Components of Variation in Chemical Analysis

6 Components of Variation in Chemical Analysis

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on August 31, 2015 | http://pubs.acs.org Publication Date: June 1, 1977 | doi: 10.1021/bk-1977-0063.ch006

R A Y M O N D C. RHODES Environmental Protection Agency, Research Triangle Park, N C

The first task in the evaluation of any analytical chemistry method is to determine the sources of variability of the results and then to minimize the total variability by searching out and controlling the major contributors. There are many sources of variability in a chemical analysis process. This work describes several of these sources that have been encountered in work by the Environmental Monitoring and Support Laboratory of EPA. Variability can be expected to occur in any or a l l of the following measurement steps within a given laboratory: 1. 2. 3. 4. 5. 6.

The material to be analyzed Materials, including reagents, used in the analysis Calibration materials or devices Environmental factors Analysts Instruments, or apparatus

While these items are not definitive, they describe the general classes of sources of variability that must be considered. It is clear that when one is measuring the reproducibility of an analytical chemistry method, i t is important that the complete method's variability is being measured. For example, in the case where events are measured under the Poisson probability distribution i t is usually improper to describe the error as resulting from this effect alone. In another example, the replication of only a portion of the measurement method, such as replicate analysis of a single extraction, is 176 In Validation of the Measurement Process; DeVoe, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

6.

RHODES


sometimes method.

Components of Variation in Chemical Analysis

erroneously

177

q u o t e d as t h e p r e c i s i o n o f t h e

Every laboratory should s y s t e m a t i c a l l y maintain a c o m p i l a t i o n o r r e c o r d o f t h e e f f e c t s o f each o f t h e above-listed factors, as o b t a i n e d from special studies conducted i n their laboratory or the laboratories of others, so t h a t i f improvement i s needed i n the q u a l i t y of the reported results, efforts to effect s u c h i m p r o v e m e n t s c a n b e made i n t h e most c o s t - e f f e c t i v e way. The p l a n n i n g o f such special studies and t h e a n a l y s i s o f t h e data therefrom i s an a r e a where statisticians and chemists, working together, can gain much i n t h e knowledge and understanding of the contributions to the total measurement v a r i a b i l i t y . Each l a b o r a t o r y should conduct p e r i o d i c quality control checks t o measure and c o n t r o l t h e combined effects of the sources o f v a r i a b i l i t y which affect their reported results. THE LABORATORY MEASUREMENT PROCESS A schematic diagram of portions of the measurement p r o c e s s o f an i n d u s t r i a l laboratory i s p r e s e n t e d i n F i g u r e 1. I n p u t s o f p h y s i c a l s a m p l e s t o t h e l a b o r a t o r y a r e shown: (1)

Samples from t h e m a n u f a c t u r i n g (a) (b) (c)

(2) (3)

process

Raw m a t e r i a l s In-process materials Final product

C a l i b r a t i o n standards Reagents and other m a t e r i a l s

The various internal factors of the laboratory measurement p r o c e s s , p r e v i o u s l y m e n t i o n e d , are also shown. The measurement process and sampling considerations f o r pollutant measurements are identical except f o r d i f f e r e n t types o f sampled m a t e r i a l s t o be a n a l y z e d . The s c h e m a t i c o f F i g u r e 1 g e n e r a l l y a p p l i e s t o any measurement p r o c e s s , whether of i n d u s t r i a l , research, government o r independent laboratories.

In Validation of the Measurement Process; DeVoe, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.


178

VALIDATION OF T H E M E A S U R E M E N T

PROCESS

Several recent articles and documents d i s c u s s the various quality assurance aspects of the laboratory measurement process. The m e a s u r e m e n t o r analytical process i n industrial situations is normally a part of the overall quality assurance system. Moreover, i n a d d i t i o n to being a part o f the quality assurance system, recent concepts, quite appropriately view t h e measurement or analytical process a s o n e w h i c h s h o u l d m a i n t a i n i t s own q u a l i t y a s s u r a n c e s u b - s y s t e m o r p r o g r a m (1., 2_, 3.). In the Environmental Protection Agency (EPA) the e n v i r o n m e n t a l m o n i t o r i n g e f f o r t s may be v i e w e d as a p r o d u c t i o n p r o c e s s w h i c h i s e s s e n t i a l l y a measurement p r o c e s s , h a v i n g as i t s p r o d u c t , environmental DATA. Accordingly, EPA i s i s s u i n g g u i d e l i n e s f o r Q u a l i t y A s s u r a n c e Programs f o r each o f i t s a i r measurement methods ( 4 ) , and has i s s u e d a " Q u a l i t y Assurance Handbook f o r A i r P o l l u t i o n Measurement S y s t e m s " ( 5 ) . The above concept i s r e c o g n i z e d i n EPA a s n o t o n l y appropriate f o rmonitoring programs, but also f o r research projects i n which i t i s d e s i r e d to obtain data of high quality. Major research projects require rather e x t e n s i v e q u a l i t y assurance programs (6). The accuracy of the a n a l y t i c a l portion of a c h e m i c a l measurement system i s a c h i e v e d by t h e use o f Standard Reference M a t e r i a l s , high q u a l i t y reagents, and by c o n t r o l of variables of the calibration process. I t s h o u l d be e m p h a s i z e d t h a t t h e b a s i s f o r accuracy of the r e s u l t s from a laboratory should emanate from outside the laboratory. Unless a laboratory h a s i t s own internal capability for p r o d u c i n g p r i m a r y s t a n d a r d s , i t m u s t d e p e n d u p o n some external source of standards. Otherwise, i t is attempting "to l i f t i t s e l f b y i t s own b o o t s t r a p s . " I f u n q u e s t i o n e d a c c u r a c y i s d e s i r e d , a l l measurements should be t r a c e a b l e t o t h e s t a n d a r d s o f t h e N a t i o n a l Bureau of Standards or other national and international standards laboratories. Even with traceable standards, accuracy depends upon their proper c a r e a n d u s e . The c e r t i f i c a t e s i s s u e d b y t h e National Bureau o f Standards for i t s Standard Reference Materials (SRM) o f t e n i n c l u d e c a r e f u l l y worded c a u t i o n s which e x p l a i n t h a t t h e SRM s have s p e c i f i c e x p i r a t i o n d a t e s a n d t h a t t h e y m u s t be g i v e n p r o p e r c a r e , and used under s p e c i f i e d c o n d i t i o n s . I n fact, t h e a c c u r a c y o f c a l i b r a t i o n s depends n o t o n l y upon the standard used, but upon the entire c a l i b r a t i o n p r o c e s s (7_). f



