Statistical Tools of Quality Control: Training Module - Notes/Domino ...

Table of ContentsIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Objectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1Quality Assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Control of Preanalytical Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2Control of Analytical Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Control of Postanalytical Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3Quality Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Quality-Control Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Statistical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Accuracy and Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4Central Tendency and Mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8Statistical Measures of Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9Quality-Control Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Selection and Use. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16Reconstitution of Quality-Control Materials . . . . . . . . . . . . . . . . . . . . . . . . .18Storage of Quality-Control Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18Level I and Level II Quality-Control Materials . . . . . . . . . . . . . . . . . . . . . . .19What is a Quality-Control Rule?. . . . . . . . . . . . . . . . . . . . . . . . . . . 20Individual Quality-Control Rules . . . . . . . . . . . . . . . . . . . . . . . . . . 21Other Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22The 1 2s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22The 1 3s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22The 2 2s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25Interpreting Quality-Control Results . . . . . . . . . . . . . . . . . . . . . . . 27Levey-Jennings Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27Calculating ±2 Standard Deviation Ranges . . . . . . . . . . . . . . . . . . . . . . . . . .28Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Practice Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Practice Exercise 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32Practice Exercise 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33Practice Exercise 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34Practice Exercise 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37Practice Exercise 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38Practice Exercise 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40Answer Keys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Practice Exercise 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41Practice Exercise 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42Part No. 7B6006 Statistical Tools of Quality Control: Training Module vii2006-03-31 VITROS Chemistry Systems

Practice Exercise 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43Practice Exercise 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46Practice Exercise 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47Practice Exercise 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49Self-Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Self-Evaluation Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Part No. 7B6006 Statistical Tools of Quality Control: Training Module viii2006-03-31 VITROS Chemistry Systems

Part No. 7B6006 Statistical Tools of Quality Control: Training Module x2006-03-31 VITROS Chemistry Systems

IntroductionIntroductionThe purpose of this module is to provide a summary of the basic conceptsand practices of quality control used in the laboratory.After completing this module, you will be able to calculate importantvalues associated with these programs and correctly interpret theinformation obtained from those calculations.ObjectivesUpon completion of this module, you will be able to:• Discuss the importance of quality assurance and quality-controlprograms in the clinical laboratory.• Name several parameters that should be monitored and evaluated by aproperly designed quality assurance program.• Explain how a quality-control system is used in the clinical laboratory toverify the accuracy of patient test results.• Define the following terms as they relate to a set of repeatedmeasurements: accuracy, precision, frequency distribution, and centraltendency.• Calculate the following statistical parameters: mean, standard deviation,coefficient of variation, and ±1, 2, & 3 standard deviation ranges.• Select the appropriate type of quality-control material for a givenlaboratory test procedure.This module will take approximately two hours to complete. You will needthe following items:• Calculator *• PencilThis module is designed with practice exercises to help you understandeach concept. The answers to the practice exercises can be found in theanswer keys at the end of the module.*Most calculators can perform the math taught here—make sure youunderstand the concepts.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 12006-03-31 VITROS Chemistry Systems

Quality AssuranceQuality AssuranceQuality-assurance programs are designed to ensure that the results providedby the laboratory are accurate. This is accomplished by establishingprotocols for quality performance in the laboratory.Quality assurance is a program of written procedures. These proceduresprovide a systematic method of monitoring factors that may affect thequality of laboratory test results. A quality-assurance program also outlinesa system for correcting any deficiencies found during the monitoringprocess, reevaluating the systems after corrections, and informing staff ofany procedural changes. Quality-assurance programs are designed tomonitor and evaluate the quality and appropriateness of patient careservices, as well as to resolve problems.Each laboratory test consists of numerous steps that begin when theclinician decides to order a test on a patient, and ends when the clinicianuses the results for diagnosis and/or treatment of the patient. Many of thesesteps can be implemented in several ways. They are known as variables.Some variables affect the final test result if they are not carried out in aspecified way. For example, when a specimen is collected, it might go to thelaboratory for processing immediately, or a delay might occur so that itarrives in the laboratory several hours later. If a transport delay causes thesubstance that is to be measured to deteriorate, then testing an old specimenwould give erroneous results. The variable in this example is time.Criteria should be established to reduce delays in the transport process ifnecessary, and monitors should be established to verify that no delaysoccur. Establishing the appropriate time frames and monitoring them is away to control the time variable.All variables that affect the testing process should be controlled. Thisincludes preanalytical, analytical, and postanalytical variables. On thefollowing pages you will find examples of these variables and a descriptionof how they should be controlled.Control of Preanalytical VariablesVariables that should be controlled before testing are called preanalyticalvariables. Examples are:• Selection of appropriate tests.• Identification and preparation of the patient.• Collecting and labeling of the sample.• Transport of the sample to the laboratory; proper handling of the samplefrom the time of collection until the time of testing.• Placement of the sample in the laboratory workload.• Storage of reagents used to perform tests.2 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Quality Assurance• Periodically verifying that procedure manuals are complete and up todate.Preanalytical variables should be monitored periodically to assure that theyare being carried out properly.Control of Analytical VariablesVariables that affect the outcome of the result while the actual testprocedure is in progress are analytical variables. They include:• Quality of the water supply.• Stability of the electrical power.• Preparation of the reagents.• Upkeep of the instruments and equipment.• Use of the proper calibration materials.• Regulation of the temperature in instruments with temperature controlcompartments.• Observance of the steps outlined in the laboratory procedure manual foreach test performed.• Recording of patient results.Monitoring the analytical variables and correcting them as needed helpsensure quality test results. Many other variables may be involved in theanalytic part of the testing process, but may be different for each testingmethod.Control of Postanalytical VariablesPostanalytical variables can impact the reported result once the testprocedure is completed. They include:• Checking the accuracy of calculations used in reporting patient results.• Reporting the patient’s results to the doctor.• Establishing and using appropriate “reference” or “normal” range.• Immediate reporting of critical results to the doctor.• Filing and storing the patients’ reports.It is very important that the laboratory staff communicate with the healthcare team of doctors, nurses, phlebotomists, and messengers to achieve thegoals outlined in a quality-assurance program.A good quality-assurance program systematically checks each of the itemsthat may cause errors in the system. Some items, such as the temperaturesof water baths, are monitored daily, so that the problems might be correctedbefore testing patient samples. Other items, such as the electrical power andwater quality, may be evaluated periodically. A quality-assurance programshould be designed so that all factors that affect the test system areevaluated over an established time frame.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 32006-03-31 VITROS Chemistry Systems

