DESIGN FOR SIX SIGMA

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NOT LONG after its inception at Motorola in the mid 1980's, Six Sigma'spractitioners reahzed that there is often a practical limit to how muchproducts or processes can be improved. This limit is sometimes referredto as the "five sigma barrier" because it is in this region of process per-formance that the financial gain of further improvement is frequentlyoutweighed by the cost of implementation. At approximat ely 233 defects permillion (dp*), a five sigma process is well above average when compared tomost manufacturing processes.

Yet a five sigma process may not be sufficient for many critical process steps.In the pharmaceutical industry, even the "world class" six sigma standar d (3.4dp*) is inadequate with respect to some critical defects. Given this dilemma,how can we achieve an appropriate level of process performance whilemaintaining a competitive operating cost? And how do we make sure that we"get it right the first time" without spending extraordinary amounts of timeand money in development?

The answer that Six Sigma's early practitioners came up with was to developan additional set of tools and techniques for the development cycle. Thesebecame known as Design for Six Sigma (DfSS). The fundamental premisebehind DfSS is that developers must thoroughly understand the process andproduct such that critical material and process parameters are identified andappropriately controlled.

It's easy to recog nLZe that the underpinnings of DfSS are closely alignedwith those of Quality by Design (QbD). Guidance documents published byICH, for example, frequently refer to the need for pharmaceutical R&D teamsto develop an "enhanced" level of process knowledge using sould scigntificmetho:ds and experimentation. Thus, these two approaches, DfSS and QbD,complement each other well.

This paper Will take a closer look at this overlap between Design for SixSigma and Quality by Design, as well as introduce DfSS tools:.-*includingMonte Carlo Simulation, Parameter (robust) Design, and Tolerance

36 FEBRUARY 2O1O PHARMACEUTICAL IV1ANUFACTURING . WWW.PHARMAMANUFACIURING;COM

Allocation-which can also be used to support a QbDprogram.

INPUTS AND OUTPUTSAccording to ICH Q8, "The aim of pharmaceutical devel-opment is to design a quality product and its manufacturingprocess to consistently deliver the intended performance ofthe product." This objective can be attained by using an "em-pirical approach or a more systematic approach to productdevelopment." DfSS and QbD are very much focused on thelatter. Both are founded upon the definition and under-standing of the product, its performance requirements, andthe processes by which it is manufactured and packaged.

The ultimate goal of most production processes is tounderstand the relationships between the critical inputsand outputs of each step. Although in early developmentteams often do not have well-defined specifications, oncegeneral performance measures have been identified, it ispossible to list inputs that may affect outputs of interest. Assuggested in ICH QB (Rl), development teams can use priorknowledge of similar products and the results of preliminaryexperimentation to create fishbone diagrams listing allpotential factors which could impact each of the outputs.This initial effort should result in an exhaustive list of inputswhich will grow and evolve as the team learns more.

Failure Mode and Effects Analysis (FMEA) and otherrisk management tools should be applied at all stages. Assuggested by ICH QB (Rl), FMEA might be used to rankthe many factors contained within the various fishbonediagrams. There are several other ways that FMEA can beapplied. Two of these that are suitable for early stages ofdevelopment include a step-by-step review of the processand a component review of the formulation. When usingthe former approach, the team must identify the intendedfunction of each process step. It must then ask what couldgo wrong with that step that could impair or prevent it fromdelivering the intended function.

Similarly, using the second approach, after listing everycomponent of the formulation, the team must ask what theintended purpose of each component is and how it could failto perform that function. The results will be rated in termsof the severity of the failure, its likelihood of occurrence,and the probability of escaped detection. The product ofthese individual ratings, the Risk Priority Number (RPN),provides a priortttzedlist of problems which present thegreatest risk. Like the fishbone diagrams, an FMEA is aliving document which should be revisited, revised andaugmented multiple times during the development cycle.

FINDING THE "VITAI FEW-DfSS, like QbD, is based upon the development of an under-standing of the relationship between specific input param-eters and the performance of the finished product. Aftercompleting the initial versions of the fishbone diagrams and

DESIGN FOR SIX SIGMA

FMEA, the team will have an extensive list of potentiallyimportant factors. How does it determine which ones areactually "critical to quality" with respect to the performanceof the finished product?

