Errors gross

Both the wavelength dispersive and energy dispersive spectrometers are well suited for quaUtative analysis of materials. Each element gives on the average only six emission lines. Because the characteristic x-ray spectra are so simple, the process of allocating atomic numbers to the emission lines is relatively simple and the chance of making a gross error is small. 

Gross errors. These result from unpredictable... 

To determine if a process unit is at steady state, a program monitors key plant measurements (e.g., compositions, product rates, feed rates, and so on) and determines if the plant is steady enough to start the sequence. Only when all of the key measurements are within the allowable tolerances is the plant considered steady and the optimization sequence started. Tolerances for each measurement can be tuned separately. Measured data are then collec ted by the optimization computer. The optimization system runs a program to screen the measurements for unreasonable data (gross error detection). This validity checkiug automatically modifies tne model updating calculation to reflec t any bad data or when equipment is taken out of service. Data vahdation and reconciliation (on-line or off-line) is an extremely critical part of any optimization system. 

Serth, R.W, B. Srikanth, and S.J. Maronga, Gross Error Detection and Stage Efficiency Estimation in a Separation Process, AlChE Journal, 39(10), 1993, 1726-1731. (Physical model development, parameter estimation)... 

Crowe, C.M., Recursive Identification of Gross Errors in Linear Data Reconciliation, AJChE Journal, 34(4), 1988,541-550. (Global chi square test, measurement test)... 

Madron, F, A New Approach to the Identification of Gross Errors in Chemical Engineering Measurements, Chemical Engineeiing Science, 40(10), 1985, 1855-1860. (Detection, elimination)... 

Phillips, A.G. and D.P. Harrison, Gross Error Detection and Data Reconciliation in Experimental Kinetics, Indushial and Engineeiing Chemistiy Reseaieh, 32, 1993,2530-2536. (Measurement test)... 

Rollins, D.K. and J.F. Davis, Gross Error Detection when Variance-Covariance Matrices are Unknown, AlChE Journal, 39(8), 1993, 13.35-1341. (Unknown statistics)... 

Romagnoli, J.A. and G. Stephanopoulos, Rectification of Process Measurement Data in the Presence of Gross Errors, Chemical Engineeiing Science, 36(11), 1981, 1849-186.3. 

Rosenberg, J., R.S.H. Mah, and C. lordache, Evaluation of Schemes for Detecting and Identifying Gross Errors in Process Data, Indushial and Engineeiing Chemistiy, Reseaieh, 26(.3), 1987, 555-564. (Simulation studies of various detection methods)... 

Serth, R.W. and W.A. Heenan, Gross Error Detection and Data Reconciliation in Steam-Metering Systems, AlChE Journal, 32(5), 1986, 7.3.3-742. 

Verneuil, VS. Jr., P. Yang, and F. Madron, Banish Bad Plant Data, Chemical Engineeiing Piogiess, October 1992, 45-51. (Gross-error detection overview)... 

Mah, R.S., G.M. Stanley, and D.M. Downing, Reconciliation and Rectification of Process Flow and Inventory Data, Indushial and Engineeiing Chemishy, Piocess Design and Development, 15(1), 1976, 175-18.3 (Reconciliation, impact of gross errors)... 

Rectification accounts for systematic measurement error. During rectification, measurements that are systematically in error are identified and discarded. Rectification can be done either cyclically or simultaneously with reconciliation, and either intuitively or algorithmically. Simple methods such as data validation and complicated methods using various statistical tests can be used to identify the presence of large systematic (gross) errors in the measurements. Coupled with successive elimination and addition, the measurements with the errors can be identified and discarded. No method is completely reliable. Plant-performance analysts must recognize that rectification is approximate, at best. Frequently, systematic errors go unnoticed, and some bias is likely in the adjusted measurements. 

Intended Use The intended use of the model sets the sophistication required. Relational models are adequate for control within narrow bands of setpoints. Physical models are reqiiired for fault detection and design. Even when relational models are used, they are frequently developed bv repeated simulations using physical models. Further, artificial neural-network models used in analysis of plant performance including gross error detection are in their infancy. Readers are referred to the work of Himmelblau for these developments. [For example, see Terry and Himmelblau (1993) cited in the reference list.] Process simulators are in wide use and readily available to engineers. Consequently, the emphasis of this section is to develop a pre-liminaiy physical model representing the unit. 

However, other bias errors are so substantial that their presence will significantly distort any conclusions drawn from the adjusted measurements. Rectification is the detection of the presence of significant bias in a set of measurements, the isolation of the specific measurements containing bias, and the removal of those measurements from subsequent reconcihation and interpretation. Significant bias in measurements is defined as gross error in the literature. 

The methods discussed in the technical hterature are not exact. Numerical simulations of plant performance show that gross errors frequently remain undetected when they are present, or measurements are isolated as containing gross errors when they do not contain any. 