Quality ControlQuality ControlThe quality-control program is a sub-unit of the quality-assurance program.It focuses on the actual testing process in the laboratory. This programincludes a system designed to monitor the accuracy and precision of thetesting process. These terms will be described in more detail later in thismodule.Quality-control procedures are used to monitor performance of analyticalmethods. Therefore, quality control is most useful to identify if theanalytical system is stable and free of significant error. If problems areidentified, corrective action should then be taken to solve the problem,thereby enabling you to produce accurate patient reports.Quality-Control SamplesControl procedures use quality-control samples to determine if the methodis working properly. The quality-control sample is a sample with knownvalues of the analyte being tested. These samples of known value have beenanalyzed many times. Based upon the results obtained from the repeatedanalysis of quality-control materials, a range of expected values for eachanalyte is developed. If the quality-control samples fall outside thisexpected range of values, an error may have developed in the test systemand patient sample results may be incorrect.Evaluation of quality-control values gives you confidence that the patientresults are accurate before reporting them to the physician. These ranges foreach analyte in the control sample are calculated using statistical formulas.Statistical ConceptsStatistical concepts serve as the foundation for the interpretation of qualitycontrolresults that provide important information about whether or not thetest system is operating correctly. Any series of measurements can beevaluated by computing and interpreting the statistics from that set ofmeasurements.Two important concepts used to assess quality control are accuracy andprecision.Accuracy and PrecisionAccuracyIf a calculated average and the true value are identical or very close, it canbe said that the measurements used to calculate the average are accurate.Therefore, let us define an accurate series of measurements as one thatproduces an average that is equal to or is very close to the true value.4 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Quality ControlThe target on the right represents a group of measurements that are neitherprecise nor accurate. They neither hit the bull’s-eye nor cluster together.These results are said to be both inaccurate and imprecise.Statistical Measure of AccuracyTo illustrate this point, suppose 22 people measured one person’s height tothe nearest tenth of an inch. They probably would get several differentmeasurements, even if they used the same yardstick.For example, if the person’s true height is 65.4 inches, the measurementsmight range from 65.1 inches to 65.7 inches, as illustrated in Figure 2:Variation in Height MeasurementMeasurement Number12345678910111213141516171819202122Height (inches)65.365.165.465.365.665.465.365.565.465.665.465.465.565.265.465.365.765.565.565.265.465.4Figure 2. Variation in Height MeasurementActually, some variation would occur even if the same person measured theheight of an individual 22 times.A certain degree of variability is allowed in the clinical laboratory, but youmust learn to distinguish between acceptable variation and test errors, andestablish parameters to distinguish between the two.In order to do this, it is important to learn how to do some necessarycomputations. Applying these computations will help you distinguishbetween acceptable variation and error.How may times does each measurement appear in Figure 2?6 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Quality ControlHeight measurement# of Occurrences (frequency)65.1 I65.2 II65.3 IIII65.4 IIII III65.5 IIII65.6 II65.7 IThe measurements shown in Figure 2 are represented on the graph inFigure 3:108MEANFrequency642065 65.1 65.2 65.3 65.4 65.5 65.6 65.7 65.8Height (inches)Figure 3. Frequency Distribution of Height MeasurementsThe individual plotted points in Figure 3 represent the height measurement(x-axis) and the frequency of the measurement (y-axis). If manymeasurements are available to plot, a bell-shaped curve results, as shown bythe solid line in Figure 3. If only a few data points are available, a straightline results, as shown by the dotted line.As shown on the graph, the value of 65.4 inches occurred 8 times, while thevalue of 65.2 occurred only 2 times.Notice that the measurements are symmetrically distributed. This meansthat if the graph were cut in half, both halves would be almost identical.Also notice the bell shape of the graph. Most of the measurements tend tocluster around a central value. This is called the mean. If the results of a setof measurements have a specific distribution around the mean, as shownhere, then they are said to have a normal distribution. There are additionalstatistical values that can describe a normal distribution that will bereviewed in later pages.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 72006-03-31 VITROS Chemistry Systems

Quality ControlAll of the statistical methods that will follow assume that data beinganalyzed will produce a normal distribution or bell shaped-curve.It is not usually necessary to actually plot frequency distributions for thepurposes outlined in this module. However, you should understand theconcept of frequency distribution. In our example, the majority ofmeasurements are clustered around a central point, in this case, 65.4 inches.Assuming that each person used an accurate yardstick and propertechnique, this central point should be close to the true height of theindividual.Central Tendency and MeanThe term associated with a clustering of measurements is called centraltendency.The most commonly used measure of central tendency is the arithmeticaverage or mean. The mean is an estimate of the true value.Let’s examine how the concept of central tendency relates to laboratoryvalues.Calculation of the MeanGlucose ResultsDay1234567891011121314151617181920Glucose (mg/dL)83 (x 1 )89 (x 2 )858584878586858488818688828782838090 (x 20 )Figure 4. Glucose ResultsFigure 4 shows glucose results from the repeated analysis of one qualitycontrolsample. This sample was analyzed once a day for 20 days. From8 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Quality Controlthese measurements, we can calculate the mean. Remember that the mean,a measure of central tendency, is another term for average.To calculate the mean or average, divide the sum of the measurements bythe total number of measurements:where: n = total number of measurementsX 1X 2( X 1 ) X 2+ ( ) + ( X 3 ) + … +( X 20 )----------------------------------------------------------------------------- = X = meannrefers to the glucose result obtained on Day 1.refers to the glucose result obtained on Day 2, and so on,for 20 days.Xis the symbol for mean.Let’s calculate the mean for the data in Figure 4.1. Add all of the results (measurements). Glucose results are commonlyreported in units of mg/dL.In this example, the sum of the 20 glucose results is 1700 mg/dL.( X 1) X 2+ ( ) + ( X 3) + … + ( X 20) = 1700 mg/dL2. Divide this sum by the total number of measurements (n), in thisexample there are 20.The number, 1700 divided by 20 is equal to 85.Therefore the mean of the 20 glucose measurements is 85 mg/dL.orPractice Exercises 1 and 2 will allow you optional practice calculatingthe mean for two sets of quality-control data. The answers are providedin the answer key at the end of this module.NOTE:1700----------- = 8520X = 85 mg/dLVITROS Chemistry Systems can calculate means and standarddeviations for collected quality-control data in the quality-controlsoftware package! Therefore the mean is calculated for you.Statistical Measures of PrecisionTo establish limits of acceptability for single observations of controlmeasurements in the laboratory, two related measures are calculated forPart No. 7B6006 Statistical Tools of Quality Control: Training Module 92006-03-31 VITROS Chemistry Systems

