a result
`of process control.
`Second, it can be expected that economics in the use of both man and machine
`power will be realized. Usually this is accomplished by an increase in output per
`man-hour and per machine-hour, which is the net result of putting man power to
`work on the investigation of variations that are identified with some assignable
`cause rather than wasting man power in a guessing game on where the trouble
`may be. It also stems from a reduction in the number of reoperations required.
`Third, statistical quality control can be expected to reduce inspection costs.
`This is accomplished by substituting process inspection for product inspection and
`utilizing scientific sampling plans for check inspection of the final product.
`Fourth, in-process control by this method can be expected to reduce the pro-
`duction of rejects.
`Fifth, the acceptance of this method of in-process control improves the relation—
`ship between the production and control groups because the method provides
`objective records which supplant subjective opinions.
`Sixth, the control department has a charted record, which, carefully read, pro-
`vides a quick history of the progress of a particular lot through the production
`process. In case of any doubtful results in the official tests, appeal
`to the chart
`allows the control department to evaluate the seriousness of such results and make
`decisions concerning the lot which are more meaningful than the usual arbitrary
`rejection or acceptance. Production quickly learns that the chart is its best friend
`and not an additional club of the control department.
`Finally, management can be assured of an improved quality level and more
`homogeneous product produced at lower costs. Also,
`the method will provide
`management with discriminating information concerning quality levels which they
`otherwise seldom get.
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`652
`
`NOEL
`
`Setting Realistic Specifications by Statistical Analysis
`
`So much for the point of view and a broad outline of the features of statistical
`quality control. At this point, let us shift from the general to the particular by con-
`sidering in some detail an application of these principles to a manufacturing pro—
`cess.
`
`Consider the problem of controlling the filling of a relatively viscous injectable
`suspension in multiple dose containers. The specification reads that ten separate 1
`cc injections shall be available from a lO-dose via]. The overall problem is simply
`how much must be put into the via] to meet this specification. It has already been
`intimated that
`there are those who would recommend putting in an adequate
`amount. This is highly laudable but not feasible under today’s condition of com-
`petition. The proper procedure is to find the right amount to fill into these vials.
`The first step is to catalog the sources of variability in both the filling and the
`testing. In this case they are:
`
`l. The residual amount of material
`syringes—syringe holdup.
`2. The residual amount of material which cannot be withdrawn from the vial and
`
`in the syringe and the variability between
`
`the variability in this amount from vial to vial—vial holdup.
`3. The specific gravity of the suspension and its variability from lot to lot.
`4. The variability of the filling equipment.
`
`The average value for each of these contributing sources of variability and a
`measure of the dispersion about it can be easily and quickly obtained. This is done
`by making several measurements (preferably 20 or more) of the syringe holdup,
`vial holdup, etc. and calculating the average value for each. The measure of
`dispersion is obtained by calculating the standard deviation (0’) which is given by
`
`0,:
`
`/):x2 — (XXV/N
`N — 1
`
`where X is equal to an individual measurement, 2 denotes summation, and N is
`equal to the number of measurements in the series. The square of this value is
`known as the variance.
`
`The averages and standard deviations are shown in Table l.
`The variability in specific gravity from lot to lot was small and well within the
`variability associated with several determinations on the same lot of material and,
`therefore,
`its contribution was insignificant. Having these values available,
`it is
`now possible to calculate what the filling figure should be. It was desired that this
`be in terms of weight, and thus the filling figure is derived from the following for-
`mula:
`
`(10.0)(1.007) + 0.506 + (10.0)(o.150) :l:3\/azs + 02v + 02".
`
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`QUALITY CONTROL IN THE MANUFACTURE OF PHARMACEUTICALS
`
`653
`
`SOURCE
`
`AVERAGE
`
`STANDARD DEVIATION
`
`Table 1.
