1. Chapter 5 Quality Assurance and
Calibration Methods

2. The Need for Quality Assurance
Check “blind” samples to assess the reliability of the lab working
Scattered measurements of Pb in river water by different labs
certified range: 62.3 M  1.3 nM
181 labs
18 reports  50% above
4 reports  50% below
9 national labs
:close to the certified value

3. Data quality standards: Get the right date Get the data right
Quality assurance is what we do get the right answer for our purpose.
:The answer should have sufficient accuracy and precision.
In this Chapter, 1) Procedures in quality control and 2) Introduction of two more calibration methods
Data quality standards:
Get the right date
Get the data right
Keep the date right

4. 5-1 Basics of Quality Assurance
Calibration
Statistics
Raw data
Treated data
Results
Individual measurement (area, volume…)
Reported values (mean, SD,…)
Concentration
Use Objectives
: States the purpose for which results will be used.
Specifications
Sampling requirement: representative samples
Accuracy and precision
Rate of false results; false positive vs. false negative
Specificity (Selectivity)
Sensitivity Acceptable blank values; method blank vs. reagent blank vs. field blank
Recovery of fortification;, spike(fortification) recovery, matrix effect
Calibration checks; analyze standard solution
Quality control sample: performance test samples (quality control samples, blind samples)

5. change in analyte concentration
Sensitivity = slope(m) of calibration curve =
change of signal
change in analyte concentration
Accuracy; uses standard reference materials(SRMs)
Blanks
- Cause interferences (changing signal of analyte) from solvent, reagent, apparatus, instrument, and environment except analyte
- Method/Reagent/Field blank
- The blank can either be subtracted from analyte signal, or used as zero point in calibration.
Matrix The medium containing analyte Everything in the unknown, other than analyte (Everything else in sample other than analyte) - A matrix effect is a change in the analytical signal caused by anything in the sample other than analyte.

6. Spike recovery - Add a small volume of concentrated standard to sample solution - Avoid matrix effect - Confirm the signal of analyte
Example
Spike Recovery
Result of unknown sample= 10.0ug/L
Spiked known sample = 5.0 ug/L
→ Concentration of spiked sample = 14.6 ug/L
⇒ Percent recovery?
Solution
Cspiked sample – Cunspiked sample
Percent recovery =
X 100
(5-1)
Cadded
14.6 μg/L – 10.0 μg/L =
X 100
5.0 μg/L =
92 %

7. Calibration checks
- Periodically check
- Analyzed solution formulated to contain known concentration of analyte
- Ensure that out instrument continues to work properly and calibration remains valid.
Performance test samples (quality control samples or blind samples)
- To help eliminate bias
- Use samples of known composition (SRMs)
To gauge accuracy:
- calibration checks
- spike recovery
- quality control samples
- blanks
To gauge precision:
- replicate samples
- replicate portions of a sample

8. Assessment
Assessment is the process of 1) collecting data to show that analytical procedures are operating within specified limits and 2) verifying that final results meet use objectives.
Control charts (Box 5-1)
Shut down conditions from control chart
1 outside the action lines
2 out of 3 consecutive measurements in the warning zones
7 consecutive measurements all above or all below the center line
6 consecutive measurements all steadily increasing or steadily decreasing
14 consecutive measurements alternating up and down
obvious nonrandom pattern

10. 5-2 Method Validation
Validation determines the suitability of an analysis for providing the desired information. • Validation can apply to sample, to methodologies, and to date. • Validation is often done by the analyst but can also be done by supervisory personal.
Method validation; the process of proving that an analytical method is acceptable for its intended
- Specificity
- Accuracy & precision
- Linearity & range;
linear range vs. dynamic range vs. linear dynamic range vs. range
- Robustness; not affected by small changes in conditions
- LOD, LOQ

11. Specificity or Selectivity
- Ability of an analytical method to distinguish the analyte from everything else that might be in the sample.
:analyte
Peak 3 and 4 are unresolved (incomplete baseline separation) ⇒ poor specificity