Quality Controleach set of quality-control materials. The control is tested at least 20 timesover a span of 20 to 30 days. Then the parameters are calculated using the20 values obtained.Important note: You can get a good estimate of precision by using 20 to 30points. However, you do not need 20 to 30 points to get a good estimate ofthe mean. Two to five points may provide a good estimate of the mean.The parameters that provide information about the reproducibility orprecision of the measurements are:•Variance• Standard DeviationLet’s look at them individually to understand what they mean.Standard DeviationStandard DeviationLine AFrequencyLine BMeasurement UnitsLine A = Small SD, more preciseLine B = Large SD, less preciseXFigure 5. Standard DeviationVariance is a measure of variability. It is used to calculate standarddeviation by taking the square root of it. The formula for variance isexplained on the following page.The value of the standard deviation is related to the spread of themeasurement values. The greater the spread of values around the mean, thelarger the standard deviation. Large standard deviations indicate lessprecision.The shape of the curve is established by the distribution of themeasurements. In Figure 5, notice that Line B has a wide distribution10 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Quality Controlcompared to Line A. Line B has a greater standard deviation than Line A.Line A has a smaller standard deviation because the values are closer to themean.Calculation of Standard Deviation(s)Figure 6 shows the formulas for the calculation of the variance and standarddeviation:Calculating Standard DeviationVariance = s 2 =∑ (X i- X) 2n-1Standard Deviation = s =√∑(X i- X) 2n-1Where∑=the sum ofX iX==each measurementthe means=standard deviationn=total number of measurements√=square rootFigure 6. Example of Standard Deviation CalculationNote that standard deviation is the square root of the variance.Recall that the symbol X refers to the mean.The symbol Σ stands for “the sum of.”The total number of measurements is represented by n in this formula.The notation for the variance is s 2 . Variance is not used to establish thequality-control limits. The standard deviation is the square root of thevariance. Its notation is a lower case s.To calculate the variance, the mean is subtracted from each result and thevalue obtained is squared. All of the squared values are then added togetherand divided by the number of measurements minus one.Many scientific calculators have been programmed to perform standarddeviation calculations according to this formula once all the values havebeen entered. If you are using a calculator, verify you are using the sampleSD calculation that uses “n–1” as the denominator. Remember, theVITROS Chemistry Systems can collect the data and calculate the meansPart No. 7B6006 Statistical Tools of Quality Control: Training Module 112006-03-31 VITROS Chemistry Systems

Quality Controland standard deviations! However, the following pages will demonstratehow this calculation can be done by hand.Calculating Standard Deviation(1)Results (X i) mg/dL8389858584878586858488818688828782838090(2) (3)(X iX) (X iX) 2-2+400-1+20+10-1+3-4+1+3-3+2-3-2-5+54160014010191619949425252X = 85 mg/dL ∑ (X iX) = 138Figure 7. Calculating Standard DeviationFigure 7 is an example of the steps to be followed to calculate the standarddeviation of the glucose measurements previously described in Figure 4.Let’s follow the steps to calculate the standard deviation:1. List the values obtained by each of the 20 measurements as shown incolumn 1.2. Calculate the mean of the 20 measurements.3. Subtract the mean from each value as shown in column 2.For example, the difference between the first value, 83, and the mean,85 = –2.Note that the values that are less than the mean result in negativenumbers in column 2 and the results that are greater than the mean arepositive numbers.4. Square each of the numbers obtained in column 2. The results of thisstep are shown in column 3.Remember, to square a number, you multiply the number by itself.Two negative numbers multiplied together equal a positive number.Consequently, all of the numbers in column 3 are positive numbers.12 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Quality ControlFrequency Distribution-2 SD Mean+2 SDFigure 8. Frequency DistributionPractice Exercises 3 and 4 will allow you to practice calculating SDs.Follow the sequence of calculations exactly as described to obtain thecorrect values.Standard Deviation and ProbabilityXFrequencyA.68.2%C.B.95.4%99.7%MEAN-3s -2s -1s +1s +2s +3sXFigure 9. Standard Deviation and ProbabilityFigure 9 shows a standard frequency plot of a theoretical set of data points.14 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Quality ControlOnce the standard deviation is known, the likelihood or probability that aparticular measurement will fall within specified ranges can be predicted.The three ranges shown on this graph labeled A, B, and C correspond to ±1standard deviation, ±2 standard deviations, and ±3 standard deviationsabout the mean.A frequency plot that looks like a symmetrical, bell-shaped curve can bedescribed as a “normal” distribution. A normal distribution can bedescribed by the mean and the standard deviation. Statisticians tell us that68% of all data points fall within ±1 standard deviation for data that can bedescribed by a symmetrical, bell-shaped “normal” curve. Additionally,about 95% of all data points will fall within ±2 standard deviations, and99.7% of all data points will fall within ±3 standard deviations.Most of the measurements are expected to be within this ±2 standarddeviation range. If 100 glucose measurements of the same control materialwere taken, approximately 95 of them would fall within the ±2 standarddeviation range, while approximately 5 measurements would fall out of thisrange.If the ±2 standard deviation criteria is used to evaluate the testing system,you can have 95% confidence that the measurement is correct when thequality-control measurements fall within this range.Which SDs Should the Lab Use?There are three sources for SDs that the lab can use.• If you choose to use medically useful criteria, you will need to have themedical director of the laboratory establish precision goals and the SDguidelines and rules that are used in determining when a quality-controlfailure is large enough to require action. Medically useful criteria areoften described by the term coefficient of variation (CV). CV isdefined as :SD------ × 100%XIt is a convenient way of expressing precision in a manner applicable toany concentration level.• If you are using VITROS Performance Verifiers as a daily control fluid,we recommend the within-lab SDs from the Performance Verifier AssaySheets. These values incorporate the expected sources of variation thatcan occur when you are using one lot number of slides overtime.• If you choose to use an SD that represents actual performance in yourlaboratory (whether using VITROS Performance Verifiers or anothermanufacturer’s fluid) you must be sure that this estimate includes all thesources of variability that can occur within a slide lot.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 152006-03-31 VITROS Chemistry Systems