On the basis of the results of the FMEA exercise, priorknowledg. and preliminaryr experimentation, the teamshould be able to create a shorter list. However, they willprobably not yet have enough knowledge or data to narrowthe list to what Dr. |oseph ]uran referred to as the "vital fewamong the trivial many." Hence, additional tools are needed.

A statistically designed experiment, often referred to asa Design of Experiments (DoE), is one way to efficientlyand scientifically narrow the list of factors. There are manydifferent designs which could be used for this purpose, eachwith their own pros and cons.

At a preliminary screening stage, it is best to test themaximum number of factors while performing the fewestpossible experiments. For example, a TaguchiLlzdesignwill allow us to evaluate the relative importance of upto 11 factors using just 12 experimental runs. One of thelimitations of this design is that, although it providesinformation regarding the relative importance of theindividual factors, it does not give information on possibleinteractions between those factors. Nonetheless, it is a goodfirst step towards ranking factors under investigation.

TRANSFER FUNCTIONOnce the list of "most important" factors has been made

ffiffi'.":ff 'l::"?t1i::il:ril,,1TI#.Tfiffi:,T,",designs can produce an empirical model which mathemati-cally describes the relationship between the inputs and theoutput(s) of interest. In DfSS jargon, this mathematicalprediction equation is known as a transfer function.

The transfer function is an extremely valuable piece ofprocess knowledg.. Given specific values for the inputs,it can provide a means to predict the averagevalue of theoutput(s). Conversely, if the desired value or a specificationrange of the output is known, it can identify optimumoperational and material parameters to achieve the desiredaverage response.

Almost always, the team is interested in more than oneoutput. Fortunately, it is possible collect data on multipleoutputs for each experimental run, and then use all of thisinformation to predict the best conditions that satisfy thespecifications for each of the outputs. This technique isknown as multiple response optim tzation.

Unfortunately, there is no guarantee that a perfectsolution exists. Although it is possible to mathematicallyexplore the experimental space described by the transferfunctions, there may or may not be a location (the designspace) that will consistently satisfy all of the specificationsat the same time. If the development team finds itself inthis situation, at least they identified this problem relatively

PHARMACEUTICAL MANU FACTU RING WWW- PHARMAMAN U FACTU RI NG. COM FEBRUARY 201O 37

TransferFunctions

Monte Carlo Simulation (MCS) applies the characteristics of known orestimated input distributions to the transfer function of each output inorder to produce an estimate of the distribution of that output. lf outputspecifications have been developed or proposed, process capability and

the associated defect rate (dpm) can also be predicted.

Figure 2: Parameter Design

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quickly and efficiently, and the knowledge gained can helpthem to regroup and find solutions later in development.

MONTE CARLO SIMULATIONA wide variety of other DfSS statistical tools can be appliedusing the transfer function. One is Monte Carlo Simulation(MCS), sometimes referred to as Expected Value Analysis(EVA). Among other things, MCS can be used to predictprocess capability-i.e., how well the process is expected toperform relative to its specification(s).

In many cases, applying the average values of inputs tothe transfer function will predict the average value of theoutput(s). Unfortunately, this approach does not considerthe fact that most inputs are not perfectly constant-that is,they are not always going to be equal to the average value.Inputs may vary from one duy to the next, from lot to lotor even operator to operator. Although controls are oftenimplemented to hold these factors constant or within aspecified range, the ability to do so is sometimes limited'by technology or cost. The advantage MCS offers is that, ifthe long-term distribution parameters (e.g., the mean andstandard deviation of a normally distributed factor) canbe estimated for each critical input, these estimates can beapplied to the transfer function and used to predict whatthe expected distribution of the output(s) will be over thelong term, across many batches.

Figure I (left) represents an Input-Process-Output(IPO) diagram which indicates that the process inputshave three different distributions. In this example, inputs

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Figure 3: Tolerance Allocation

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Tolerance Allocation evaluates the effect of individually increasrng and

decreasing the standard deviation of process inputs. In this example,reducing the variation of X, (the green dashed line represents the distri-bution resulting from a tightened specification) has significantly reducedthe variation of the output (green output histogram). This approachallows the team to identify which inputs will have the greatest impact onthe output variation and thereby helps to balance cost-benefit trade-offsand set appropriate specifications for each of the process inputs.

