BME 353 BIOMEDICAL MEASUREMENTS AND INSTRUMENTATION MEASUREMENT PRINCIPLES Definition of Terms True value: standard or reference of known value or a theoretical value. Accuracy: closeness to the true value; closeness with which an instrument reading approaches the true or accepted value of the variable (quantity) being measured. It is considered to be an indicator of the total error in the measurement without looking into the sources of errors. Precision: a measure of the reproducibility of the measurements; given a fixed value of a variable, precision is a measure of the degree to which successive measurements differ from one another i.e., a measure of reproducibility or agreement with each other for multiple trials. Sensitivity: the ability of the measuring instrument to respond to changes in the measured quantity. It is expressed as the ratio of the change of output signal or response of the instrument to a change of input or measured variable. Resolution: the smallest change in measured value to which the instrument will respond, i.e. the smallest incremental quantity that can be reliably measured. Error: deviation from the true value of the measured variable. Linearity: the percentage of departure from the linear value, i.e., maximum deviation of the output curve from the best-fit straight line during a calibration cycle. Tolerance: maximum deviation allowed from the conventional true value. It is not possible to build a perfect system or make an exact measurement. All devices deviate from their ideal (design) characteristics and all measurements include uncertainties (doubts). Hence, all devices include tolerances in their specifications. If the instrument is used for high-precision applications, the design tolerances must be small. However, if a low degree of accuracy is acceptable, it is not economical to use expensive sensors and precise sensing components. Ruler Static calibration curves for a multi- input single-output system Accuracy Accuracy is defined as the degree of conformity of a measured value to the true (conventional true value CTV) or accepted value of the variable being measured. Example on Accuracy A voltmeter is used for reading on a standard value of 50 volts, the following readings are obtained: 47, 52, 51, 48 Conventional true value (CTV) = 50 volts, Maximum (V MAX ) = 52 volts and minimum (V MIN ) = 47 volts. CTV V MIN = 50 47 = 3 volts; V MAX CTV = 52 50 = 2 volts. Absolute accuracy = max of {3, 2} = 3 volts. Relative accuracy = 3/50 = 0.06 and % accuracy = 0.06x100 = 6% Precision Precision is composed of two characteristics as conformity and the number of significant figures. Conformity: Precision (Pr) = max {(V AV V MIN ), (V MAX V AV )} Bias: The difference between CTV and average value (V AV ) Accuracy versus Precision Most accurate and precise Worst precision Systematic error? Illustration of Accuracy and Precision Significant Figures Calculations Using Significant Figures Two resistors, R 1 and R 2, are connected in series. Individual resistance measurements using a digital multimeter, yield R 1 = 18.7 and R 2 = . Calculate the total resistance to the appropriate number of significant figures. R 1 = 18.7 (three significant figures) R 2 = (four significant figures) R T = R 1 + R 2 = (five significant figures) = 22.3 If the result would be instead, it would be rounded to 22.4 Types of Errors Constant and Proportional Type Errors Analysis of Measured Data Distribution of 50 Voltage Readings Normal (Gaussian) Distribution Errors in Digital Systems Example An analog voltmeter is used to measure a voltage. It has 100 divisions on the scale. The voltage read is 6 volts and the meter has two ranges as 0 10 volts and 0 100 volts. Find the uncertainty in the measured value in both ranges. Uncertainty = V FSD / # of divisions, where V FSD is the voltage measured at full-scale deflection of the meter. On 10 V range, uncertainty = 10 / 100 = 0.05 V yielding V = 6 0.05 volt. On 100 V range, uncertainty = 100 / 100 = 0.5 V yielding V = 6 0.5 volt. Relative uncertainty: on 10 V range, 0.05/6 = 1/120 = ; On 100 V range, 0.5/6 = 1/12 = Percentage uncertainty: on 10 V range, (0.05/6)x100 = 0.83%, and On 100 V range, (0.5/6)x100 = 8.3% 3 rulers with different divisions Population and Sample Normal Distribution for Population and Sample An Engineer Must: Design the experiment from a problem description Conduct the experiment; use proper equipment and procedures to collect data Analyze and interpret data; write analysis reports on data collected from the field. The assessment of this student outcome can be done by verifying the achievement of following indicators: Identify the constraints and assumptions for the experiment (cost, time, equipment), and apply them into experimental design. Determine proper data to collect and predicts experimental uncertainties. Design the experiment and report the results of the design. Use suitable measurement techniques to collect data. Conduct (or simulate) the experiment and report the results. Select and explain different methods of analysis (descriptive and inferential) and depth of analysis needed. Use proper tools to analyze data and self-explanatory graph formats to present the data. Apply statistical procedures where appropriate. Verify and validate experimental data. Develop mathematical models or computer simulations to correlate or interpret experimental results. List and discuss several possible reasons for deviations between predicted and measured results from an experiment, choose the most likely reason and justify the choice, and formulate a method to validate the explanation. Reasons for Experiment To be familiar with test equipment, experimental set-up and procedures; i.e. to gain hands-on experience. To verify data available in literature. To obtain information that is not otherwise available. To test the proposed solution in the laboratory by controlling the experimental factors. To test the proposed solution in the field under naturally set conditions. Experimental conditions: The system to be studied must be physically available to the experimenter; The problem to be studied should be possible to formulate with quantitative concepts that can be accurately formulated; There should be no political or social constraints to carry the experiments. Design of an Experiment Optimization A patient undergoing examination by radioisotopes Three essential factors to consider: Cost factor Accuracy Damage factor Measuring Voltages and Currents Instrument Loading Measurement Using Oscilloscope