J. clin. Path., 1972, 25, 989-996

The role of operational research in clinical chemistryJ. PETO', L. G. WHITBY, AND D. J. FINNEY

From the Departments of Statistics and Clinical Chemistry, University of Edinburgh

SYNOPSIS This paper begins with a critical examination of the published account (Carruthers,1970) of a pioneering study of simulation in a clinical chemistry laboratory. It next considers thebasic requirements for the formal mathematical description of such a laboratory: these include thesetting of criteria, the resource and input variates, and the definition of success by means of criterionvariates. Investigation of criterion variates can be by direct measurement, or by a theoretical approachwhich may include simulation. The aims of simulation are discussed and an attempt to simulate theoperation of a large clinical chemistry laboratory is described.The difficulty of constructing an overall measure of efficiency is considered in relation to improving

performance within an existing framework, to evaluating new equipment such as computers on-lineto laboratory apparatus, and to inter-laboratory comparisons of performance. It is concluded thatcomplex operational research techniques, including simulation, have little to offer at least for thepresent, and may even lead to misleading conclusions.

Clinical chemistry laboratories are experiencingrapid increases in the number of analyses performed,often as much as a doubling every four years. Tocope with these work loads, automatic methods ofanalysis have been introduced on a large scale, andthese have helped to overcome shortages of trainedstaff. Increasing work loads, shortages of staff, andthe efficient operation of expensive automaticequipment demand good organization and operationof the laboratory. In most big laboratories thesefeatures, and particularly the automatic equipment,have created a factory situation for a large propor-tion of the specimens handled: in principle, a samplerequiring a specified set of assays passes, or shouldpass, through the various parts of a laboratory in afixed order and on a fixed schedule. Factory methodsof operation naturally suggest that operationalresearch techniques, which have proved so useful inindustrial planning and reorganization, might assistthe study of laboratory efficiency.The operational research approach to a problem

normally involves definition of an overall index, ofefficiency or profit, maximization of which is assertedto determine the best mode of operation. In principle,this is the ideal basis for decision. In practice,however, establishment of a realistic index may be so'Present address: Institute of Psychiatry, University of London.Requests for reprints to Professor L. G. Whitby, Department ofClinical Chemistry, University of Edinburgh.Received for publication 21 August 1972.

complex that recourse is had to arbitrary estimatesof the financial consequences of possible changes. Amedical environment presents peculiar difficulties inobtaining agreed values, on a monetary or any otherscale, to be placed on benefits to patient care,improvements in the use of time by physicians, andincreases in hospital efficiency. Two main types ofoperational research can be distinguished:

1 Direct Measurement

In this, the introduction of new equipment or neworganization is compared with the situation pre-viously obtaining.

2 Theory

This attempts to predict the effects of possible but asyet untried changes in organization and equipment.

Direct measurement has the attraction of seemingto be realistic, but its application is limited tocircumstances where advantage can be taken ofchanges already approved, or so minor as to beacceptable experimentally for a short period. More-over, since any major change in equipment, eg, theintroduction of a laboratory computer, is likely to beaccompanied by changes in staffing dispositions andorganization not in themselves essential to the changein equipment, but made contemporaneously for a

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variety of reasons, discrimination between effectsmay be impossible.

Theoretical studies may range from simplearithmetic evaluation of the extra work that mightbe undertaken if an additional technician is employed(assuming an average and predictable work content),through mathematical analysis of rates of flow ofwork, to the numerical simulation on a computerprogrammed to correspond to the whole perfor-mance ofa system. Although the theoretical approachavoids many of the problems of direct measurement,it is often open to the criticism that the theory fails torepresent realities completely and exactly.

