7 Steps to Calculate Measurement Uncertainty isobudgets PDF

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Menu Home Uncertainty Training Calculators Blog July 20, 2020 by Richard Hogan Downloads About You are here: Contact 1. Home 2. ISOBudgets blog by Rick Hogan h... 7 Steps to Calculate Measurement Uncertainty

7 Steps to Calculate Measurement Uncertainty

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Introduction Calculating measurement uncertainty is not easy. In fact, I speak with people every day who are having problems with estimating uncertainty. Therefore, I decided to put together this guide disclosing my exclusive seven step process to calculating measurement uncertainty. In this guide, you will learn how to calculate measurement uncertainty in seven easy steps. Also, you will learn what information you need to calculate uncertainty, how to identify contributors to uncertainty, and how to evaluate your calculations to prevent overestimating or underestimating uncertainty. Furthermore, I will share with you some of my exclusive tips to help you calculate uncertainty like a pro. Now, this guide is not a complete “how to” manual. Nor, will it answer all of your questions. Instead, it should be used as a quick reference guide to simplify the uncertainty estimation process into seven steps and learn some of my personnel secrets used when I calculate uncertainty. So, read this guide and use my advice to help you calculate uncertainty. If you have questions, make sure to contact me. Additionally, feel free to use this guide to help you write an uncertainty procedure for your laboratory. Click here to download the simple uncertainty calculator for free!

How to Calculate Measurement Uncertainty Estimating measurement uncertainty can be a difficult task. Especially, since most measurement uncertainty guides do not give you a process or procedure. Therefore, I developed a seven-step process that you can use every time you estimate measurement uncertainty. Just follow the steps below to when you need to create an uncertainty budget. 1. Specify the Measurement Process 2. Identify Sources of Uncertainty 3. Quantify Sources of Uncertainty 4. Characterize Sources of Uncertainty Convert Uncertainties to Standard Deviations Calculate the Combined Uncertainty Calculate the Expanded Uncertainty Evaluate Your Uncertainty Budget

p 1. Specify the Measurement Process and Equation Before you dive in and begin calculating uncertainty, it is best to have a plan. The first part of your plan should be to identify the measurement process or system that you wish to evaluate. This will help you frame your uncertainty analysis and focus your attention on what matters most.

How to Specify the Measurement Process To specify the measurement process, follow the instructions below: 1. Select the test or measurement function to evaluate. 2. Select the measurement method or procedure to be used. 3. Select the equipment that will be used. 4. Select the desired range of the measurement function. 5. Determine the test-points to be evaluated. Where applicable, identify the mathematical equation that characterizes the measurement function.

Need More Help If you are having trouble with this process, try answering the following questions: 1. What am I measuring? 2. How will I measure it? 3. What method will I use? 4. What equipment will I need? 5. What is the range (e.g. min and max) of my measurement capability? 6. What are my target test-points?

After answering the questions above, use your answers to identify what measurement process you are evaluating. Then, add that information to your uncertainty budget. Take a look at the image below. Once you have outlined what you will be evaluating, you can move on to the next step.

What About Indirect Measurements? If you are performing indirect measurements that require you to calculate your measurement results, then you should evaluate the equation used to determine your measurement result. Each variable in the equation will have its own uncertainty that will directly affect the uncertainty associated with the calculated measurement result. To help you out, think of using dead weight testers or calibrating torque transducers and standard resistors. Each one of these measurement processes require you to use an equation to calculate a result for comparison purposes. To estimate uncertainty, you will want to break down the equation and evaluate the uncertainty of each variable in the equation. If you want to learn more about specifying the measurement function and process for your uncertainty analysis, check out this guide: How to Start Every Uncertainty Analysis: Specify the Measurement Process

Step 2: Identify and Characterize the Uncertainty Sources Now that you have determined the measurement process that you are going to evaluate, you need to identify the factors that influence uncertainty in measurement results. This process is not typically easy and can be very frustrating. So, stay calm, be patient, and keep researching. You may be surprised by how many influences can affect your measurement results. Before you begin, I recommend that you find a book or guide on the measurement process you are evaluating. Physics, Chemistry, and Engineering textbooks can come in handy for understanding background and detailed information about your measurement process. If new textbooks are too expensive, you should be able to buy reasonably priced used books on websites like eBay, Amazon, or Chegg.