12. Linearity
- The R2 (square of correlation coefficient) values must be very close to 1 to represent a linear fit.
- A y-intercept of calibration curve (after the response of the blank has been subtracted from each standard) should be close to 0(zero).
Range of R2 value = 0~1 - R2 near 1 indicates that a regression line fits the data well. - For major component: >0.995 (or ~0.999)
(5-2)
Accuracy
Nearness to the truth
Ways to determine accuracy (systematic error)
- Analyze a certified reference material as a standard (known composition and concentration)
- Compare your results from two or more different analytical method
- Analyze “blank” samples spiked with a known addition of analyte. : The matrix must be same as your unknown sample - Make standard additions(Section 5-3) of analyte to the unknown sample

13. How is accuracy established ?
While precision is easy to measure simply by replication, a measurement of accuracy involves comparing the experimental results to a “known” or “true” value.
⇒ Reference Methods or Standard Reference Materials.

14. Precision The reproducibility of a result Types of precisions
- Instrumental precision (or injection precision): the reproducibility observed when the same quantity of one sample is repeated introduced (precision for repeated sample loading)
- Intra-assay precision: analyzing aliquots of a homogeneous material several times by on person on one day with the same equipment.
- Intermediate precision (or Ruggedness): observed when an assay is performed by different people on different instruments on different days in the same lab.
- Interlaboratory precision: observed when aliquots of the same sample are analyzed by different people in different lab.

15. BOX 5-2: The Horowitz Trumpet: Variation in Interlaboratoty Precision
Coefficient of variation (CV) or
Relative Standard Deviation(RSD) = s/x
: smaller CV  more precise
⇒ CV is usually expressed as a
percentage
CV (%) = %RSD = 100×s/x
⇒ Inter laboratory precision becomes poorer
as the level of analyte decrease.

16. Range
: Concentration range over which linearity, accuracy, and precision meet specifications for analytical method.
for Major component
Correlation coefficient(linearity): R2≥ 0.999
Spike recovery(accuracy): 100±2%
Interlaboratory precision: ±3%
for Impurity
Correlation coefficient: R2≥ 0.98
Spike recovery: 100±10%
Interlaboratory precision: ±15%

17. Limits of Detection and Quantitation
Detection limit (DL or Lower limit Of Detection(LOD)); the smallest quantity of analyte that is “significantly different” from the blank.
Procedures for Determination of Detection Limit (DL, LOD)
1) Prepare a sample whose concentration is ~1 to 5 times the detection limit.
2) Measure the signal from n replicate samples (n≥7).
3) Compute the standard deviation(s) of the n measurements.
4) Measure the signal from n blanks and find the mean, yblank.
5) The minimum detectable signal(ydl) is defined as
(5-3)
Signal (S)
Noise (N)
S/N = 3
ydl = yblank + 3s
(5-3)
6) Corrected signal (ysample – yblank) is proportional to sample concentration:
ysample – yblank = m×sample concentration
(5-4)
ysample = m×sample concentration + yblank
ydl = m×LOD + yblank
yblank + 3s = m×LOD + yblank
where, ysample = signal of sample
yblank = signal of blank
m = slope of the linear calibration curve
s = SD of sample signal
⇒ Minimum detectable concentration (DL)
LOD(DL) = 3s m
(5-5)
Lower limit of Quantification (LOQ); Lower limit of quantification, or the smallest amount that can be measured with reasonable accuracy.
LOQ =
10s m
(5-6)

18. LOD from calibration curve
Detection limit
Detection limit
LOD
LOQ 3s
10s
LOD from calibration curve
Signal detection limit = b + 3sy
y = mx + b
= mx + yblank
LOD = yblank + 3sblank
= b + 3sblank

20. To be useful, a calibration curve must:
5-3 Standard Addition
To be useful, a calibration curve must:
• Have a defined relationship a measurable quantity (usually concentration) and the signal measure.
• Often this relationship is linear, but other relationships can also be useful.
• Be collected under the same, or near same, conditions as what exists for the analyte.
- Similar matrix
- Similar species
- Similar experimental conditions (sample holder, lab temperature, instrument settings, etc.)
• A minimum of 3 data points over a range of concentrations should be collected to define the line (or other calibration relationship). The concentration of the analyte must lie within the calibration range.