Operational research methods have been appliedto the study of outpatient departments (Blanco-White and Pike, 1964), surgical admissions (Weir,Fowler, and Dingwall-Fordyce, 1968), x-ray depart-ments (Fraser, 1969; Jeans, Berger, and Gill, 1972),haematology (Rath, Alverez Balbas, Ikeda, andKennedy, 1970), and clinical chemistry laboratories(Carruthers, 1970). Examples of relatively simple butarbitrary indices of efficiency or profit have includedattempts to apply a costing figure to alterations in thetime required for reporting results of laboratorywork, and to place monetary values on work con-ducted at different levels of analytical precision. Thepurpose of this paper is to discuss the application ofoperational research techniques to clinical chemistrylaboratories.

Simulation in a Clinical Chemistry Laboratory: aDiscussion of the Example Reported by Carruthers(1970)

Critical examination of this pioneering study drawsattention to some of the main issues facing any userof operational research in a large clinical chemistrylaboratory, and helps to identify some of theprinciples on which further advances must be based.The author described three laboratory schedules,listing for each assay and each day the latest timethat a specimen could be accepted for analysis onthat day. For each schedule, the delay suffered byeach of a random sample of request forms before allthe analyses requested had been completed was foundby a computer simulation. The financial consequencesof the different schedules were estimated on theassumption that each day in hospital cost thecommunity at least £10, and that at least 10% of thedelays in the issue of reports from the laboratoryattributable to the slower schedules of work resultedin consequential delays in the discharge of inpatientsfrom hospital. Carruthers suggested that comparisonof these estimated financial consequences with thecosts of implementing the different laboratoryschedules would identify the best schedule. Certain

assumptions implicit in this method must beexamined.

In the first place, the capacities of the severalsystems were assumed to be adequate and thereforeirrelevant to the selection of the best schedule. Inpractice, there is no simple relationship between workload and a laboratory's theoretical analyticalcapacity since automatic equipment may be installedbecause expected increases in work load could not beaccommodated and standards of reliability main-tained by non-automated methods (eg, Whitby,1967). On the other hand, it is not always reasonablein practice to ignore the effects of technical break-downs on analytical capacity, as mentioned againlater.

Secondly, in comparing the cost-effectiveness ofthe three schedules, Carruthers assumed, for anarbitrary proportion of cases, that delay in reportingresults prolonged the stay of patients in hospital byan amount corresponding to the difference inreporting times attainable with the different sched-ules. He appears to have assumed, tacitly, that allresults corresponding to a particular request wouldbe reported together. In fact, it is widely heldlaboratory practice to report results on the day theybecome available (as interim reports) rather thanwait until all assays requested on a specimen havebeen completed. Furthermore, clinical decisionsabout treatment are only sometimes held up until theresults of chemical investigations become available,and it is unusual for patients who are clinically fit fordischarge to have the time of their discharge delayedpending the results of chemical investigations. It isquestionable, therefore, whether delays in reportingresults would have direct and consequential effectson the time of discharge on the scale suggested byCarruthers, even assuming that all the request formshe was reviewing had originated from inpatients. Ifsome of the request forms had comefrom outpatients,delays in the laboratory would probably not have hadsignificant consequent-al effects on the costs to theNational Health Service for these analyses; inevaluating any schedule it is important to know thesources from which requests are drawn as well as thetypes of analyses being requested.A third assumption by Carruthers was that

variation in the rate of arrival of requests for analysis,not sufficient to produce persistent queues, was theonly stochastic element in the laboratory: by'stochastic' is meant 'dependent on effectivelyrandom chances and expressible only in terms ofprobabilities instead of being exactly calculable'.Although this simplification would be acceptable ifthe work load were large enough to be stable and theanalytical equipment reasonably reliable, in everydaywork some requesting rates show considerable