Other resources that you may want to consider are ASTM and ISO methods. However, if you like free resources (like I do), you may want to search National Metrology Institute websites, such as NIST, NPL, and BIPM. They may have downloadable guides related to your specific measurement processes.

Finding Sources of Uncertainty Finding sources of uncertainty can be difficult. It requires a lot of time and effort to conduct research. It is the most time-consuming process when evaluating measurement uncertainty. Based on my experience, finding factors that influence uncertainty typically requires 50% of the time you spend estimating uncertainty. Take a look at the graph below to see how you will typically spend your time estimating uncertainty.

However, if you spend time evaluating your process and conducting research, you should be able to identify several sources of uncertainty for your analysis. Afterward, make a list of these items. You will attempt to quantify them later.

Pro-Tip: Save and archive your notes and the resources you spent so much time searching for. It will save you time in the future.

How to Find Sources of Uncertainty To find sources of uncertainty for your analysis, follow steps listed below: 1. Evaluate the test method, calibration procedure, or measurement process. 2. Evaluate the measurement equations (if available). 3. Evaluate the equipment, reference standards, and reagents. 4. Identify the minimum required sources of uncertainty. 5. Research various sources of information.

6. Consult an expert.

Best Places to Find Sources of Uncertainty When you need to find sources of uncertainty, it helps to have a list of available resources. Below is a list of places, including links, that you can use to help you find sources of uncertainty. 1. Manufacturer Manuals 2. Manufacturer Datasheets 3. White Papers 4. Technical Notes & Guides 5. Conference Papers Textbooks NIST Special Publications 250 Series NIST Internal Reports NIST Journal of Research NPL Good Practice Guides BIPM Publications MSL Technical Guides EURAMET Calibration & Technical Guides Metrologia CalLab Magazine 16. NCLSI Measure Magazine

Measurement Functions with Equations If your measurement function includes equations, then the process to estimate uncertainty is a little different. You will want to identify each variable in the equation and think about what influences each variable. For example, if you are evaluating the calibration of a torque transducer, you will first write out the equation.

When you evaluate the equation further, you begin to account for other factors that influence the equation. In this example, we begin to consider the radius of the torque arm and cable, the mass of the weights and pan, and the local gravity. If needed, we can evaluate the equation even further to account for more influences and increase the complexity of your uncertainty analysis.

hat you have identified the equation and the variables, you can start to research what factors may cause es or variations to each variable. Using the example above, think about how temperature variations can thermal linear expansion or contraction of the arm radius, and how it can affect air density which affects air ncy correction that can vary the magnitude of applied force. u can see, evaluating equations can help you find sources of uncertainty. While this process may seem easy, it can become quite difficult depending on the complexity of the equation. Knowing the rules for the propagation of uncertainty can come in handy in step 5.

Measurement Functions without Equations Most of the measurement functions that you evaluate will not have equations. So, you will need to evaluate the measurement process to find the factors that influence measurement uncertainty. Start by evaluating the core elements of the measurement process, including the: 1. Method, 2. Equipment, 3. Personnel, 4. Environment, 5. Unit Under Test, and 6. Results By evaluating these categories, you will find sources of uncertainty that influence measurement results. Take a look at the table below. Start breaking down each category to see what you find.

You may get lucky and find a paper or guide with a cause and effect (a.k.a. fishbone) diagram or an uncertainty t already prepared with information applicable to your uncertainty analysis. ain thing that you must do to find sources of uncertainty is to investigate and research. rn more about finding sources of measurement uncertainty, check out this guide: 15 Places to Find Sources of Uncertainty in Measurement

Step 3. Quantify the Magnitude of Uncertainty Components Before calculating measurement uncertainty, you must first determine the magnitude of each contributing factor. To accomplish this, you may need to perform some data reduction and analysis.