Quality-Control MaterialsBoth types of commercial quality-control materials may be prepared inlarge batches by the manufacturer. Each batch is assigned a specificnumber. These numbers are referred to as lot numbers.Important points to remember about control lots used for daily qualitycontrol:• Many labs prefer to have one year’s supply of each control on hand.They should be stored according to the manufacturer’s directions.• Different lot numbers of control fluid must not be mixed togetherbecause each has a different concentration of analytes.• The mean must be calculated or evaluated before a new lot number ofquality-control material is used because each lot number has its ownconcentration of the analyte.The mean should also be reassessed when new lot numbers of reagents areput into use. For VITROS Systems, you should re-evaluate means whennew lot numbers of slides, VITROS Reference Fluid, or Immuno-WashFluid are put into use.• Use only the lot number of quality-control material for which you haveestablished the mean and standard deviation.• SDs should be derived from the laboratory’s established precision goalsfor each analyte. Some manufacturers provide recommended SDs foreach analyte. For VITROS Chemistry Systems, this information isprovided on the Performance Verifier sheets.Types of Quality-Control MaterialsQuality-ControlMaterialsLiquidFormLyophilized“Freeze Dried”Figure 10. Types of Quality-Control MaterialsCommercially available quality-control materials (Figure 10) can be liquidor lyophilized. Liquid controls may contain stabilizers such as ethyleneglycol, a chemical preservative. Controls made with ethylene glycol arePart No. 7B6006 Statistical Tools of Quality Control: Training Module 172006-03-31 VITROS Chemistry Systems

Quality-Control MaterialsAllow the quality-control fluid in the cup to come up to room temperature(following the recommendation of the manufacturer), and then run the fluidon the analyzer. Cold fluids are more viscous and will spread less evenly onthe slide. VITROS slides are optimized for use with room temperaturefluids.Also, be sure to use reconstituted control materials within themanufacturer’s specified time period for each constituent.Level I and Level II Quality-Control MaterialsIMPORTANT: Some VITROS Performance Verifiers have 3 levels. Meanand standard deviation must be established for all levels inuse.A mean and standard deviation must be established or available for eachconcentration and lot number of control material. Traditionally, twodifferent quality-control materials with different concentrations of analytesare analyzed every 24 hours as long as patient samples are being tested.Controls commonly have values assigned so that one level has theconcentration of analytes at or near the reference interval for those analytes.A second level has concentrations at or near concentrations associated withthe presence of disease or a medical decision point.Using two levels allows you to evaluate the performance of the analyzersystem at different concentration ranges. That is, at least two levels arerequired to evaluate the accuracy and precision of the test system.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 192006-03-31 VITROS Chemistry Systems

What is a Quality-Control Rule?What is a Quality-Control Rule?A quality-control rule is used to help you decide when your analyzer systemis performing within expectations. Expectations can be determined by youor by the manufacturer of the system. When the system is performing asexpected, you have confidence in the patient results reported by the system.Quality-control rules describe statistical procedures used to interpretquality-control data and identify unusual occurrences that characterizeunstable analytical system performance.Most of the rules use the mean and standard deviation (SD) to describe asituation. The mean and SD are calculated from quality-control data.Manufacturers of quality-control (QC) fluids and equipment sometimesdetermine mean and SD values that they recommend for use in the lab.Control rules are written in the following format: “X y.” Control rulescombine either a statistical procedure or the number of observations (X)and a control limit (y).For example, “1 3s ” is a control rule where 1 observation of a QC fluid result(X=1) is reviewed to see if that one result differs from the mean by ±3 SD(y= 3s ).This is the same as using a Levey-Jennings chart with an established meanand an acceptable range set at ±3 SD around the mean.Quality-control rules may be used individually or in combination with eachother to determine if the analyzer system is functioning properly. The nextsection tells you which quality-control rules are appropriate for use onVITROS Systems. And after that, we will describe how to use those rulestogether to determine whether your VITROS System is functioningproperly.20 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Individual Quality-Control RulesIndividual Quality-Control RulesThe approach presented in this document uses two levels of quality-controlfluid. However, the number and concentration of quality-control fluidsshould be selected based on your testing needs.Quality-control rules are applied to the data of the 2 levels of qualitycontrolfluid individually and together.There are three quality-control rules that are appropriate to use on theVITROS System. They are the 1 2s rule, the 2 2s rule, and the 1 3s rule. Table1 lists these quality-control rules:RuleQuality-Control Rule Explanation1 2s The 1 2s rule describes a situation where one control value for any of the twolevels of control is outside the mean ± 2 SD.1 3s The 1 3s rule describes a situation where one control value for any of the twolevels of control is outside the mean ± 3 SD.2 2s The 2 2s rule describes a situation where both control fluids or two consecutivecontrol values of one fluid are outside the mean by either +2 SD or –2 SD.Table 1. Quality-Control RulesThe three quality-control rules just described are used together when themean value for the quality-control fluids has been established. The diagrambelow should help you better understand the three rules.Three Quality-Control RulesControlData1 2sViolated?NoIn Control:Continue &Accept ResultsYes1 3sViolated?NoNo2 2sViolated?YesYesOut of Control - InvestigateFigure 11. Three Quality-Control RulesPart No. 7B6006 Statistical Tools of Quality Control: Training Module 212006-03-31 VITROS Chemistry Systems