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variation and failures in machine performance cancause substantial delays in starting or completinganalyses.These criticisms mean that this simulation study

failed to take account of the fact that the financialevaluation ofany laboratory schedule of work shouldbe based on a detailed knowledge of the sources andtypes of specimen affected, as well as the distributionof their arrival times in the laboratory throughout theday. Important though these criticisms are on pointsof detail, they do not detract from the assertion byCarruthers that simple and useful specification oflaboratory schedules is possible, nor from hisrecognition that delays in performing laboratorywork can have direct-although not easily assessed-financial consequences. Nevertheless, the criticismsmust be taken as a warning against the temptationto exaggerate the accuracy of apparently sophisti-cated methods, and to claim that they therefore leadautomatically to the best decision.Another drawback to this approach is that it is

unlikely to lead to the optimal allocation of re-sources, since only complete work schedules arebeing considered. For example, changing from thefirst to the second schedule described by Carruthers(1970) would, amongst other effects, reduce themaximum delay in the determination of serumprotein-bound iodine (PBI) from one week to threedays. If this change could be effected quite cheaplyfor PBI determinations alone, it might be well worthwhile, but it need not require changing the labora-tory's whole method of operation to schedule 2.Simple inspection of data relating to specific assaysor groups of assays, as tabulated by Carruthers,shows where the greatest improvements in labora-tory performance can be obtained from changingwork schedules; inspection by itself is likely to leadtowards the best schedule, providing data aboutsources of specimens and their arrival times in thelaboratory are available.

Ihe Formal Mathematical Description ofan AnalyticalLaboratory

A fundamental reason for studying the performanceof a hospital laboratory, or system of laboratories, isto find ways of improving performance. Such studiesusually start from the assumption that the work isbeing done well-for instance, that every chemicalanalysis has acceptable standards of reliability.Any processing system, whether a factory or an

analytical laboratory, consists of a set of elementaryunits, each of which has its own characteristics ofoperation; the units may be arranged in series, inparallel, or in a combination of the two. If theperformance of each unit can be expressed quanti-

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tatively in respect of the time it requires to fulfilits function, or of constraints on the quality andquantity of its performance, together with anynecessary stochastic element to represent the inherentvariability of each unit, theoretically the perfor-mance of the whole system can be predicted. Besidesvariability within the system, stochastic variation inthe input may require specification. Unless allstochastic variation is negligible, the output of aprocessing system will be subject to random varia-tion; description of this is often of fundamentalimportance for the evaluation of the system. Insimple systems, the structure may allow the equationsrelating output to input, and to the behaviour of theelementary units, to be solved completely; quanti-tative evaluation of any property of the system can beachieved. The system does not have to be verycomplicated, however, before a mathematicalsolution of the equations becomes impossible.

SETTING OF CRITERIAInterest lies in the effects of changing the manyfactors that define the facilities of the laboratory andtheir manner of utilization. These include numbersof staff in various categories, numbers and types ofitems of equipment (AutoAnalyzers', etc), andmodes of operation, sizes of 'stores' (samplesawaiting analysis, patients awaiting tests, etc) andscheduling of the programme of work in relation todifferent tests. These factors can all be expressedquantitatively, although adequate description ofsuch concepts as scheduling possibilities is compli-cated. The factors constitute an array of differentvariates, for instance: x1 = number of Auto-Analyzers; x2 = number of technicians; X3 = timeof day for last acceptance of samples for test A, etc.These factors may be collectively described as the'resource variates' and collectively referred to as xwithout a subscript.A second category of variates, y, is needed to

define the input. These specify the daily demands onthe laboratory (numbers of samples classifiedaccording to analyses requested, times of receipt ofsamples, etc). They may be named Yi, Y2.... andtermed the 'input variates'. Resource variates arewithin the control of the laboratory management,apart from limitations of finance and staff recruit-ment, whereas input variates correspond to externaldemands.A third category of variates is needed to define

success, the 'criterion variates'. Although ways ofimproving -he performance of the laboratory arebeing sought, the proper choice of a measure ofsuccess is not self-evident; the number of samplesanalyzed per day, the time from receipt of a sample'Technicon Instruments Co., Basingstoke, Hants.