6.

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Components of Variation in Chemical Analysis

179

The r e l a t i v e a c c u r a c y among l a b o r a t o r i e s c a n b e measured through the use of interlaboratory comparison studies, represented by an i n p u t - o u t p u t relationship on F i g u r e 1. The objective of i n t e r l a b o r a t o r y c o m p a r i s o n s t u d i e s , i n w h i c h t h e same samples a r e a n a l y z e d by v a r i o u s l a b o r a t o r i e s , i s to make c o m p a r i s o n s w i t h r e s p e c t t o a c c u r a c y . Two t y p e s of interlaboratory studies are conducted. Collaborative studies are generally c o n s i d e r e d as t h o s e s t u d i e s w h i c h a r e c o n d u c t e d among a group o f selected laboratories t o evaluate a newly developed analytical method (^ S

s

a

185

gives s

.352 1.064


.322 The a b o v e e x a m p l e i s p r e s e n t e d t o i l l u s t r a t e t h e basic principles i n d e t e r m i n i n g t h e components o f variance. Most o f t e n t h e e x p e r i m e n t a l d e s i g n f o r t h e a n a l y s i s o f components o f v a r i a n c e i s more complic a t e d t h a n t h i s ( 1 4 ) ; however t h i s f a c t , w h i c h u s u a l ly requires a statistician's assistance i n planning such a study and i n a n a l y z i n g thedata therefrom, does n o t d e t r a c t from t h e importance o f t h i s type o f study.

five

The c o m p o n e n t s of variation r e s u l t i n g from t h e separate analyses a r e presented i nTable I I I .

A general pattern should e x i s t across levels f o r the three components of variation. The s t a n d a r d d e v i a t i o n s f o r t h e w i t h i n sample-day v a r i a b i l i t y and between sample variability a r e p l o t t e d on F i g u r e 2 for thevarious concentration levels. Since no g e n eral pattern, either i n c r e a s i n g o r decreasing, exi s t s , thepooled, i . e . , s t a t i s t i c a l l y averaged, values f o r these s t a n d a r d d e v i a t i o n s a r e : s

- .276 f o r w i t h i n s a m p l e - d a y

q

s

s

= .394 f o r b e t w e e n - s a m p l e

The p l o t o f t h e b e t w e e n - d a y s t a n d a r d d e v i a t i o n s ( F i g u r e 3 ) , h o w e v e r , d o e s show a g e n e r a l increasing pattern with i n c r e a s i n g concentrations, with the exc e p t i o n o f s e r i e s 2000. Omitting theresults f o r ser i e s 2000, t h e s t a n d a r d r e g r e s s i o n r e l a t i o n s h i p o f t h e between-day standard d e v i a t i o n t o c o n c e n t r a t i o n l e v e l i s a s shown o n F i g u r e 3. The s t a t i s t i c a l l y more correct weighted* regression relationship i salso shown, a n d i s a p p r e c i a b l y d i f f e r e n t f r o m t h e s t a n d a r d

*A w e i g h t e d r e g r e s s i o n i s a p p r o p r i a t e b e c a u s e o f v i o l a t i o n o f t h e a s s u m p t i o n o f homogeneous variances the v a r i a t i o n o f sample s t a n d a r d d e v i a t i o n s i s g r e a t er f o r l a r g e r expected o r true standard d e v i a t i o n s .


VALIDATION O F T H E M E A S U R E M E N T

186


Table

Series

III.

Components o f V a r i a n c e O b t a i n e d from A n a l y s i s o f V a r i a n c e

Within Sample-day

Between-Sample

cs )

(s )

e

PROCESS

Between-Day

s

(s ) d

S t a n d a r d D e v i a t i o n s , yg 1000 2000 3000 4000 5000 Pooled

.367 .207 .285 .136 .322 .276

.221 .493 .401 .447 .352 .394

.230 zero* .714 .804 1.064

(The z e r o v a l u e - - a c t u a l l y i t was n e g a t i v e - - i s p o s s i b l y due t o p e c u l i a r c o m b i n a t i o n s o f i n d i v i d u a l values. In t h i s p a r t i c u l a r study, the lack of a b e t w e e n - d a y e f f e c t f o r s e r i e s 2000 i s s u s p e c t e d t o be d u e t o some a s s i g n a b l e b u t u n k n o w n c a u s e . )



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Components of Variation in Chemical Analysis

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