Individual Quality-Control RulesOther RulesAdditional rules, like the Westgard rules, are also available, such as the 4 1srule and the 10 1s rule. These rules are used only after a 1 2s violation isnoted. The 4 1s rule violation occurs when four consecutive controlobservations fall on the same side of the mean and all four are outside of±1 SD. The 10 1s rule violation occurs when 10 consecutive controlobservations fall on the same side of the mean outside of ±1 SD.These rules are useful when a system is subject to frequent changes, likefrequent calibration. They are very sensitive to small systematic errors.Because VITROS Chemistry Systems are so infrequently calibrated, usingthese rules can cause you to react when nothing is wrong and is notrecommended. Therefore, not all rules are appropriate for VITROSSystems.Let’s take a detailed look at the three rules that are appropriate for VITROSSystems. We will use Levey-Jennings charts to help “visualize” the controlrules, but you do not need these charts to use the rules.The 1 2s RuleThe 1 2s rule is a warning rule. This rule is violated when one of the twolevels of control results falls outside of the mean ±2 standard deviationrange. One control level result is within ±2 SD and the other control levelis outside ±2 SD.Violation of the 1 2s rule constitutes a warning and requires evaluation todetermine whether the 1 3s rule and the 2 2s rule have also been violated. Itcautions you to watch closely for present or developing sources of error.The 1 2s warning rule by itself is not cause for rejecting a run. When this rulehas been violated, the next rule in the sequence must be evaluated.For example, suppose that the mean of a Level I control material forcholesterol is 180 mg/dL and the ±2 standard deviation range is from 160to 200 mg/dL. A result either above 200 mg/dL or below 160 mg/dL wouldviolate the 1 2s warning rule.The 1 3s RuleIf the 1 2s warning rule is violated, the 1 3s rule is evaluated next. The 1 3s ruleis violated when either result of the two levels of control fall outside of themean ±3 standard deviation range for either control level.When this rule is violated, your system behavior may have changed andinvestigation is needed before proceeding. No other rules need to beevaluated. Remember, 99.7% of the time, results are expected to fall withinthe mean ±3 SD range.22 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Individual Quality-Control RulesIf the 1 3s rule is violated, the method must be evaluated to determine thesource of the error. The problem must then be corrected and the controlsrepeated before running patient samples.The 2 2s RuleIf the 1 3s rule is not violated, the 2 2s rule is evaluated next. The 2 2s rule canbe violated three different ways (Figures 1 to 3).1. One QC point of Level I control and one QC point of Level II whenassayed at the same time are greater than their respective 2 SD limitswith same sign (+ or -). In this example, both values are outside the+2 SD limit.Rule 2 2s Violation 1Level ILevel II+2SD+2SDXX-2SD-2SD1Days21Days2Figure 12. Rule 2 2s Violation 1Part No. 7B6006 Statistical Tools of Quality Control: Training Module 232006-03-31 VITROS Chemistry Systems

Individual Quality-Control Rules2. Two sequential QC points from the same fluid are greater than thesame 2 SD limit. In this example, the 2 recent values for Level I areoutside the +2 SD limit.Rule 2 2s Violation 2Level ILevel II+2SD+2SDXX-2SD-2SD1Days21Days2Figure 13. Rule 2 2s Violation 23. Two sequential QC points, one from Level I and the other from LevelII, are outside of their respective 2 SD limits with the same sign(+ or -). In this example, the value for Level I on day one is outside+2 SD limit and the value for Level II on day two is also outside+2 SD limit.Rule 2 2s Violation 3Level ILevel II+2SD+2SDXX-2SD-2SD1Days21Days2Figure 14. Rule 2 2s Violation 324 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Individual Quality-Control RulesIf the 2 2s rule is violated, your system’s behavior has changed andinvestigation is needed. If a problem is identified, it must be corrected andthe controls repeated. The patient results can be reported only when thecontrols used in the repeat assay do not violate any of the rules.Once you have corrected the problem that caused a rule to be violated, thecontrol values that indicated a problem should not be used to evaluate the2 2s status next time controls are assayed (but do not delete from QCrecords).ExamplesThe following are examples of the evaluation process using these threecontrol rules.Control Rule Violations 2 2sGlucosemg/dL96(+3s)92(+2s)88(+1s)84(X)80(-1s)76(-2s)72(-3s)Glucose (Level I)X= 84 mg/dLs= 4 mg/dL0 5 10 15 20 25 30 31Day of the MonthGlucosemg/dL214(+3s)206(+2s)188(+1s)180(X)172(-1s)164(-2s)156(-3s)Glucose (Level II)X= 180 mg/dLs= 8 mg/dL0 5 10 15 20 25 30 31Day of the MonthFigure 15. Control Rule Violation 2 2sIn this example (Figure 15), on day 10 of these Levey-Jennings charts, eachquality-control level violated the 1 2s warning rule. The 1 3s rule, however,was not violated. Further inspection shows that the 2 2s rule is also violatedsince both controls are outside of the two standard deviation range.Remember, one way that a 2 2s rule violation occurs is when the qualitycontrolresults of both levels either exceed the +2 standard deviation limitor exceed the -2 standard deviation limit. In this example, the results of bothquality-control levels exceed the +2 standard deviation limit. This methodPart No. 7B6006 Statistical Tools of Quality Control: Training Module 252006-03-31 VITROS Chemistry Systems

Interpreting Quality-Control ResultsInterpreting Quality-Control ResultsTo interpret your quality-control data, the results on the controls arecompared to a range of acceptable values. The most common criteria usedto define the range of acceptable values are the mean ±2 SD and the mean± 3 SD. These ranges can be thought of as having an upper and lower limit.For a control result to be acceptable it must fall within these limits.Levey-Jennings ChartOnce quality-control ranges are established, each quality-control resultshould be recorded and evaluated before patient-test results are reported.One of the most common manual ways to do this is to plot the controlresults on a Levey-Jennings chart. The mean and acceptable ranges of thequality-control material are plotted against the days of the month as shownin Figure 17.Levey-Jennings ChartGlucosemg/dL96(+3s)92(+2s)88(+1s)84(X)80(–1s)76(–2s)72(–3s)Glucose (Level I)X= 84 mg/dLs= 4 mg/dL1 5 10 15 20 25 30 31Day of the MonthFigure 17. Levey-Jennings ChartThe Levey-Jennings quality-control chart provides a convenient way torecord and visualize quality-control results over a period of time.Please note that the VITROS Chemistry System can record quality-controldata when the sample is run. You can request printouts of Levey-Jenningscharts from the VITROS quality-control program. See “Calculating±2 Standard Deviation Ranges” in this section for calculation.To obtain the values included in the control limit range two mathematicalcalculations must be performed. First calculate the mean and select thePart No. 7B6006 Statistical Tools of Quality Control: Training Module 272006-03-31 VITROS Chemistry Systems