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to reporting the corresponding analyses, the per-centage of samples not analysed and reportedcompletely within 24 hours, etc, are all possibilities.These different criterion variates, named zl, Z2 . . . .

(collectively referred to as z) may be in conflict. Forexample, other things being equal, a schedulingchange designed to reduce the time for processing aparticularly important sample may reduce the totalnumber of samples analysed that day.

MEASUREMENT OF CRITERIARecommendations for improving laboratory per-formance can be derived only if the relevant criterionvariates (z) are to some extent dependent upon theresource (x) and input (y) variates chosen formeasurement, and if, for stated values of the x andy variates, prediction of one or more of the z variatesis practicable. Exact determination of Z2, for instance,cannot be expected from knowledge of the x and yvariates because the measured x variates are at bestonly the more important members of a much largerset.For purposes of inference, any criterion variate

needs to be averaged over the various conditionsrepresented by the frequency distribution of the inputvariates, since normally the latter cannot be con-trolled by the laboratory. Unless the variabilityarising from stochastic sources and from unmeasuredresource variates is negligible, for a criterion such asthe time required to process a sample the distributionof the variate about its mean value will also need tobe taken into account. The mean and standarddeviation of the time per sample might then beadopted as two distinct criterion variates, sinceoverall assessment of the quality of laboratoryperformance must recognize that excessive variabilitymay seriously reduce the acceptability of a particularwork schedule, no matter how satisfactory theaverage processing time may seem. If the frequencydistribution of a z variate for specified values of x, yis very skew, percentiles or probabilities may be moreuseful. For example, the processing time exceeded bythe most extreme 1O% of samples, or the probabilitythat the analysis of a sample will not be completedwithin 48 hours, may be useful measures of efficiency.

Values for z variates corresponding to specifiedvalues of x, y may be sought either by direct measure-ment or by theory. If normal laboratory operationpermits Z3, for instance, to be recorded on a numberof occasions where different x, y either occurnaturally or can be adjusted to suit the investigation,empirical knowledge of the relation between Z3 andx, y can be built up. Provided that the relation isfairly regular and variability is not too great,interpolation may thzn allow adequate prediction ofZ3 for other combinations of x, y values not

previously tried. However, if the number of x and yvariates is large, and if determination of a singlevalue of z3 requires the records for a whole day'slaboratory work, accumulation of sufficient data willtake a long time. In addition, the effects of irrelevantchanges may be included within the measuredcriteria. Perhaps the biggest disadvantage, however,is the fact that the ranges of values of resourcevariates that can be studied, in the course of normaloperation, will commonly be much narrower thanare of interest for inferring the optimal structure.The alternative, theoretical approach covers a

much wider range of possibilities. In the simplestsystems, elementary arithmetic may suffice to connectz3 with x, y as in a physical system in which neitherhuman intervention nor occasional faults disturb theuniformity. If a liquid is to be conveyed by a straightpipe, for example, the volume carried will depend onthe diameter of the pipe and on the pressure andviscosity of the liquid. Even if Z3 is not exactlydetermined by x, y, the system may permit maxi-mum and minimum values to be calculated byextreme assumptions. However, full theoreticalspecification of a complex system often leads to setsof equations that are intractable by formal mathe-matical analysis. It is important also to rememberthat the theoretical approach is valid only in so far asthe equations used adequately describe the behaviourof the system for all combinations of x, y variates,and this holds whether the equations are solvedmathematically or subjected to simulation.

SIMULATION AS APPLIED TO AN ANALYTICALLABORATORYSimulation is often used as an alternative to thetheoretical formal description of a process. It isusually assumed to refer to a computer technique,but this is not a necessary feature. In simulation, thehistory of a single product or sample passing throughthe system is followed according to the rules appli-cable to each unit, every instance of stochasticvariation being taken into account by a randomselection from the appropriate frequency distribution.In this way, the final properties of one particularsimulated item running through the whole processcan be described numerically. Repetition of thesecalculations, with a new random selection ofvariables each time, enables frequency distributionsto be constructed for the properties of the outputfrom the system. If different versions of the wholesystem are to be compared, each can be simulatedsufficiently often to ensure that any importantdifferences are made apparent by the forms of thefinal frequency distributions.

