UNIT-1 Measurement Uncertainty of Instruments
- 1. MEASUREMENT UNCERTAINTY An accurate measurement is the closeness to the true value read by the measuring instruments. As every measurement is prone to error, it is often stated that a measurement result is complete only when accompanied by a quantitative statement of its uncertainty. This uncertainty assessment is required in order to decide if the result is adequate for its intended purpose (fit for purpose) and to ascertain if it is consistent with other similar or previous results. Sources of measurement uncertainty: Because real measurements are never made under perfect conditions, errors and uncertainties can come from the following sources: 1.The measuring instrument: Instruments can suffer from errors including bias, changes due to ageing, wear, or other kinds of drift, poor readability, noise (for electrical instruments) and many other problems. 2.The item being measured: Sometimes the measuring item may not be stable. For example, imagine trying to measure the size of an ice cube in a warm room. 3.The measurement process: The measurement itself may be difficult to make. For example, measuring the weight of small but lively animals presents particular difficulties in getting the subjects to co- operate.
- 2. 4. Imported uncertainties: Calibration of instrument has an uncertainty which is then built into the uncertainty of the measurements made. (But remember that the uncertainty due to not calibrating would be much worse.) 5. Operator skill: Some: measurements depend on the skill and judgement of the operator. One person may be better than another at the delicate work of setting up a measurement, or at reading fine detail by eye. The use of an instrument such as a stopwatch depends on the reaction time of the operator. 6. Sampling issues: The measurements made must be properly representative of the process which are trying to assess. For example, if the temperature at the workbench to be measured, it should not be measured with a thermometer placed on the wall near an air conditioning outlet. If the samples from a production line is chosen for measurement, the first ten product made on a Monday morning should not be taken always. 7. The environment: Temperature, air pressure, humidity and many other conditions affect the measuring instrument or the item being measured.
- 3. TYPES OF MEASUREMENT UNCERTAINTY There are following four types of measurement uncertainty: (a)Type A uncertainty (b)Type B uncertainty (c)Combined uncertainty (d)Expanded uncertainty 1.Type A Evaluation of Measurement Uncertainty Type A uncertainty is an evaluation of a component of measurement uncertainty calculated by a statistical analysis of measured data obtained under defined measurement conditions. 2.Type B Evaluation of Measurement Uncertainty Type B uncertainty is an evaluation of a component of measurement uncertainty determined by means other than a Type A evaluation of measurement uncertainty. Type B evaluation of standard uncertainty is usually based on scientific judgment using all of the relevant information available, which may include: (i)Previous measurement data (ii)Experience with the behaviour and property of relevant materials and instruments (iii)Manufacturer's specifications
- 4. iv. Data provided in calibration and other reports and v. Uncertainties assigned to reference data taken from handbooks. 3.Combined Measurement Uncertainty Combined uncertainty combines both type A and type B into one value of 68% confidence. Combined standard uncertainty may contain relations whose components are derived from Type A and Type B evaluations without discrimination between types. 4.Expanded Measurement Uncertainty It is the quantity defining an interval about the result of a measurement which may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand. ESTIMATION OF.MEASUREMENT UNCERTAINTY Measurement uncertainty is critical to risk assessment and decision making. Organizations make decisions every day based on reports containing quantitative measurement data. If measurement results are not accurate, then decision risks will increase. If the ability to assess the quality of the measurement results were present, organizations and individuals could make decisions more confidently. Improving quality is the key factor to reduce risks and associated costs. So, the measurement uncertainty is a parameter which is essential because it affects quality, costs, decisions and risks. Measurement uncertainty should be involved and acknowledged to assess the quality of the results stated to meet the established accuracy requirements.