DESIG N FOR SIX SIG MA

Figure 1. Monte Carlo Simulation

Estimated InputDistributions

Predicted 0utputDistributions

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Parameter Design explores the experimental space looking for regionswhich make the process tolerant of the known variation of some difficultto control process inputs. In this example, the average value of X, has

been reduced and the average value of X, has been increased (inputdistributions have been shifted from the blue to the green histograms).Effectively the variability of the inputs and the average response remainthe same, but the variation around the average response has been sig-nificantly reduced (green output histogram) resulting in a process whichis tolerant (robust) to the variation of the inputs. To simplify the example,only one response has been used in this illustration, but multiple re-sponses can be evaluated simultaneously.

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Xr, X2, and X, appear to be normally,exponentially, and uniformlydistributed. The MCS will "randomlydraw" one value from each of thesedistributions and apply those valuesto the transfer function to generatea single result for the predictedvalue of the output(s). It will repeatthis process as many as one milliontimes. The histogram of the resultingvalues will provide an estimate of theoutput distribution which can then becompared to the specifications for thatperformance metric.

The ability to predict processoutput capability not only allows theteam to estimate the defect rate forthe intermediate or finished productunder investigation, but also allowsa direct comparison of the relativeperformance of various formulationoptions, processes or products whichmay be under consideration.

PROCESS ROBUSTNESS ANDSPECI F ICATIONSAry process should be "robust" to thevariation of process inputs which aredifficult or expensive to control. Let'ssay the particle size distribution (PSD)of a micron rzedactive pharmaceuti-cal ingredient (API) is difficult tocontrol. If PSD is an important factorwith respect to dosage uniformity,rather than tightening the specifica-tion and perhaps paying a premium tothe supplier, it would be preferable tofind operationai conditions which aretolerant of this variation; that is, teamscan identify conditions under whichthe dosage uniformity is relativelyunaffected even in the presence of thePSD variation.

Several DoE techniques can helpmake a process robust to variationin certain input variables, thoughmany of these become difficult andcumbersome to apply when dealingwith multiple responses. Another DfSStool, Parameter Desigr, explores theexperimental space looking for regionswhich make the process relativelyinsensitive to the known variation of

the inputs. Parameter Design shifts theaverage response of the various inputsand evaluates the effect on the outputdistributions. If successful, it will finda combination of average input settingswhich achieve the same average outputresponse, but with less variationaround that average.

If the team is not able to find anyrobust regions within the design space(they may not exist), they may tightenthe input specifications to reduce theoutput variation. Intuitively, manyprocess scientists and engineers believethat tightening the specification of aninput will reduce the output defectlevel, and in fact this is often true.However, what is often not intuitiveis the ability to identify which factorswill have the greatest impact and towhat degree specifications need to betighten.d. Tpically, asking suppliersor the manufacturing team to meet atighter specification on a raw materialattribute, or an operating parameter,will result in an increase of operationalcost. Consequently, it's importantto prevent a situation where inputspecifications are tightened "just to besure."

Tolerance Allocation allows theteam to understand the effect ofchanging the variation of each input

DESIGN FOR SIX SIGMA

on the variation of the output(s). Incontrast to Parameter Design whichshifts process averages, ToleranceAllocation will evaluate the effects ofindividually increasing and decreasingthe standard deviations of each ofthe input factors. It will estimatethe expected number of defects permillion (dp*) under each of these trialconditions. The resulting matrix givesthe team the knowledge required toset appropriate specifications for eachinput.

coNcLUsroNsDfSS and QbD share a common phi-losophy based upon the principle thatemploying a systematic and struc-tured approach to product develop-ment will increase the amount ofprocess knowledg. the developmentteam obtains. This will allow theteam to make better decisions andincrease the probability of develop-ment success @

About the AuthorMurray Adams is a certified Master Black Beltand the Managing Director of OperationalExcellence, a consulting company that providesSix Sigma andDlSS analysis, training, andcoaching. He can be reached at murray.adams@rogers.com.

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