Expressed in these terms, simulation may soundvery attractive, but it is appropriate only when the

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system to be analyzed is too complex for the con-sequences of the alternative systems under considera-tion to be calculated by a direct mathematicalapproach. Simulation can have one of three aims:(1) to predict the effects of changes in the system, orin the input to the system, ie, changes in x and yvariates, upon the operation and upon particularcriterion (z) variates; (2) provided that the effectsjust mentioned can be evaluated financially, orcombined into a single index of efficiency, togenerate numerical values of the index for differentx, y; (3) to maximize this index of efficiency, andthereby to find automatically the optimal conditionsof operation. Generally, the third aim is onlypracticable when a computer is used for the simu-lation, with appropriate programming to vary thesimulated structure so as to make it evolve towardsthe optimal conditions. Prerequisites for the employ-ment of simulation are:1 Enough is known about the manner in which zdepends upon x, y for the simulation to be construc-ted realistically, even though the correspondingequations may defy explicit solution.2 The components of random variation introducedinto the simulation or permitted to occur arequantitatively good approximations to those of thereal system.3 The ranges of x and y that can be covered by thesimulation are at least as wide as those appropriateto the real system.

Unless these prerequisites are met, there is adefinite danger that the simulation will correspondless to reality than to the investigator's concept ofhow the system should perform. Thus simulationmust assume very close (ideally, exact) correspon-dence between simulated values of z1 and values thatwould be observed for the same x, y. Also, knowledgeof the theory must suffice for interpolation within theframework of the simulation; simulation measuresz, for specified x, y but subsequent inference mayrequire to estimate z1 for intermediate x, y.

Investigation of rules that enable criteria to bepredicted from x, y may demand recourse tosimulation if some of the following conditionsobtain:a The formulae relating a criterion variate to x, yare so complicated that the theory is intractable andaccumulation of sufficient observations from thereal system would take too long a time.b Records from an observational approach wouldbe acquired very slowly (eg, one per day), whereassimulation makes possible a much more rapidadvance in understanding:e For specified values of x and y, variation in z1 isso great (on account of unidentified or unmeasurablevariates) that large numbers of observations would

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be required even to estimate the mean of z1, and stilllarger numbers for any study of the frequencydistribution of individual values about the mean.d The extent to which resource and input variatescan be varied, or will vary naturally while obser-vations are being collected, is much less than therange desired for future inference.e In the particular circumstances, simulation issubstantially cheaper than feasible alternatives.

Further Observations Relevant to Operational Re-search in Clinical Chemistry

The concepts discussed in this paper are relevant to astudy which began with the collection of datarelating to the clinical chemistry laboratory in theRoyal Infirmary, Edinburgh, on the basis of whichthe intention was to develop a simulation program ora mathematical model. The flow of work throughsuch a laboratory is basically simple. Specimensarrive at the reception area and samples are distri-buted to the appropriate analytical benches wheremuch of the work is carried out with AutoAnalyzers.The raw data are recorded, corrected, and convertedto the relevant units for reporting purposes, andissued as reports after collation and assessment.From the analytical viewpoint, if the equipment isreliable, each bench should be capable of operatingat a predictable speed throughout the day except forperiods of maintenance of equipment and prepara-tion for analysis. Any tendency for occasional over-loading in the reception area tends to be met by thetemporary redeployment of staff; regular over-loading would require more staff or could theo-retically be catered for by alternative arrangementssuch as staggering the times for submission ofrequests from different wards or clinicians.As indicated, the initial approach was by simu-