How to Quantify Uncertainty To quantify uncertainty, you need to follow the four steps below: 1. Collect Information and Data 2. Evaluate and Select the Right Data 3. Analyze the Data 4. Quantify Uncertainty Components

Collect Information and Data To get started, you need to collect information and data related to your uncertainty analysis. You should have found a lot most of this information in Step 2. Take a look at the list below and gather the following items. You will need them to quantify sources of uncertainty. a. Last 3 Calibration Reports b. Repeatability and Reproducibility (R&R) Studies c. Method or Procedure d. Experiment Results

e. Manufacture Manuals and Specifications f. Technical Documents and Guides g. Published papers, studies, journal articles, etc. Using the items in the list above, you should be able determine how much uncertainty is contributed from each source. If you need help, you can contact me for additional guidance or hire me to analyze the data for you.

Evaluate Information and Select the Right Data Next, you need evaluate the information that you have and find data that you will use for estimating uncertainty. You need to find data related to your uncertainty analysis and eliminate everything else from consideration. hould include information and data related to your: measurement function, measurement range, and test-point.

ze the Data Then, analyze the data that you have using appropriate methods of analysis to find the magnitude of each uncertainty component. You can analyze data in many ways, so choose methods that are appropriate for the data you are analyzing. If you need help, get a quality statistics textbook or check the free NIST SEMATECH Engineering Statistics Handbook. You can also check out some of my guides on quantifying sources of uncertainty.

Quantify Uncertainty Components Finally, use your results to quantify each uncertainty component and add the values to your uncertainty budget or uncertainty calculator. You can add the uncertainty and unit of measurement directly into your uncertainty budget.

Or, you can add uncertainties, their unit of measurement, and a sensitivity coefficient to your uncertainty budgets. The option is yours.

People use different techniques, and that is okay. Just make sure that you are able to explain where your data came from and the way it is evaluated. I recommend adding detailed notes to your uncertainty budgets. It will help you remember how you did it and why.

Sources of Uncertainty Below, you will see a list of uncertainty components that you should include in every uncertainty budget. Many of these factors are required by section 6 of the A2LA R205 requirements document. While this is not a requirement for everyone, I like their list of minimum required uncertainty contributors and have decided to use them in each one of my uncertainty analyses. Additionally, I prefer to include more sources of uncertainty in my budgets since I find them to typically be significant. The additional sources I like to consider are long-term stability, bias, and drift. Here is my list of the minimum recommended sources of uncertainty to include in every uncertainty budget. 1. Repeatability 2. Reproducibility 3. Stability 4. Bias 5. Drift 6. Resolution 7. Reference Standard Uncertainty 8. Reference Standard Stability 9. Other Significant Contributors

Repeatability Repeatability is an evaluation of the variability in your measurement process under similar conditions.

Calculate Repeatability

w these instructions to calculate repeatability: 1. Repeat a measurement ‘n’ number of times 2. Record the results of each measurement. 3. Calculate the standard deviation.

Reproducibility Reproducibility is an evaluation of the variability in your measurement process under different conditions.

How to Calculate Reproducibility

Follow these instructions to calculate reproducibility: 1. Perform a Repeatability Test. 2. Calculate the mean of average. 3. Change a variable and repeat the Repeatability Test 4. Calculate the mean or average. 5. Calculate the standard deviation of the test averages.

ity ty is an evaluation of the variability in your measurement process over time.

How to Calculate Stability

Follow these instructions to calculate stability: 1. Review your last 3 calibration reports. 2. Record the results from each calibration report. 3. Calculate the standard deviation of the calibration results.

Bias Bias is an evaluation of the systematic error in your measurement process.

How to Calculate Bias

Follow these instructions to calculate bias: 1. Review your latest calibration report. 2. Find the As Left value or measurement result. 3. Find the Nominal value or standard value. 4. Calculate the difference.

