Model Diagnostics in the presence of measurement error

The problem of using information available from one variable X to make inferenceabout another Y is classical in many physical and social sciences. In statistics this isoften done via regression analysis where mean response is used to model the data. Onestipulates the model Y = µ(X) +ɛ. Here µ(X) is the mean response at the predictor variable value X = x, and ɛ = Y - µ(X) is the error. In classical regression analysis, both (X; Y ) are observable and one then proceeds to make inference about the mean response function µ(X). In practice there are numerous examples where X is not available, but a variable Z is observed which provides an estimate of X. As an example, consider the herbicidestudy of Rudemo, et al. [3] in which a nominal measured amount Z of herbicide was applied to a plant but the actual amount absorbed by the plant X is unobservable. As another example, from Wang [5], an epidemiologist studies the severity of a lung disease, Y , among the residents in a city in relation to the amount of certain air pollutants. The amount of the air pollutants Z can be measured at certain observation stations in the city, but the actual exposure of the residents to the pollutants, X, is unobservable and may vary randomly from the Z-values. In both cases X = Z+error: This is the so called Berkson measurement error model.In more classical measurement error model one observes an unbiased estimator W of X and stipulates the relation W = X + error: An example of this model occurs when assessing effect of nutrition X on a disease. Measuring nutrition intake precisely within 24 hours is almost impossible. There are many similar examples in agricultural or medical studies, see e.g., Carroll, Ruppert and Stefanski [1] and Fuller [2], , among others. In this talk we shall address the question of fitting a parametric model to the re-gression function µ(X) in the Berkson measurement error model: Y = µ(X) + ɛ; X = Z + η; where η and ɛ are random errors with E(ɛ) = 0, X and η are d-dimensional, and Z is the observable d-dimensional r.v.

Characterization of human and instrument related measurement errors

Measurement is the act or the result of a quantitative comparison between a given quantity and a quantity of the same kind chosen as a unit. It is generally agreed that all measurements contain errors. In a measuring system where both a measuring instrument and a human being taking the measurement using a preset process, the measurement error could be due to the instrument, the process or the human being involved. The first part of the study is devoted to understanding the human errors in measurement. For that, selected person related and selected work related factors that could affect measurement errors have been identified. Though these are well known, the exact extent of the error and the extent of effect of different factors on human errors in measurement are less reported. Characterization of human errors in measurement is done by conducting an experimental study using different subjects, where the factors were changed one at a time and the measurements made by them recorded. From the pre‐experiment survey research studies, it is observed that the respondents could not give the correct answers to questions related to the correct values [extent] of human related measurement errors. This confirmed the fears expressed regarding lack of knowledge about the extent of human related measurement errors among professionals associated with quality. But in postexperiment phase of survey study, it is observed that the answers regarding the extent of human related measurement errors has improved significantly since the answer choices were provided based on the experimental study. It is hoped that this work will help users of measurement in practice to better understand and manage the phenomena of human related errors in measurement.

Photothermal Investigations on Certain Plasma Polymerized Thin Films and Near IR Overtone Studies of Some Organic Molecules