lation. Distributions of arrival times of specimensrequiring particular assays or groups of assays wereobserved, as were the normal starting times on eachbench, time spent in the reception area whilespecimens were registered and prepared for analysisbefore distribution to the appropriate bench orbenches, and so on. The simulation program couldallow for the progressively reduced service whichwould operate if increasing proportions of the staffwere absent.The first prerequisite of any simulation must be

that, when it is based on the observed distributions ofx and y, the resulting distributions of the criterionvariates, z, are very similar to those currentlyachieved. The initial program failed to do this-thesimulation described the 'official' timetable, corre-sponding very closely to the schedule achieved on thefew days when no interruptions occurred. Allowance

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was then made for the observed distributions ofvarious delays, including equipment failure, thererunning of unsatisfactory specimens, delays inchanging from one analysis to another, etc, therebyproducing a simulation which was virtually in-distinguishable, at least in output, from the labora-tory in operation under the then existing conditions.The question next arose whether it was possible or

desirable to proceed to simulate alternative arrange-ments, assuming that the delays now incorporatedinto the program were inherent properties of thesystem. It was clear that the optimal capacity of thelaboratory was equal to the number of specimensthat the staff and equipment could analyse if theyworked continuously from 9 am to 5 pm; such aschedule would require specimens to arrive earlyenough for AutoAnalyzers to operate withoutinterruption, and possibly extra staff in the receptionarea, but these requirements could have been mettheoretically. However, it was clear that a computerwas hardly necessary to calculate the correspondingcapacity, which was the theoretical optimum for thelaboratory. More marginal improvements couldreadily be predicted without recourse to the com-puter if assays were to be grouped differently, or theway in which specimens were distributed modified,without altering the existing operating characteristicsof the separate units in the simulation. In the beliefthat the computer simulation was unnecessarilysophisticated, the actual processes in the laboratorywere next examined further.With the exception of automatic equipment used

for assaying different substances on the same day,analysis rates and the length of time during whichautomatic equipment was operated should havedetermined the capacity of the laboratory for thoseassays carried out on this type ofapparatus. Applyingsuch simple calculations, it soon became apparentthat the automatic equipment, mostly Mark IAutoAnalyzers, could (with the exception of the ureaand electrolyte analyzer) theoretically handle abouttwice the current demand for analyses. The differencebetween the theoretical and actual throughputs ofwork, in those instances where queues built up, waslargely attributable to machine failures of varyingduration and grades of severity. The scheduling ofusage for most of the automatic equipment was,however, deliberately being kept sufficiently lax as toleave a reasonable margin for dealing with theseunscheduled breakdowns; laxity of scheduling isclearly necessary if machine failure is common. Ifthroughput were to be increased and maintainedwithout additional capital expenditure, and theefficiency of use of staff and equipment therebyimproved, observations on each assay over a periodwere needed rather than theoretically sophisticated

operational research (whether by simulation orotherwise) to determine the amounts of potentialoperating time lost.

These observations were made and were dividedbetween machine failures per se and other losses (latestarting for reasons other than machine failure,delayed changing of plates of specimens for Auto-Analyzers, time spent on analyzing duplicatesamples, etc), and the causes of loss of efficiencyrecorded. Since AutoAnalyzers run at constantspeeds, widely spaced visits to each bench sufficedfor recording the starting and stopping times foranalyses and for identifying the occurrence of delays.Discrepancies between theoretical and actualthroughputs of specimens were then clarified byenquiries made the same day from the staff con-cerned. Some delays were undoubtedly due to humanerror, but these were sufficiently rare for excessivequestioning to be unnecessary and for cooperationnot to be impaired by any implication that thecompetence of staff was the real subject of the study.

