QualityControl Charts in the QuantitativeAnalysis Laboratory Using Conductance Measurement Frederk C. Laquer University of Nebraska at Omaha. Omaha, NE 68182 Quality control is an important part of any analytical laboratory work. Many social and legal decisions are made as the result of chemical analyses (I). These decisions may affect an individual's career, as in the case of a blood test for the mesence of drue metabolites, or the economic success of a manufacturing operation producing a pharmaceutical or other oroduct. In 1947 Mitchell (2) observed that chemists had been slow to embrace the methods of Shewhart 13) with reeard to t h e a ~ d i c a t i o nof auality control tochemical tests. t gat has siuck-changed. N ~ Wq&lity control is a serious matter in industrial and contract laboratory practice (4-6). The standard handbook for the analysis of water dedicates eight pages to quality control operations (7). If quality control is so important, then why is it that many recent textbooks in quantitative analysis do not cover the subject of quality control a t all, and only a few treat the subject in even a theoretical fashion1? None of the textbooks surveved offer ~racticalexoeriences or laboratory experimen& in qualit; control fdr the student. The analvtical chemist entering a field that is becoming increasing$ complicated is thus poorly served with this deficiency in his or her education. Industrial engineers have a textbook on the subject (8); the clinical chemists and medical technologists are exposed to quality control early in their practical training (9);hut the analytical chemistry student must find his or her information in the literature (4, 5) or in advanced books on statistics (10).
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Ouallty Control Charts Analytical chemists performing routine tests need to monitor the reproducibility of an analytical measurement over time so as to be sure the analytical process is "in control". The main tool a t the chemist's disposal for monitoring quality control is the control chart, sometimes called the "Shewhart" chart after its originator (2,ll). A control chart may be defined as a chart on-which are plotted the results of a measurement (usually of a standard) made a t regular time intervals. A fundamental assumption is that while an analytical measurement is under control, then the only variation in the result is that due to random or indeterminant error. If the system is out of control, then a determinant error is "resent = - - - - - and needs to be corrected before the analvtical process is allowed to continue. In application, the chemist submits a standard or "controlled samule" to the analytical process with every batch of samples to check the performance of the test method. The results of the standard's analysis are then plotted in the form of a chart, with the X axis the date or sequence number, and the Yaxis the concentration of the standard (shown in the figure). The control sample datum should be plotted immediately after it has been measured so that a prompt decision as to whether the analytical process is in control may he made (5). If the data are not plotted in "real time" and if the process is out of control, then all of the samples determined since the process was last in control would need to be reanalyzed.
' A list may be obtained from the author upon request 900
Joumal of Chemical Education
Two forms of the quality control chart are commonly in use. The "property" chart (shown in the figure) uses either a single measurement or the average of several measurements of ;single sample (5). The second style or "precision" chart, plots the range of duplicates or the standard deviation of multiplets in a similar fashion (5). The economic benefits of multiple analysis to maintain close control of a process must be weighed against the costs of the analytical procedure. Duplicate samples are a compromise, so the "precision" chart may be called a range chart when the difference of duplicates is plotted (5). Other styles of control charts are available (5.8-10.12). An analytical iroc&w that has been in long use has welldefined limits to the variation that mav be exoected due to indeterminant error. The central line on the Y axis of a "property" chart is the expected value of the standard. The analyst plots warning limits (WL)on the Y axis a t two standard deviations from the mean of expected value, and control limits (CL)a t three standarddeviations. On a statistical basis, the WL should not be exceeded more than once in everv 20 measurements. and the CL should never be exceeded in normal practice. knnotations as to problems encountered in the analysis are appropriate (the figure, week 10).In a range chart, the average range determined by long experience is dotted at the central line. the lower WL and CL are zero, add the upper WL and CL are a t 2.512 and 3.267 times the averaee ranee value, resoectivelv (5). Other .kalytical paraket&s may be plotted using this sort of chart ( 5 ) .Blank values mav be plotted to aid in maintaining a low detection limit andireventing sample contamination (13). The instrument response to the presence of a standard, for example, the abso~hancein atomic absorption spectroscopy, or the retention time in chromatography may also be olotted for instrumental oualitv control. Because standari curves are used to calibiate the instrument resuonse. it mavnot be obvious that the instrument or column i e r f o r k n c e h a s declined without the information provided by a control chart.
w t i l y comrol chsnfor a conductivity standard, where the mean Is 80.0pmho and Me standard devietion, o, is 1.5 who cm-'.
cm-'
The Experiment In order to provide an undergraduate laboratory experience on the process of preparing quality control charts, a simple measurement of a material in common use by the students that is used over the course of the semester is required. The analytical measurement needs to be simple, sensitive, and reliable, so that the student may easily make it a routine part of each laboratory session and may then concentrate on the process of constructing a quality control chart and not on the mechanics of the measurement. The material LO be assayed needs to be familiar to the students and yet have sufficient uncertainty that small variations mav be observed. Finallv the exoeriment cannot take much time away from the usuil suite df experiments performed in the auantitative analvsis laboratorv. he determination of the conductivity of the distilled water is a measurement that meets these criteria. Distilled water is a very important reagent in its own right with critical specifications depending on the application (7).In many chemical laboratories the still is located remotely from the laboratory. The distilled water is made available in the lab from a tap, and we trust it, just as we trust our drinking water. However, the distilled water from such systems often shows a significant level of contamination with Na+ and C1ions. In the quantitative analysis laboratory, C1- is commouly determined in an aqueous matrix, and the failure of the distilled water system would result in a major error in the experiment.