`
`Syringe holdup (1 cc dose)
`Vial holdup (10 cc vial)
`Specific gravity
`Variation in filling equipment
`
`0.150 g
`0.506 g
`1.007
`10.00 cc
`
`0.0052 g = as
`0.0430 g = av
`Nil
`0.034 g = “1:
`
`This formula converts 10 cc to grams by multiplying by the average specific grav-
`ity and adds the average vial holdup in grams, the average syringe holdup in
`grams, and finally takes into account three times the square root of the sum of the
`contributing variances in grams, viz:
`
`(10.0) (1.007) + 0.506 + (10.0)(0.150) 57000522 + 0.0432 + 0.0342
`
`__ {12.241
`
`11.911'
`
`_
`
`The reason for including three times the square root of the sum of the variances
`can be explained best by the diagram shown in Figure 1. In terms of weight,
`10.07 g must be averagely obtained for ten 1 cc injections. The vial holdup will
`be on average 0.506 g and the holdup in the syringe is on average 0.15 g/cc or
`1.5 g for 10 cc. These total an amount equal to 12.076 g. The individual values,
`however, which made up the respective averages vary about them according to
`the normal or Gaussian curve and it is possible to calculate a value about each of
`these separate averages which will include about 99.73% of the individual values
`making up the average. This is done by adding and subtracting from each average
`an amount equal to three times the standard deviation for the respective measure-
`ments. However, the distribution of the sum of N normal and independent vari-
`ables each of normal form also produces a normal or Gaussian curve whose stan-
`dard deviation is equal to the square root of the sum of the individual standard
`deviations squared (variances). In this example, the square root of the sum of the
`variances was 0.055 g. This is the total standard deviation (0,) and 3t;t = 0.165 g
`(Fig. 1).
`
`When the filling machines are set to deliver an average of 12.241 g (Fig. 1),
`one can expect about 99.73% of the vials to contain between 12.076 g and 12.406
`g, respectively. That is, there is a chance that approximately 3 out of 1000 vials
`will contain a quantity outside of these ranges; and further since the curve is sym-
`metrical,
`the chances are equal (0.00135) that a vial will exceed the upper or
`lower limit, respectively. Thus, the probability of distributing into the trade an
`underfilled vial is 0.00135.
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`

`654
`
`NOEL
`
`in more Gms.
`
`
`
`H.9ll Gms.
`
`|2.24| Gina.
`
`
`
`
`”.731. at Oh. Yolal Ann
`I
`
`B
`
`Filling Machine! Sat
`at i - I214: em
`
`
`
`I I I |
`
`| I |
`
`l2.076 Gmsv
`
`
`
`l2.406 Gm.
`
`
`99.73% M "to Total MN
`
`Figure I. Distributions of filling weights.
`
`Process Control Through SQC Charts
`
`The analysis of the variables affecting this particular filling problem has now
`led to the establishment of a realistic specification for the operation as it now
`stands even though an overfil] of more than 20% does not appear to be too
`economical. The fact remains, however,
`that this is about all that can be done
`
`'
`
`unless a major change is made to reduce the magnitude of some of the contribut-
`ing variables. The next step is to follow the performance of the filling machines
`with control charts. Such charts will reveal, first of all, whether the specifications
`arrived at will be met continually and secondly, they will be of use in maintaining
`this specification as well as providing clues that may result in establishing and
`maintaining a more economical specification.
`Figure 2 shows a control chart on the performance of two machines in filling a
`batch of the material following the establishment of the specification. In operating
`a control chart, small samples are taken periodically from the production flow and
`
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`QUALITY CONTROL IN THE MANUFACTURE OF PHARMACEUTICALS
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`655
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`MACHINE A
`
`MACHIN
`AVERAGE CHARTS
`
`I
`_X_*A:E-_'=_-4£5_ _
`
`mi - 0.268
`
`i-Agfi-rzms
`
`RANGE CHARTS
`
`o.fi-o.330
`
`‘°°°t
`
`2345519
`
`I
`
`2
`
`345073910
`
`SAMPLENO.