After comparing current performance with thebest theoretically achievable, given high machinereliability and rigid scheduling, steps could be takento reduce the larger deficiencies. On the basis ofobserved performance, improvement in the reliabilityof AutoAnalyzer equipment seemed to be the chiefneed, particularly of the Technicon Mark III flamephotometer, with conditions of operation during theday so organized as to interrupt the continuous flowof analyses as little as possible. To this end, withstandard (non-computerized) methods of chartreading, staff duties needed to be arranged so thatchart reading and calculation of results correspond-ing to the preceding plate of samples, and pre-paration of specimens and loading of the subsequentsample plate, were undertaken, on a long analyticalrun, during the time that the current plate of sampleswas being analysed. Improvements in machinereliability, eg, from preventive maintenance, thatreduced the down time before the start of a run, orthe frequency of breakdowns in the middle of a run,improved efficiency by lessening the time spent ondiagnosing faults or on repeating the analysis ofspecimens adversely affected by machine failure.

Discussion

Operational research is intended to provide a basisfor inference about the consequences of changes in asystem, especially changes in the resource variates(x) introduced as a policy for improving performancebut also changes in the input variates (y). Changes iny are less immediately controllable, but may becontemplated as a long-term development, forexample, because of a proposal to adopt a general

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programme of screening patients by a range oflaboratory tests, or because of an increase in thecatchment area. If the relation between outputcriteria (z) and x, y has been determined, the pro-cedure is to use this relation to predict how much thecriteria will be altered as x and y change, for instanceto find optimal values for some or all of the xvariates under certain constraints on the values of ythat will be encountered. 'Optimality' is defined asproducing the most desirable values for one or morecriteria, for example, maximizing the utilization ofexpensive equipment. However, where aims are notentirely compatible, a formal compromise such as asingle index of performance based on various criteriamay be misleading, since such indices are liable to bemore or less arbitrary unless the criteria on whichthey are based can be accurately assessed financially.It might, for example, be impossible to find agenerally acceptable formula which included pre-cision, speed of issuing reports, and working con-ditions of staff.Whether the criteria are studied by direct measure-

ment or by theory (with or without simulation), thevalidity of inferences depends entirely upon theadequacy of the model. If the theory were correct,deductions from it would be in no doubt; in real life,theory seldom has this exactness. Measurement hasthe advantage of guarding against flaws in the model,by making certain that the z variates correspond withthe x and y, thus ensuring reasonable estimation ofany criterion from knowledge of values x and y,provided that other unspecified variates are un-important. However, if planned changes in the x andy variates are associated with unavoidable or evenunsuspected changes in other relevant variates,inferences and predictions may be seriously mis-leading. Inference becomes more secure if thetheoretical and measurement approaches can be usedto reinforce one another. The stochastic elements in aclinical chemistry laboratory are few and simple incontrast to clinics, in which attendance by patients isnecessary, and where consequently a complex queuestructure is encountered. In the laboratory, the mostimportant factors are those that affect the availabilityand reliability of resources, notably machine break-downs, reduced hours of operation, and staffshortages. If the effects of such factors can bepredicted approximately by elementary calculation,there is little to be gained by more complex studyunless the predicted changes in output variates canbe precisely evaluated financially. The contention ofthis paper is that such financial evaluation cannot bedone, and that decisions about the most suitable waysof running an individual laboratory should continueto be made by heuristic assessment of the effects ofchanges in method of operation on output, rather

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than by invoking sophisticated theory. The com-parative evaluation of different systems of laboratoryoperation is most usefully achieved by listing theprecision of analytical work, the speed of reportingresults, the costs of running the laboratory, its workload, and its capacity for expansion-informationthat is mostly available. These data can be satis-factorily recorded and examined as individual items,not needing to be combined into formulae morecomplex than a simple overall figure such as theaverage cost per analysis in a laboratory; even thissimple figure may be misleading if used to comparetwo or more laboratories, because laboratories maydiffer considerably in their patterns of work.