Interpreting Quality-Control ResultsTherefore, the range that includes 2 standard deviations would includeall the values from 76 mg/dL to 92 mg/dL.Mean ±2 Standard Deviation = range of values76.0 to 92.0 mg/dLRemember that 4.5% of the time, or approximately 1 in 20 times, a qualitycontrolvalue will fall outside of this range due to chance (even when thereis nothing wrong).Figure 18 represents an analyte with a mean of 84 and 1 SD of 4.0 mg/dL.The dotted line on either side of the mean represents the +2 and –2 standarddeviation limits. In the example, the standard deviation = 4.0 and 2 x 4.0 =8. Thus, the line above the mean is 84 + 8, or 92, and the line below themean is 84 – 8, or 76.Standard Deviation Range+2 SD (92.0 mg/dL)Test valuemg/dLMean (84.0 mg/dL)-2 SD (76.0 mg/dL)DaysFigure 18. Standard Deviation RangeTo become familiar with calculating standard deviation ranges, doPractice Exercises 5 and 6.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 292006-03-31 VITROS Chemistry Systems

SummarySummaryThis module presented the basic math concepts used for quality control inthe clinical laboratory. You now know how to calculate a mean and astandard deviation. You know how to create a Levey-Jennings chart, andyou have learned basic information about quality-control fluids.In the next module you will learn more about interpreting Levey-Jenningsplots and determining the proper mean and SD to use in setting up theseplots.This concludes “Statistical Tools of Quality Control.” You may nowcomplete the Self-Evaluation.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 312006-03-31 VITROS Chemistry Systems

Practice ExercisesPractice ExercisesPractice Exercise 1Using the formula below, calculate the mean for the following data:( X 1 ) + ( X 2 ) + ( X 3 ) + … + ( X 20 )----------------------------------------------------------------------------- = X = meannDay Calcium (mg/dL)1 9.72 9.33 10.04 9.85 9.76 9.97 9.68 10.19 9.810 9.611 9.912 9.713 9.814 9.815 9.516 9.417 10.018 9.919 9.720 9.7Fill in the blanks:1. The sum of all measurements is( X 1 ) X 2+ ( ) + ( X 3 ) + … + ( X 20 ) = ____________________2. The total number of measurements is n = ________________The calculated mean is X = ___________________.Check your work with the answer key.32 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Practice Exercise 2Calculate the mean for the following new data:Day Creatinine (mg/dL)1 3.62 3.83 3.44 3.95 4.06 4.17 4.18 4.29 3.510 4.111 4.212 4.113 3.914 3.815 4.116 3.617 3.918 4.219 4.320 4.01. The mean or X = _________________Check your work with the answer key.Practice ExercisesPart No. 7B6006 Statistical Tools of Quality Control: Training Module 332006-03-31 VITROS Chemistry Systems

Practice ExercisesPractice Exercise 3Using this formula, calculate the mean and standard deviation for thefollowing data:Standard Deviation= s =Σ( X i – X) 2------------------------n – 1Where:X iXΣn= each measurement= the mean= “the sum of”= total number of measurements= square rootDay Glucose (mg/dL)1 2052 1923 1904 2135 2016 1947 1998 2159 21610 19211 19412 19813 20214 20515 21016 20117 19418 19719 20420 1981. The mean or X = _________________34 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Practice ExercisesCalculate the standard deviation. Fill in the blanks and complete the tablebelow.Column 1 Column 2 Column 31 2052 1923 1904 2135 2016 1947 1998 2159 21610 19211 19412 19813 20214 20515 21016 20117 19418 19719 20420 1982. Subtract the mean from each value to obtain the ( X i– X)values andrecord each value in column 2.3. Square each of the numbers obtained in column 2 to obtain the( – X) 2 values and record these in column 3.X i4. Add all of the numbers in column 3 to obtain the sum of the squareddifferences.Σ( X i– X) 2= _______mg 2 /dL 2 .5. Divide the sum by one less than the total of measurements to obtainyour variance or s 2The total number of measurements (n) is __________.X iTherefore, n – 1 = __________________.( – X) ( X i– X) 22Σ( X i – X)----------------------n – 1= ________= s 2Part No. 7B6006 Statistical Tools of Quality Control: Training Module 352006-03-31 VITROS Chemistry Systems

Practice Exercises6. Take the square root of the result in step 5 to obtain the standarddeviation:s 2= ______mg/dL = sCheck your work with the answer key.36 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Practice Exercise 4Practice ExercisesCalculate the mean and standard deviation for the following data.DayUrea Nitrogen(mg/dL)1 532 503 554 625 516 517 558 509 6210 5311 5412 5513 5714 4815 5016 5617 5218 5719 5820 51( – X) ( X i– X) 2X i1. The mean or X = _________________2. The standard deviation = ____________________________.Check your work with the answer key.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 372006-03-31 VITROS Chemistry Systems