approximately 1.0 cm-'. The conductivity of the solution K , is the product of the conductance and the cell constant and has units of mho cm-1. The SI unit for conductance is the siemens, S. The conversion of common conductivity units is 1 pmho em-' = 0.1 mS 6'
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The conductivitv electrode must be calibrated bv determining the cell constant and then measuring the conductivity of a standard KC1 solution. The exoected value of the conductivity of a standard solution may be calculated from t h e molarity of the solution. At 25 OC, and for KC1 concentrations between and 0.04 mol L-', the molar conductivity (S m-') is given by (15-17) ~~~
r,
., = 14.9840 - 9.484a3" + 5.86102(log( a ) ) + 22890'
a
Calculations Most American meters measure conductance, C in ohms-' or nlhos and use conductivitgcells with a cell constant, H, of The handout supplied to the students is available upon request. R includes a section on conductivity theory for those students who have not yet taken physical chemistry.
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~~~~
- 26.42a5" (2)
where a is the concentration of the KC1 solution in mol L-1. Given the accuracy of most inexpensive conductance meters, only the first three terms of eq 2 need to be used; the calculation is still accurate to better than 1' for solutions less than 0.01 M. Alternative equations have been published (16,18) and are in current use (7). T o convert to common conductivity units (pmho cm-I), multiply by lo4. If the water used to prepare the solution has a significant conductivity compared to the solution prepared, it will add to the expected conductivity of the solution. The conductivity of solutions is also very sensitive to temperature, t. Over the range 10 'C to 45 OC the expected conductivity for KC1 solutions at t ( O C ) is n,
The students perform the experiment weekly throughout the course of the semester, requiring only 10 min each lab period. Ihring the firat laboratory period,;he students dry a sample of reagent-grade KC1 for 1 h while checking into the lab. After allowingtthe sample to cool, they prepare 500 mL of a 0.01 M solution, weighing the KC1 t o 0.0001 g. Fresh distilled, deionized water (18MO resistivity) is used to dilute to volume. For more accurate work, the mass of water may be measured, which along with the temperature of the water allows the volume to be determined. Samples should be stored in a elass stoooered bottle. but oolvethvlene bottles will work f& the co&e of a semester. A 1:20d h t i o n of the stock 0.01 M KC1 solution.aaain usina 18MD water, vieldsa 0.500 mM working standarh that 411 be used w&kly to check that the conductance meter and cell are functionine properly. Each week the students determine the conductiv~ ity of their standard, taking care torecord the identity of the conductivity cell and the batch number of their standard, since they will likely need toremake the sample a t least once during the semester. The students repeat their measurements on the tap distilled water that they ordinarily use in the laboratorv and on a svntbetic Drocess samole ("oroduct XYZ") proviied by the l ~ b o r a t o r ~ u s t r u c t o~r .h i s ' s k ~isl e to model a oroductthat mav be manufactured and must stav within tolerance limits. The process sample has batch number that is different from week to week. The temperatures of the standard, sample, and distilled water solutions are all measured to 0.1 "C using an ASTM type 90C thermometer, immediately following the conductance measurement. Solutions may be thermostated a t 25 ' C for greater precision (7, 14) but with a greater time requirement for the experiment. Temperature corrections may be made as shownbelow.
(1)
= n2,ec(l
+ 0.01984(t - 25.0) + 5.81 X 10-'(t
- 25.0)')
(3)
recalculated from data in ref 19,accurate to within 0.2%. The cell constant, 9 (cm-I), may be calculated from the ratio of the expected conductivity, nt (S cm-I), and the measured conductance, G , (S), as displayed on the meter 0 = n,/G,
(4)
The cell constant is nominally 1.00 cm-1. Sometimes specialpurpose cells are used with cell constants of 0.10 em-' for low ionic strength solutions or 10 cm-' for high-salt solutions. The distilled water and "process" samples are reported corrected to 25.0 OC, using the formula (7),
Dlscusslon The students' reports include their solution preparation data, calculations, and three graphs including their standard, the distilled water, and the process control sample. The average of the first three weeks' data is used as the "expected value" for the student standard and the process control sample quality control chart. While one usually uses a standard deviation determined from a t least 20 measurements to determine the warning and control limits (5, 7), that is not possible for this experiment. The standard deviation is arbitrarily selected to be 1.5 pmho em-' based on previous years' experience. The date axis, which usually is the day of the year (Julian day), is instead the week of the semester since the experiment is performed weekly. From previous experience our tap distilled water has an expected value of 2.3 pmho cm-' with a standard deviation of 0.7 pmho cm-I. The students are assigned the following discussion questions to be completed and included a t the end of the term in their lab report. 1. What should be the warning and control limit values for the
standard solution, the process control sample, and the distilled water, based on vour data? 2. The distilled water probably never fell below the lower warning limit. Given the physical limitations on the solutkm discuss whether the distribution of values ior the distilled water ia "norVolume 67 Number 10 October 1990
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mal" (Gaussian).Is there a better statistic to be used in this case, and, if so, what? 3. Did thesolutima youstudiedever fnlloutside the warning limits or the contnrl limits? 1)isruss posaihle causes and their remedies.