- 5. Steps in Calculating Measurement Uncertainty 1.Specify the measurement process and equation 2.Identify and characterize the uncertainty sources 3.Quantify the magnitude of uncertainty components 4.Characterize sources of uncertainty 5.Convert uncertainty components to standard deviation equivalents 6.Calculate the combined uncertainty 7.Calculate the expanded uncertainty 8.8. Evaluate your uncertainty budget. Step 1: Specifying the measurement process and equation To specify the measurement process, the following instructions are considered as mentioned below. 1.The test or measurement function should be selected to evaluate. 2.The measurement method or procedure to be used should be selected. 3.The equipment should be selected that will be used. 4.The desired range of the measurement function should be selected. 5.The test-points to be evaluated should be determined. Next, the mathematical equation should be found out wherever necessary to characterize the measurement function.
- 6. Step 2: Identifying and characterizing the uncertainty sources The sources of uncertainty for the analysis should be identified as per the list below. 1.The test method, calibration procedure or measurement process should be evaluated. 2.The measurement equations should be evaluated. 3.The equipment, reference standards and reagents should be evaluated. 4.The minimum required sources of uncertainty should be identified. 5.Various sources of information should be analysed. 6.An expert should be consulted. If the measurement function includes equations, then the process to estimate uncertainty is slight different. Each variable in the equation and its influences on it should be identified. Step 3: Quantifying the magnitude of uncertainty components To quantify uncertainty, below steps are followed. 1.Information and data should be collected. 2.Right data should be evaluated and selected. 3.Data should be analysed. 4.Uncertainty components should be quantified.
- 7. Step 4: Characterizing sources of uncertainty To characterize the sources of uncertainty, below steps are followed. 1.Each source of uncertainty should be categorized as Type A or Type B. 2.A probability distribution should be assigned to each uncertainty component. It is an important step to determine how source of uncertainty is converted to a standard deviation. Step 5: Converting uncertainty components to standard deviation equivalents To convert uncertainty components to standard deviations, the following steps are listed below. 1.A probability distribution to each source of uncertainty should be assigned. 2.The divisor should-be found for the selected probability distribution. 3.Each source of uncertainty should be divided by its respective divisor to convert them to a standard uncertainty. Step 6: Calculating the combined uncertainty To calculate the combined standard uncertainty, below instructions should be performed. 1.The value of each uncertainty component should be squared 2.All the results in step l should be added together. 3.The square root of the result in step 2 should be calculated.
- 8. Step 7: Calculating the expanded uncertainty To calculate the expanded measurement uncertainty, just follow these steps: 1.The combined uncertainty should be calculated. 2.The effective degrees of freedom should be calculated. 3.A coverage factor (k) should be found and 4.The combined uncertainty should be multiplied by the coverage factor. Step 8: Evaluating uncertainty for appropriateness After calculating the expanded uncertainty, the uncertainty estimate for appropriateness should be evaluated using some standard uncertainty models to make sure about the measurement uncertainty estimate for adequacy of the measurement process which should not be overestimated or underestimated. STATISTICAL ANALYSIS OF MEASUREMENT DATA The mathematical analysis of the various measurements is called statistical analysis of the data. Some statistical tools are also used to calculate the uncertainty of measurement. They are as follows. 1.Analysis of data 2.Frequency distribution 3.Control chart 4.Acceptance sampling.