Practice ExercisesPractice Exercise 5Using the formula, calculate the mean, standard deviation, and the ±1, 2,and 3 standard deviation ranges for Level I quality-control data shownbelow.Standard Deviation= s =Σ( X i – X) 2------------------------n – 1Where:X iXΣn= each measurement= the mean= “the sum of”= total number of measurements= square rootDayTotal Bilirubin(mg/dL)1 0.72 0.43 0.54 0.65 0.66 0.77 0.58 0.69 0.710 0.811 0.612 0.713 0.514 0.715 0.716 0.817 0.918 0.719 0.620 0.7( – X) ( X i– X) 2X i1. The mean of X = _________________38 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Practice ExercisesTo calculate the standard deviation and the ±1 standard deviation range,follow steps 2 through 6 and fill in the blanks.2. Calculate the sum of the ( X i – X) 2 values.Σ( X i– X) 2 = _______________.3. Divide the sum of ( X i – X) 2 by one less than the total ofmeasurements to obtain your variance or s 2 .The total number of measurements (n) is ______.Therefore, n – 1 = _________.2Σ( X i – X)----------------------n – 1= _______________ = s 2 = variance.4. Take the square root of the variance to obtain the standard deviation:s 2= ______ = s5. You now have the mean and the standard deviation. Calculate the ±1standard deviation range by filling in the blanks:Mean = _______.Standard deviation = _________.Multiply the standard deviation by 1:standard deviation x 1 =__________ = 1 standard deviationCalculate your ±1 standard deviation range by adding 1 standarddeviation to the mean to obtain the upper limit and then subtracting1 standard deviation from the mean to obtain the lower limit:mean +1 standard deviation =_________.mean –1 standard deviation =_________.Therefore the ±1 standard deviation range = _______ to _________.6. Now calculate the ±2 and ±3 standard deviation ranges:The ±2 standard deviation range = _______ to _________.The ±3 standard deviation range = _______ to _________.Check your work with the answer key.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 392006-03-31 VITROS Chemistry Systems

Practice ExercisesPractice Exercise 6Calculate the mean, standard deviation, and ±1 SD range for this one levelof quality control.Day Cholesterol (mg/dL)1 3722 3603 3484 3815 3656 3687 3858 3739 37010 35911 35512 38913 36414 37115 36416 35217 37818 34419 37520 3711. The mean or X = _________________The standard deviation = _______________.The ±1 standard deviation range = ________ to _________.Check your work with the answer key.40 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Answer KeysAnswer KeysPractice Exercise 1Using the formula below, calculate the mean for the following data:( X 1 ) X 2+ ( ) + ( X 3 ) + … + ( X 20 )----------------------------------------------------------------------------- = X = meannDay Calcium (mg/dL)1 9.72 9.33 10.04 9.85 9.76 9.97 9.68 10.19 9.810 9.611 9.912 9.713 9.814 9.815 9.516 9.417 10.018 9.919 9.720 9.7Fill in the blanks:1. The sum of all measurements is( X 1 ) X 2+ ( ) + ( X 3 ) + … + ( X 20 ) = 194.92. The total number of measurements is n = 20The calculated mean is X= 9.7 mg/dL.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 412006-03-31 VITROS Chemistry Systems

Answer KeysPractice Exercise 2Calculate the mean for the following new data:Day Creatinine (mg/dL)1 3.62 3.83 3.44 3.95 4.06 4.17 4.18 4.29 3.510 4.111 4.212 4.113 3.914 3.815 4.116 3.617 3.918 4.219 4.320 4.01. The mean or X =78.8---------20= 3.942 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Practice Exercise 3Answer KeysUsing this formula, calculate the mean and standard deviation for thefollowing data:Standard Deviation= s =Σ( X i – X) 2------------------------n – 1Where:X iXΣn= each measurement= the mean= “the sum of”= total number of measurements= square rootDay Glucose (mg/dL)1 2052 1923 1904 2135 2016 1947 1998 2159 21610 19211 19412 19813 20214 20515 21016 20117 19418 19719 20420 1981. The mean or X = 201 mg/dL.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 432006-03-31 VITROS Chemistry Systems

Answer KeysCalculate the standard deviation. Fill in the blanks and complete the tablebelow.Column 1 Column 2 Column 3X i– X–1 205 4 162 192 –9 813 190 –11 1214 213 12 1445 201 0 06 194 –7 497 199 –2 48 215 14 1969 216 15 22510 192 –9 8111 194 –7 4912 198 –3 913 202 1 114 205 4 1615 210 9 8116 201 0 017 194 –7 4918 197 –4 1619 204 3 920 198 –3 92. Subtract the mean from each value to obtain the ( X i– X)values andrecord each value in column 2.3. Square each of the numbers obtained in column 2 to obtain the( – X) 2 values and record these in column 3.X i4. Add all of the numbers in column 3 to obtain the sum of the squareddifferences.Σ( X = 1156 mg 2 /dL 2 i – X) 2.5. Divide the sum by one less than the total of measurements to obtainyour variance or s 2 .The total number of measurements (n) is 20.Therefore, n – 1 = 19.( ) ( X iX) 22Σ( X i– X)----------------------n – 1=1156----------- = 6019= s 244 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Answer Keys6. Take the square root of the result in step 5 to obtain the standarddeviation:s 2= 7.8 mg/dL = sPart No. 7B6006 Statistical Tools of Quality Control: Training Module 452006-03-31 VITROS Chemistry Systems

Answer KeysPractice Exercise 4Calculate the mean and standard deviation for the following data.DayUrea Nitrogen(mg/dL)1 53 -1 12 50 -4 163 55 1 14 62 8 645 51 -3 96 51 -3 97 55 1 18 50 -4 169 62 8 6410 53 -1 111 54 0 012 55 1 113 57 2 414 48 -6 3615 50 -4 1616 56 2 417 52 -2 418 57 3 919 58 4 1620 51 -3 91. The mean or X = 54 mg/dL.X i2. The standard deviation = 3.9 mg/dL.( – X) ( X i– X) 246 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Practice Exercise 5Answer KeysUsing the formula, calculate the mean, standard deviation, and the ±1, 2,and 3 standard deviation ranges for Level I quality-control data shownbelow.Standard Deviation= s =Σ( X i – X) 2------------------------n – 1Where:X iXΣn= each measurement= the mean= “the sum of”= total number of measurements= square rootDayTotal Bilirubin(mg/dL)1 0.7 .05 .00252 0.4 –.25 .06253 0.5 –.15 .02254 0.6 –.05 .00255 0.6 –.05 .00256 0.7 .05 .00257 0.5 –.15 .02258 0.6 –.05 .00259 0.7 .05 .002510 0.8 .15 .022511 0.6 –.05 .002512 0.7 .05 .002513 0.5 –.15 .022514 0.7 .05 .002515 0.7 .05 .002516 0.8 .15 .022517 0.9 .25 .062518 0.7 .05 .002519 0.6 –.05 .002520 0.7 .05 .00251. The mean or X = .65 mg/dL.X = 0.65( X–X) 2Part No. 7B6006 Statistical Tools of Quality Control: Training Module 472006-03-31 VITROS Chemistry Systems