This test does not require reconciliation before it is applied. However, should the null hypothesis be rejected, it only indicates that a gross error might be present. It does not isolate which of the measurements (or constraints) are in error. Consequently, gross-error isolation must be done subsequently. 

Measurement Test This test compares the adjusted measurements to the actual measurements. In so doing, each measurement is tested for gross error. From the reconciliation development,... 

Unlike the other two tests, this is associated with each measurement. Reconcihation is required before this test is apphed, but no further isolation is required. However, due to the limitations in reconciliation methods, some measurements can be inordinately adjusted because of incorrectly specified random errors. Other adjustments that do contain gross errors may not be adjusted because the selected constraints are not sensitive to these measurements. Therefore, even though the adjustment in each measurement is tested for gross error, rejection of the mill hypothesis for a specific measurement does not necessarily indicate that that measurement contains gross error. 

The authors test two methods coupled with the measurement test. In one, they sequentially eliminate measurements and rearrange the constraints to isolate the specific measurements that contain gross errors. In the other, streams are added back as the search continues. 

This inexact performance leads to the recommendation that measurement sets should be discarded in their entirety when gross errors are detected. Therefore, actual isolation of which measurements contain error is not necessary when entire sets are discarded. 

Recommendation When all measurements were recorded by hand, operators and engineers could use their judgment concerning their validity. Now with most acqmred automatically in enormous numbers, the measurements need to be examined automatically. The goal continues to be to detect correctly the presence or absence of gross errors and isolate which measurements contain those errors. Each of the tests has limitations. The hterature indicates that the measurement test or a composite test where measurements are sequentially added to the measurement set are the most powerful, but their success is limited. If automatic analysis is required, the composite measurement test is the most direct to isolation-specific measurements with gross error. 

However, given that reconciliation will not always adjust measurements, even when they contain large random and gross error, the adjustments will not necessarily indicate that gross error is present. Further, the constraints may also be incorrect due to simphfications, leaks, and so on. Therefore, for specific model development, scrutiny of the individual measurement adjustments coupled with reconciliation and model building should be used to isolate gross errors. 

The adjusted mea.surements are not unique and may he no better than the actual mea.surements. Simulation studies testing reconciliation methods in the absence of gross error show that they arrive at a better estimate of the actual component and stream flows 60 percent of the time 40 percent of the time, the acdual measured values better represent the unit performance. 

Gro.s.s-error-detection methods detect errors when they are not pre.sent and fail to detect the gro.s.s errors when they are. Couphng the aforementioned difficulties of reconciliation with the hmitations of gross-error-detection methods, it is hkely that the adjusted measurements contain unrecognized gross error, further weakening the foundation of the parameter estimation. 

The duration of a particular test is likely to be determined by practical factors such as the need for some information within a particular limit of time, or the nature of the operation or process with which the test is concerned. Tests are rarely run too long however, this can happen, particularly in laboratory tests where the nature of the corrosive environment may be changed drastically by the exhaustion of some important constituent initially present in small concentration, or by the accumulation of reaction products that may either stifle or accelerate further attack. In either case, the corrosivity of the environment may be altered considerably. Gross errors may result from the assumption that the results apply to the original conditions of the test rather than to some uncertain and continually changing conditions that may exist during the course of too extended a test period. 

It is clear that neither NMEA nor NDPA is appropriate for an internal standard in NDMA determination if criteria are interpreted strictly, but both compounds have been used for this purpose. Addition of a nitrosamine, not normally present in the sample, is helpful in detecting any gross errors in the procedure, but the addition should not be considered to be internal standardization. Utilization of NMEA or NDPA to indicate recovery of NDMA can lead to significant errors. In most reports of the application of these "internal standards", recovery of all nitrosamines was close to 100%. Under these conditions, any added compound would appear to be a good internal standard, but none is necessary. NDMA is a particularly difficult compound for use of internal standardization because of its anomalous distribution behavior. I mass j ectrometry is employed for quantitative determination, H- or N-labeled NDMA could be added as internal standard. Because the labeled material would coelute from GC columns with the unlabeled NDMA, this approach is unworkable when GC-TEA is employed or when high resolution MS selected ion monitoring is used with the equipment described above. 

By automation one can remove the variation of the analysis time or shorten the analysis time. Although the variation of the analysis time causes half of the delay, a reduction of the analysis time is more important. This is also true if, by reducing the analysis time, the utilization factor would remain the same (and thus q) because more samples are submitted. Since p = AT / lAT, any measure to shorten the analysis time will have a quadratic effect on the absolute delay (because vv = AT / (LAT - AT)). As a consequence the benefit of duplicate analyses (detection of gross errors) and frequent recalibration should be balanced against the negative effect on the delay. 

Nounou, M. N., and Bakshi, B. R., On-line multiscale fillering of random and gross errors without process models, AIChE J., 45(6), 1041 (1999). 

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