Conclusions Variations of this exoeriment have been oerformed for three years in the sophomore-level quantitati;e analysis laboratory. After two weeks the students are reasonably proficient a t the measurements and take less than 10 min each to oerform them. Bv the end of the term, the students have 12 t o 15 measuremekts. While this is really not a large enough sample size (20 is better) to determine the best warning and control limits, i t is a t least an introduction to the process. The experiment works well in a small class; larger classes should use two setuos to orevent time wasted waiting in line. Students' responses have varied from acceptance to enthusiasm. The greatest criticisms concern the complexity of the calculations; however, with the increasing availability of computers this should be less of an issue. The quality control data may be entered into a spreadsheet for ease of calculation and plotting (20,21).The quality control chart aspect of the experiment will work using materials a t room temperature. without correction to 25 "C, although the variation in the iesnlts will increase. Inexpensive cinductance meters are readily available, so that the principles discussed here are easily implemented. The class unknown, or process controlsample, may be prepared weekly by dilution of a concentrated stock solution, except for those weeks when the product is intended to be out of specification, i.e., different from the orevious several week's level. A dve mavalso be added a t a rLndom point in the semester to test the students observation skills. ~
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Acknowledgment The author thanks the several classes of ouantitative analysiastudents for their constructivecommentson thisexperiment. The Universitv Committee on lmorovement of Instruction funded the purchase of a YSI-3iconductance meter and conductivity dip cell that led to the development of this experiment. Lllerature Clted 1. Keith, L. H.: Crummett, W.; Oeegao, J., Jr.; Libby, R. A,; Taylor. J. K.: Wentier, G. Anal. Cham. 1983,55,2210-2218. 2. Mitchell. J. A. Ind. Eng. Chem., And. Ed. 1947.19. 961487. 3. Shewhart, W. A. Eeowmir Control of Quality of Monvfoefured Pmduel: Van Nostrand: New Yark, 1931. 4. Ksteman. 0.: Piinera. F. W. Quolifv contra1 in Anolytirol Chemlatry; wiiey: New Yark, 1981. 5. Taylor, J. K. Qualify Assurance ofchmicol Me=wremnfs Lewis: Chelsea, MI, 1987. 6. Keith, L. H.,M.Pnnciploso/EnuironmanfolSompling;Americao ChemicalSociety: Washington. DC.1988. 7. American Public Health Aluoeiation. Stondord Mathod8 for the Erominolion of Wolmnnd Wonawarer, 18thed.:AmericsnPublieHedthAssocietion: Wmhington, DC, 1985: pp 2E-32. 8. Grant, E. L.; Leavenworth, R. S. Sfolistieol Qualify Control, 5th ed.; McGrsn-Hill: New York, 1980. Klee, G. 0. In Fundomentalsofclinicol Chemistry,3rdd.:Tietl, N. 9. woslgard. J. 0.; W., Ed.: Seundera: New York, 1981: Chapter 8. lo. Miller, J. C.; Miller. J. N. Stofistics of Andyticol Chemistry, 2nd ed.: Homiood: Chichater, England. 1981: Chapter 4. 11. Wernimonl,G.Ind. Eng. Chom.,Anal.Ed. 1346.18.587-592. 12. Wentgard,J. 0.: Barry,P. L.: Hunt,M.R.:Gmth,T. Clincham. 1981.27.493-501. 13. Lewis. D. L., Principles o/ Enuzronmenfol Sampling: Keith: L. H.. Ed.; American Chemical Society: Washington. OC,1988; Chapter 8. 14. ASTM Method D 1125.52. Annual B w k of ASTM Stondords; ASTM: Philadelphia. PA, 1988:Vol. 11.01. 15. Juaticr J. C. J. Chim. Phys. Phys. Chim. B i d 1968,64353-367. 16. Juheaz,E.; Marsh, K. N.PUeApp1. Chom. 19SL,53,1&(1-1845. 17. Shoemaker. D. P.: Garland, C. W.: Nihler, J. W. Ezpwimenls in Physical Chemistry, 5th ed.; MeGrsw-Hill: New York, 1989; Chapter 8, Experiment 17. 18. Lind, J. E.: Zwolenik, J. J.;Fuoss, R. M, J.Amer Chem Soc. 1959,831.1557-1559. 19. Hsrned. H. S.; 0wen.B. B. ThaPhysieol Chemistry of Electrolytic Solutiow. 3rd ed.; Reinhold: New York. 1958; 1,233. 20. 0uchi.G. 1.Am.Lab. 1981.19(2l.82-95. 21. Ouchi, G. I. Am. Lab. N e w E d . 1987,19(6AI, 24.30. ~
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