It is, nevertheless, potentially useful to comparethe performance of similar laboratories. This shouldbe possible by using a simple proforma for thecollection of data such as those listed in the precedingparagraph, and these might draw attention toshortcomings in individual laboratories; no specialoperational research teams should be needed. Suchcomparisons could reveal differences in reliability ofequipment, or in operating costs, and might serve toindicate standards of reliability and performancethat should be able to be approached in routinepractice. The main emphasis in inter-laboratorycomparisons so far has been on the quality ofanalytical work; such comparisons of analyticalreliability reveal minimal acceptable standards forthe quality of performance, since there is no reasontheoretically why laboratories using similar equip-ment should not achieve closely similar results.Examination of discrepancies should reveal differ-ences in the operation of analytical methods, forinstance in the maintenance or operation of theequipment.

Simulation finds its greatest usefulness whenapplied to complex systems, the output characteristicsof which can be summarized easily in terms ofefficiency or productivity. In such studies, distinctionbetween structural complexity and functionaldiversity is essential. In a car factory, for example,the effects of changes in the system are difficult topredict because the overall system is structurallycomplex; the schedulings of the various processesare so interdependent that simulation would pro-bably be needed to predict the effect on output of anychanges. To assess the financial value of a givenchange in output is simple, however, because the solepurpose of the process is the production of cars. Ahospital laboratory, by contrast, presents verydifferent problems: to predict at least approximatelythe effect of changes in operation, eg, in altering thecapacity for work, or in affecting the speed of issuingreports, may be easy, but the evaluation of theseeffects in financial terms may be extremely difficult.

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These considerations again indicate that simulationis not appropriate for operational research applied toa clinical chemistry laboratory.These conclusions on the dangers of attempting

to synthesize overall measures of laboratory effi-ciency, on which to base decisions on future planning,apply without modification to the evaluation ofradically new systems. Several clinical chemistrylaboratories have been operating on-line computersystems of various degrees of complexity, and thehealth departments are naturally concerned that theybe compared with traditional systems on some basisof cost-effectiveness. Such comparisons must not besimplified by attempting to separate computer-related from other activities, and then comparingsome derived index such as staff efficiency in theseareas with the 'efficiency' previously obtaining. Theeffects of introducing a computer into a laboratoryare inescapably complex and, apart from observedchanges in criteria such as analytical precision, speed,cost, work load, and capacity, a comparativeevaluation should take account of improvementswhich could be effected within the original system bymethods not requiring the introduction of thecomputer.

This project was financed by a grant from the ScottishHome and Health Department, and the authors arevery grateful for this support. The detailed work wasbegun by Dr Brenda J. Fraser and continued by oneof us (J.P.). We wish to express our thanks to DrFraser, and to the many members of laboratory staff

who assisted with this study, particularly Dr I. W.Percy-Robb and Mr J. Proffitt.

Addendum

Since this paper was submitted, a further account ofa laboratory simulation has been published (Cundy,1972). This study illustrates the main points putforward in the present paper, and could be subjectedto detailed criticism. We do not share the author'soptimism about the application of his simulationmodel to the whole of the clinical laboratory system,and would draw attention to the inability of hispresent model to match existing conditions.

References

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Carruthers, M. E. (1970). Computer analysis of routine pathologywork schedules using a simulation programme. J. clin. Path., 23,269-272.

Cundy, A. D. (1972). A simulation study of the clinical laboratoryoffice. In Spectrunt 71: a Conference on Medical Computing,edited by M. E. Abrams, pp. 124-138. Butterworths, London.

Fraser, B. J. (1969). The organisation of a radiology department in adistrict general hospital. Ph.D Thesis, University of Reading.

Jeans, W. D., Berger, S. R., and Gill, R. (1972). Computer simulationmodel of an X-ray department. Brit. med. J., 1, 675-679.

Rath, G. J., Alverez Balbas, J. M., Ikeda, T., and Kennedy, 0. G.(Spring 1970). Simulation of a hematology department. HlthServ. Res., 5, 25-35.

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