1. Variogram-derived measures for QC purposes
Variogram-derived measures for QC purposes
Markku Ohenoja
Control Engineering group
University of Oulu
Faculty of Technology / Control Engineering / Markku Ohenoja
11/18/2018

2.
Faculty of Technology / Control Engineering / Markku Ohenoja

3.
Background
All measurements retain some amount of uncertainty, but also sampling errors may affect on the result
Utilization of different measurements collected with very different sampling rates requires evaluation of their information content
Environmental measurements are often periodic, sparsely collected and from various sources
Variographical analysis used for evaluating sampling errors and information content of the measurement
Faculty of Technology / Control Engineering / Markku Ohenoja

4. Outline What is Variogram and how it is calculated?
Outline
What is Variogram and how it is calculated?
Variogram-derived measures
Examples within MMEA
Faculty of Technology / Control Engineering / Markku Ohenoja

5. Variographical analysis
Variogram
Tool for empirical estimation of sampling errors incl. analytical error
Enables optimizing the sampling strategy with respect to variance of the sampling error and number of samples takes
Provides an estimate of the standard error of the lot mean and the minimum possible error (MPE) of sampling
Semi-variogram
Chrono-variogram
Variographical analysis
Geostatistics
Kriging
Variography
Chronostatistics
Faculty of Technology / Control Engineering / Markku Ohenoja

6. Variogram Collection of the data
Variogram
Collection of the data
At least 30 samples with systematic sampling
1/5 smaller sampling interval than routine samples
Flowrate/sample weight should be included
Calculation of the heterogeneity of the data
Calculation of the experimental variogram v(j)
Relationship between the samples and the lag distance j
Estimation of the intercept v(0) (=MPE)
Graphically, separate experiment…
Auxiliary functions for comparing sampling strategies
Point-to-point calculation, algebraic modeling…
Faculty of Technology / Control Engineering / Markku Ohenoja

7.
Variogram
σ2, σ, 2σ, ...
Faculty of Technology / Control Engineering / Markku Ohenoja

8.
Variogram 3x
Faculty of Technology / Control Engineering / Markku Ohenoja

9. indices Variogram-based indices applied for QC and PAT purposes
indices
Variogram-based indices applied for QC and PAT purposes
Standard error of the mean
MPE/σProcess
v(1)/σProcess
Faculty of Technology / Control Engineering / Markku Ohenoja

10. indices Variogram-based indices applied for QC and PAT purposes
indices
Variogram-based indices applied for QC and PAT purposes
Standard error of the mean
MPE/σProcess
v(1)/σProcess
Process stability measure
Bisgaard & Kulahci, Quality Engineering, 17(2), 2005
DQOs for control charts
Minnit & Pitard, Journal of SAIMM, 108(2), 2008
Drift estimation
Paakkunainen et al., Chemometrics and Intelligent Laboratory Systems, 88(1), 2007
Fault diagnosis
Kouadri et al., ISA Transactions, 51(3), 2012
Temporal uncertainty propagation
Jalbert et al., Journal of Hydrology, 397(1-2), 2011
Faculty of Technology / Control Engineering / Markku Ohenoja

11. Standard error of the mean
Standard error of the mean
Variance estimate of the sampling attained from variogram
Standard error of the mean calculated based on variance estimate and number of samples collected during a selected time frame
Recursive calculation possible for online measurements  moving average and its confidence intervals from the selected time frame
Faculty of Technology / Control Engineering / Markku Ohenoja

12. Standard error of the mean
Standard error of the mean
Faculty of Technology / Control Engineering / Markku Ohenoja

13. Standard error of the mean
Standard error of the mean
TIEDEKUNTA TIEDEKUNTA / osasto osasto osaston osasto / Etuniminen Sukuniminen-Sukuniminen

14.
Data comparison
Multiple measurement sources with different sampling rates
Data harmonization and comparison
Based on MPE
Comparable averaging of the dense data around sparse samples,
Variographical analysis for whole averaged dense data mimicking more densely collected laboratory measurements
Information content evaluation based on v(1)/σProcess
Faculty of Technology / Control Engineering / Markku Ohenoja

15.
What sparse cannot see?
Faculty of Technology / Control Engineering / Markku Ohenoja

16. When dense is not representative?
When dense is not representative?
TIEDEKUNTA TIEDEKUNTA / osasto osasto osaston osasto / Etuniminen Sukuniminen-Sukuniminen

17. Summary Variogram can be utilized for
Summary
Variogram can be utilized for
Sampling error estimation
Sampling optimization
Moving average and confidence interval calculation
Information content evaluation
Recursive calculation enables e.g. monitoring, filtering, decision making
Information content evaluation allows comparison of measurement sources
Faculty of Technology / Control Engineering / Markku Ohenoja