Answer KeysTo calculate the standard deviation and the ±1 standard deviation range,follow steps 2 through 6 and fill in the blanks.2. Calculate the sum of the ( X i – X) 2 values.Σ( X i– X) 2 = 0.273. Divide the sum of ( X i – X) 2 by one less than the total ofmeasurements to obtain your variance or s 2 .The total number of measurements (n) is 20.Therefore, n – 1 = 19.2Σ( X i – X)----------------------n – 1= 0.0142 (use .014) = s 2 = variance.4. Take the square root of the variance to obtain the standard deviation:s 2= 0.118 (round to 0.12) = s5. You now have the mean and the standard deviation. Calculate the ±1standard deviation range by filling in the blanks:Mean = 0.65.Standard deviation = 0.12.Multiply the standard deviation by 1:standard deviation x 1 = 0.12 = 1 standard deviationCalculate your ±1 standard deviation range by adding 1 standarddeviation to the mean to obtain the upper limit and then subtracting1 standard deviation from the mean to obtain the lower limit:mean +1 standard deviation = 0.77.mean –1 standard deviation = 0.53.Therefore the ±1 standard deviation range = 0.53 to 0.77.6. Now calculate the ±2 and ±3 standard deviation ranges:The ±2 standard deviation range = 0.41 to 0.89.The ±3 standard deviation range = 0.29 to 1.01.48 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Practice Exercise 6Answer KeysCalculate the mean, standard deviation, and ±1 SD range for this one levelof quality control.Day Cholesterol (mg/dL)1 3722 3603 3484 3815 3656 3687 3858 3739 37010 35911 35512 38913 36414 37115 36416 35217 37818 34419 37520 3711. The mean or X = 367 mg/dL.The standard deviation = 11.9 mg/dL.The ±1 standard deviation range = 355 to 379.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 492006-03-31 VITROS Chemistry Systems

Self-EvaluationSelf-EvaluationTo complete this self-evaluation:• Fill in the blanks to correctly complete the following statements.• Calculate the mean, standard deviation, and the ±1, ±2, and ±3SD rangesfor 20 days of glucose data.• Plot data on a Levey-Jennings chart and interpret the chart results.1. A program designed to provide a systematic method to monitor andevaluate factors which may affect the quality of laboratory test resultsis_________________. A system designed to monitor the accuracyand precision of the testing process is called___________________.2. The three types of variables that may affect the testing process are:3. The reproducibility of a value upon repeated measurement is referredto as ______________ and the term used to define the quality or stateof being correct in clinical chemistry (e.g., when the calculated meanand true value are very close) is _________________.4. Current regulations require that a minimum of two levels of control berun with patient samples at least every____________ of testing.5. Given the 20 days of data for this one level of glucose (see databelow), calculate the mean, the standard deviation, and the ± 1, ± 2,and ± 3 SD ranges.50 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Self-EvaluationDayGlucose(mg/dL)1 1122 1073 1064 1095 1306 1127 1138 1149 11610 10611 10812 10913 11114 11215 11516 11017 11118 10819 10720 105a. The mean or X = _________________b. The standard deviation =__________________.c. The ± 1 SD range is _________________ to ________________.The ± 2 SD range is _________________ to ________________.The ± 3 SD range is _________________ to ________________.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 512006-03-31 VITROS Chemistry Systems

Self-Evaluationd. Using the data on the previous page, label the Levey-Jennings chartbelow and plot the first 8 days results.+3SD+2SD+1SDMean–1SD–2SD–3SDDays 1 2 3 4 5 6 7 8Check your work with the answer key.52 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Self-Evaluation Answer KeySelf-Evaluation Answer KeyTo complete this self-evaluation:• Fill in the blanks to correctly complete the following statements.• Calculate the mean, standard deviation, and the ±1, ±2, and ±3 SDranges for 20 days of glucose data.• Plot data on a Levey-Jennings chart and interpret the chart results.1. A program designed to provide a systematic method to monitor andevaluate factors which may affect the quality of laboratory test resultsis quality assurance. A system designed to monitor the accuracy andprecision of the testing process is called quality control.2. The three types of variables that may affect the testing process are:preanalytical variablesanalytical variablespostanalytical variables3. The reproducibility of a value upon repeated measurement is referredto as precision and the term used to define the quality or state of beingcorrect in clinical chemistry (e.g., when the calculated mean and truevalue are very close) is accuracy.4. Current regulations require that a minimum of two levels of control berun with patient samples at least every 24 hours of testing.5. Given the 20 days of data for this one level of glucose (see datafollowing), calculate the mean, the standard deviation, and the ±1, ±2,and ±3 SD ranges.Part No. 7B6006 Statistical Tools of Quality Control: Training Module 532006-03-31 VITROS Chemistry Systems

Self-Evaluation Answer KeyDayGlucose(mg/dL)1 1122 1073 1064 1095 1306 1127 1138 1149 11610 10611 10812 10913 11114 11215 11516 11017 11118 10819 10720 105a. The mean or X = 111.1 mg/dL.b. The standard deviation = 5.4.c. The ±1 SD range is 105.7 to 116.5.The ±2 SD range is 100.3 to 121.9.The ±3 SD range is 94.9 to 127.3.54 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

Self-Evaluation Answer Keyd. Using the data on the previous page, label the Levey-Jennings chartbelow and plot the first 8 days results.◆127.4+3SD121.9+2SD116.5+1SD111.1Mean◆◆◆◆◆◆105.7–1SD◆100.3–2SD94.9–3SDDays 1 2 3 4 5 6 7 8Part No. 7B6006 Statistical Tools of Quality Control: Training Module 552006-03-31 VITROS Chemistry Systems

Self-Evaluation Answer Key56 Statistical Tools of Quality Control: Training Module Part No. 7B6006VITROS Chemistry Systems 2006-03-31

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