Photothermal effect refers to heating of a sample due to the absorption of electromagnetic radiation. Photothermal (PT) heat generation which is an example of energy conversion has in general three kinds of applications. 1. PT material probing 2. PT material processing and 3. PT material destruction. The temperatures involved increases from 1-. 3. Of the above three, PT material probing is the most important in making significant contribution to the field of science and technology. Photothermal material characterization relies on high sensitivity detection techniques to monitor the effects caused by PT material heating of a sample. Photothermal method is a powerful high sensitivity non-contact tool used for non-destructive thermal characterization of materials. The high sensitivity of the photothermal methods has led to its application for analysis of low absorbance samples. Laser calorimetry, photothermal radiometry, pyroelectric technique, photoacoustic technique, photothermal beam deflection technique, etc. come under the broad class ofphotothermal techniques. However the choice of a suitable technique depends upon the nature of the sample, purpose of measurement, nature of light source used, etc. The present investigations are done on polymer thin films employing photothermal beam deflection technique, for the successful determination of their thermal diffusivity. Here the sample is excited by a He-Ne laser (A = 6328...\ ) which acts as the pump beam. Due to the refractive index gradient established in the sample surface and in the adjacent coupling medium, another optical beam called probe beam (diode laser, A= 6500A ) when passed through this region experiences a deflection and is detected using a position sensitive detector and its output is fed to a lock-in amplifier from which the amplitude and phase of the deflection can be directly obtained. The amplitude and phase of the signal is suitably analysed for determining the thermal diffusivity.The production of polymer thin film samples has gained considerable attention for the past few years. Plasma polymerization is an inexpensive tool for fabricating organic thin films. It refers to formation of polymeric materials under the influence of plasma, which is generated by some kind of electric discharge. Here plasma of the monomer vapour is generated by employing radio frequency (MHz) techniques. Plasma polymerization technique results in homogeneous, highly adhesive, thermally stable, pinhole free, dielectric, highly branched and cross-linked polymer films. The possible linkage in the formation of the polymers is suggested by comparing the FTIR spectra of the monomer and the polymer.Near IR overtone investigations on some organic molecules using local mode model are also done. Higher vibrational overtones often provide spectral simplification and greater resolution of peaks corresponding to nonequivalent X-H bonds where X is typically C, N or O. Vibrational overtone spectroscopy of molecules containing X-H oscillators is now a well established tool for molecular investigations. Conformational and steric differences between bonds and structural inequivalence ofCH bonds (methyl, aryl, acetylenic, etc.) are resolvable in the higher overtone spectra. The local mode model in which the X-H oscillators are considered to be loosely coupled anharmonic oscillators has been widely used for the interpretation of overtone spectra. If we are exciting a single local oscillator from the vibrational ground state to the vibrational state v, then the transition energy of the local mode overtone is given by .:lE a......v = A v + B v2 • A plot of .:lE / v versus v will yield A, the local mode frequency as the intercept and B, the local mode diagonal anharmonicity as the slope. Here A - B gives the mechanical frequency XI of the oscillator and B = X2 is the anharmonicity of the bond. The local mode parameters XI and X2 vary for non-equivalent X-H bonds and are sensitive to the inter and intra molecular environment of the X-H oscillator.

MS Measurements

RMS measuring device is a nonlinear device consisting of linear and nonlinear devices. The performance of rms measurement is influenced by a number of factors; i) signal characteristics, 2) the measurement technique used and 3) the device characteristics. RMS measurement is not simple, particularly when the signals are complex and unknown. The problem of rms measurement on high crest-factor signals is fully discussed and a solution to this problem is presented in this thesis. The problem of rms measurement is systematically analized and found to have mainly three types of errors: (1) amplitude or waveform error 2) Frequency error and (3) averaging error. Various rms measurement techniques are studied and compared. On the basis of this study the rms -measurement is reclassified three categories: (1) Wave-form-error-free measurement (2) High-frequncy-error measurement and (3) Low-frequency error-free measurement. In modern digital sampled-data systems the signals are complex and waveform-error-free rms measurement is highly appreciated. Among the three basic blocks of rms measuring device the squarer is the most important one. A squaring technique is selected, that permits shaping of the squarer error characteristic in such a way as to achieve waveform-errob free rms measurement. The squarer is designed, fabricated and tested. A hybrid rms measurement using an analog rms computing device and digital display combines the speed of analog techniques and the resolution and ease of measurement of digital techniques. An A/D converter is modified to perform the square-rooting operation. A 10-V rms voltmeter using the developed rms detector is fabricated and tested. The chapters two, three and four analyse the problems involved in rms measurement and present a comparative study of rms computing techniques and devices. The fifth chapter gives the details of the developed rms detector that permits wave-form-error free rms measurement. The sixth chapter, enumerates the the highlights of the thesis and suggests a list of future projects

Evaluation Of A Novel Method Of Real Time Computer Assisted Spine Surgery

In this paper the effectiveness of a novel method of computer assisted pedicle screw insertion was studied using testing of hypothesis procedure with a sample size of 48. Pattern recognition based on geometric features of markers on the drill has been performed on real time optical video obtained from orthogonally placed CCD cameras. The study reveals the exactness of the calculated position of the drill using navigation based on CT image of the vertebra and real time optical video of the drill. The significance value is 0.424 at 95% confidence level which indicates good precision with a standard mean error of only 0.00724. The virtual vision method is less hazardous to both patient and the surgeon