`
`Figure 2. Control charts on performance of two filling machines.
`
`two samples
`the average and range measurements are computed. In this case,
`were removed and weighed approximately every 20 minutes. The average fill was
`calculated as was the range (largest weight minus smallest weight) for each sam-
`ple and the values plotted as shown. The reason for using the range as a measure
`of dispersion instead of the standard deviation is that the range of a small sample
`is a sufficiently efficient statistic for this purpose and is easier for production peo-
`ple to comprehend. In fact a good estimate of the standard deviation can be made
`by dividing the average range (R) by a factor (d2) which varies with sample
`size. *
`The next step‘is to calculate the average of the sample averages (i) and the
`average range (R). Control limits are then computed according to the formulae
`appearing in Figure 2.
`
`* The factors A2, D4, d2, etc. may be obtained for different sample sizes from a table which appears in the
`A. S. T. M. Manual on Presentation of Data including Supplements A and B published by the American Society
`for Testing Materials, 206 S. Broad St., Philadelphia, PA.
`
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`

`656
`
`NOEL
`
`GM-
`
`MACHINE A
`
`MACHINE a
`
`AVERAGE CHARTS
`
`g
`dd:
`
`23
`
`i _________itali- 12.163 ___________________
`ll nan:
`
`_
`_____7!1‘1 _-12an4_ ._ - -
`
`IZJO
`
`12.20
`I210
`'
`I200
`
`”.90
`
`250
`
`200
`
`.ISO
`
`.IOO
`
`.050
`
`,000
`
`
`
`RANGE CHARTS
`
`_____________________
`
`Figure 3.
`
`Performance of filling machines after process improvements.
`
`
`SAMPLE N0
`
`It can be seen that Machine A is filling vials within the predicted limits. At first
`glance it would appear that Machine A was capable of doing much better since the
`averages were well within the control limits. The relatively wide spread in the
`range chart, howev_e_r, is responsible for these wide limits since they are calculated
`from the formula 3: :bAzfi and the averages can be expected to vary over the
`entire width of these control bands by chance cause alone.
`Machine B shows an even larger dispersion in the range chart as well as points
`outside of the control limits on the average chart. These points which exceed the
`control limits are not due to chance and their causes must be investigated.
`Assuming that the causes for the misbehavior in Machine B can be found and
`eliminated, there remains the problem of reducing the dispersion in both range
`charts. This would allow for the establishment of narrower control limits on the
`
`average chart, thus making it possible to reduce the overfill and still maintain the
`same degree of assurance of meeting the specifications. At this point the other
`technology of the industry is called upon. It is not the purpose of this paper to dis—
`cuss process management, because that would involve the discussion of a whole
`host of engineering specialties. For the problem at hand, however,
`it can be
`
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`QUALITY CONTROL IN THE MANUFACTURE OF PHARMACEUTICALS
`
`657
`
`pointed out that nothing can be done about syringe holdup as their manufacture is
`not under our control. Something might be done about vial holdup and certainly a
`good deal of effort should be spent in an effort to reduce the variability of the
`filling machines. That this can be accomplished is attested to by the control chart
`shown in Figure 3, which represents a production batch of some months later.
`One need only to compare the two charts and one will have no difficulty in con-
`cluding that more vials are forthcoming from the batch produced at the later date
`and further, that the filled vials are much more homogeneous in their contents.
`
`Conclusion
`
`It is planned to discuss several other applications of statistical analysis in the
`pharmaceutical industry in subsequent issues of this journal. The field of applica-
`tion can cover the use of a whole host of individual tools:
`tests of significance,
`analysis of variance, sequential methods, design of experiments, single and double
`sampling methods, simple correlation, multiple correlation, to mention but a few.
`The most pertinent to the subject matter of this introductory paper, however,
`is
`the control chart method which has been briefly discussed.
`
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