Drift Drift is an evaluation of the systematic change in your measurement process or system over time.

How to Calculate Drift

Follow these instructions to calculate drift: 1. Review your last 3 calibration reports. 2. Record the results from each calibration report. 3. Record the date each calibration was performed. 4. Calculate the average daily drift rate. 5. Multiply the average daily drift rate by your calibration interval (in days).

Resolution Resolution is an evaluation of the smallest incremental change observed in your measurement process or system.

Find Resolution

w these instructions to find resolution: 1. Look at your measurement system or equipment. 2. Find the least significant digit. 3. Observe the smallest incremental change.

Reference Standard Uncertainty Reference Standard Uncertainty is the traceable uncertainty associated with calibration of equipment or reference materials used in your measurement process.

How to Calculate Reference Standard Uncertainty

Follow these instructions to find reference standard uncertainty: 1. Review your latest calibration report. 2. Find the reported estimate of measurement uncertainty.

Reference Standard Stability Reference Standard Stability is an evaluation of the variability in your Reference Standard Uncertainty over time.

Calculate Reference Standard Stability

w these instructions to calculate reference standard stability: Review your last 3 calibration reports. Record the uncertainty estimate from each calibration report. Calculate the standard deviation.

Other Significant Contributors Make sure to include any other significant contributors to measurement uncertainty. A significant contributor is considered a source of uncertainty that contributes 5% or more to the total combined standard uncertainty. To learn more about sources of uncertainty and how to quantify them, check out these guides: 8 Sources of Uncertainty to include in Every Uncertainty Budget Linearity Uncertainty Hysteresis Uncertainty Uncertainty Due to Thermal Expansion

Step 4: Characterize Sources of Uncertainty Now that you identified and quantified your sources of uncertainty, your next step will be to characterize each factor by uncertainty type and probability distribution.

How to Characterize Sources of Uncertainty To characterize your sources of uncertainty, perform the following tasks below: 1. Categorize each source of uncertainty: Type A or Type B,

2. Assign a probability distribution to each uncertainty component.

Uncertainty Types The first step to characterizing your uncertainty components is to categorize them as either Type A or Type B. Read the sections below to learn the difference between Type A and Type B uncertainty.

Type A Uncertainty ding to the Vocabulary in Metrology (VIM), Type A uncertainty is an “evaluation of a component of rement uncertainty determined by a statistical analysis of measured quantity values obtained under defined rement conditions.”

B Uncertainty ding to the Vocabulary in Metrology (VIM), Type B uncertainty is an “evaluation of a component of measurement uncertainty determined by means other than a Type A evaluation of measurement uncertainty.”

How to Pick an Uncertainty Type If you are not sure which uncertainty type you should pick, ask yourself the following questions: 1. Did you collect the data yourself via testing and experimentation? a. If YES, go to question 2 b. If No, choose Type B 2. Is the data older than 1 year? a. If YES, choose Type B b. If No, choose Type A

Probability Distributions This is an important step because the probability distribution that you select will determine how your source of uncertainty is converted to a standard deviation in the next step. Although there are many different types of probability distributions that you can choose from, the Normal (i.e. Gaussian) and Rectangular (i.e. Uniform) distributions are the most commonly used.

Probability Distributions for Estimating Uncertainty Some of the most common probability distributions used to estimate uncertainty are; Normal (i.e. Gaussian) Distribution Rectangular (i.e. Uniform) Distribution Triangular Distribution Log-Normal Distribution Quadratic Distribution U-shaped Distribution Rayleigh Distribution Use the chart below to help you select the appropriate probability distribution.

ign the appropriate distribution, consider how to characterize the data set for each source of uncertainty. evaluated Type A uncertainty data, calibration results, or used an accuracy specification, you most likely o assign a Normal distribution. If you evaluated resolution, environmental or physical influences, you may want to use a rectangular distribution. If you are not sure what d...