- 9. 1. Arithmetic mean or arithmetic average: When the number of readings of the repeated measurement are taken, the most likely value from the set of measured value is the arithmetic mean of the number of readings taken. The arithmetic mean value is mathematically obtained by 2. Median: At the same time, when the number of readings is large, the calculation of mean value is complicated. In such a case, a median value is calculated which will be a close approximation to the arithmetic mean value. Case (i) If the total number of measurements is odd, the middle value is taken as median. Case (ii) If the total number of measurements is even, the median is taken as the average of middle two number. For example, in a 10-number set of measurements, the median is
- 10. 3.Mode The mode is a statistical term which refers to the most frequently occurring number found in a set of numbers. For example, a set of measurements having the following values, 1, 1, 3, 5, 6, 6, 8, 8, 7, 8, the mode will be 8 because it occurs the most of all the values in the set. 4.Average deviation: The deviation indicates the departure of a given reading from the arithmetic mean of the data set. 5. Standard deviation: Standard deviation of an infinite number of data is the square root of the sum of all the individual deviations squared and divided by the number of readings. It is expressed by
- 11. 6. Skewness: Skewness is a measure of the asymmetry of a distribution. A distribution is asymmetrical when it is left side and right side are not mirror images. When a distribution has zero skew, it shows the distribution as symmetrical. It means, both left and right sides are mirror images. For example, normal distributions have zero skew because the distribution on will be equal from its peak. A right-skewed distribution is longer on the right side of its peak than on its left. Right skew is called positive skew. 7. Kurtosis: Kurtosis is a statistical measure which is used to describe a characteristic of a dataset. When normally distributed data is plotted on a graph, it generally forms the shape of an upside- down bell called bell curve. The plotted data from the mean of the data usually form the tails on each side of the curve. Kurtosis shows how much data resides in the tails.
- 12. MEASUREMENT SYSTEM ANALYSIS Measurement System Analysis (MSA) is the first step of the measure phase along the DMAIC pathway to improvement. DMAIC stands for Define, Measure, Analyse, Improve and Control. A complete MSA system generally consists of six parts as follows. (a) Instrument Detection Limit (b) Method Detection Limit (c) Accuracy (d) Linearity (e) Gauge R&R and (f) Long term stability.
- 13. CALIBRATION OF MEASURING INSTRUMENTS Calibration is a comparative process between a known measurement which means, the standard measurement value and the measurement using instruments in terms of actual values. The two main reasons of performing calibrating instruments are as follows. 1.To reduce over time 2.To minimize uncertainty An instrument should be calibrated at different situations as given here. i. After an event ii. When the measurement don’t function correctly iii. When instructed by the manufacturer Calibration of measuring instruments are performed for • It checks the accuracy of the instruments • It determines the traceability of the measurement. Methods of Calibration 1. Working curve method 2. Standard addition method
- 14. PRINCIPLE OF AIR GAUGING A gauge which is used for measuring air pressure is known as air gauge. In a pneumatic comparator, the rate of escape of air between the surface under test and one of known surface curve fitting. It measures the difference between these two surfaces. Examples of air gauges for external dimensions measurements: (i) Ring gauge (ii) Snap gauge (iii) Taper gauge (iv) Multi gauging (v) Average diameter gauges. Examples of internal diameters air gauges: i. Plug gauge ii. Taper gauge iii. Multi gauging iv. Average diameter gauge v. Roundness vi. Flatness vii. Straightness viii.Squareness ix. Parallelism x. Concentricity. Industrial applications of air gauging: 1. Automotive 2. Aerospace 3. Bearings 4. Medical 5. Moulds 6. Machinery components and 7. Packaging.
- 15. Advantages of air gauging for measurement: 1.Ease of use which means, the operator will not be required to be specially trained to use the equipment. 2.Operators will not be able to influence the results of the measurement. 3.Air gauging can be used to measure complex geometric tolerance. 4.It provides high accuracy and repeatability. 5.At is possible to measure parts without cleaning. 6.Technology is particularly well suited to automation process. Disadvantages of air gauging for measurement: 1.Complexity is involved in air gauge design and quality. 2.Accuracy of the setting masters is difficult. 3.Air supply control is difficult.
- 16. IS0 STANDARDS ISO (International Organization for Standardization) is an independent, non-governmental international organization with a membership of 167 national standards bodies. ISO standards are internationally agreed by experts. It is based on a product, managing a process, delivering a service or supplying materials. Also, ISO standards cover a huge range of activities. Monitoring and measuring resources process: 1. It determines resources needed for accurate results 2. It provides resources 3. It measures to verify products/services against requirements 4. It documents the results for monitoring.