21. Standard Addition (표준물 첨가)
- Known amounts of analyte are added to aliquots of sample
- Signals are measured as a function of concentration added
- Modeling process: Signal = mC added + b
- Equation is solved for concentration where Signal = 0 (an extrapolation process)
- Accounts for sample matrix, but not for instrumental drift
Why is standard addition used?
- Std. Add. is effective at correction of “matrix effects”, i.e., the sensitivity (signal/conc) is sample-dependent
- Std. Add. will NOT correct for additive interferences, i.e. if another species is present that contributes signal at the sensor being measured.
- Std. Add.is standard practice in some techniques.
Processes of standard addition
Analyte=Standard
Standard
(Analyte, known)
Step 1: Analyte(unknown) signal
Step 2: Analyte(unknown) + Standard(known) signal
Step 3: Calculate unknown concentration
Analyte (unknown)

22. (X(analyte, unknown) =S(standard, known)) Standard addition equation:
Concentration of analyte in initial solution
signal from initial solution =
Concentration of analyte plus standard in final solution
signal from final solution
(X(analyte, unknown) =S(standard, known))
Standard addition equation:
(5-7)
[X]i: initial conc. of analyte
[X]f: diluted conc. of analyte
[S]f: conc. of standard in the final solution
[S]i: conc. of standard solution
V0: initial volume of unknown
Vs: added volume of standard
Where,
Total volume(V) = V0 + Vs
(5-8)
Dilution factor
[S]f = (2.08M)(5.00mL/100mL)=0.104M
[X]f = [X]i(95.0mL/100.0mL)
∴[X]i = [Na+]i = 0.113M

23. Graphical Procedure for Standard Addition to a Single Solution
Increasing standard (known, S): IS+X VS V V0
Analyte(unknown, X): IX
9 points
(=Is+x)
(5-9)
(=[S]f) y m x
(5-10)
Sy : SD of y, m ; slope of the line, ; mean value of y (nine points)
xi ; the individual values of x (nine points),
n ; number of date points for the calibration line y
x ; mean value of x (nine points)

24. Graphical Procedure for Multiple Solutions with Constant Volume
Step 1:
Place 5 mL of unknown(X) in each flask 5
IS+X 4 3
Step 2:
Add 0, 5, 10, 15 and 20 mL of standard(S)
Unknown only 2 1
Step 3:
Fill each flask to the 50 mL mark and mix(X+S)
[S]f
Step 4: plot IS+X vs. [S]f  [X]I = x-intercept

25. 5-4 internal Standards Requirements for an internal standard
• A substance known as an “internal standard” is added to samples and standards (chemically similar to analyte)
• Used to correct for instrumental drift (changes in sensitivity over time) and matrix effects (sample-related changes in sensitivity)
Requirements for an internal standard
- Technique must be multi component-must separately measure signals for analyte and internal standard
- No interferences: between analyte and internal std or
between sample matrix and internal std
- Internal standard must emulate drift and matrix effect behavior
- Internal standard is not native in the sample

26. Concentration determination from Response factor
Response factor : differences in the detector signal between the analyte(X) and internal standard(S).
Area of analyte signal
Area of standard signal
= F ( )
(5-9)
Concentration of analyte
Concentration of standard
F=1: equally response to standard(X) and internal standard(S)
F=2: doubly response to standard(X) comparing internal standard(S)
Where, Ax, As : the peak areas for the analyte(standard) and internal standard
[X], [S] : the concentrations of analyte(standard) and internal standard
(Sample: Anthracene)
(Internal Standard: Naphthalene)

27. Using an Internal Standard
Example
Using an Internal Standard
1) For mixture of M analyte(X, known) M internal standard(S) ⇒ Signals: AX=423, AS=347
2) 10.0 mL of 0.146M S added to 10.0mL analyte X(unknown), then diluted to 25.0 mL
⇒ Signals: AX=553, AS=582 ⇒ Find [X]
Solution
1) Preliminary experiment
Standard mixture
- For mixture of known(X) + standard(S)
2) Analysis
: 10.0 mL of M S added to 10.0 mL X(unknown) ⇒ diluted to 25.0 mL
Unknown mixture
- For mixture of unknown(X) + standard(S)

28. Concentration determination from Calibration Curve
참 고
Concentration determination from Calibration Curve
: A fixed amount of the internal standard species is added to all samples, standards, and blanks.
Ix/Is o o o o o
Unknown o
[X]/[S]
[S]
[X]