White Paper

Introduction

Oftentimes getting a calibration certificate is all we are looking for in a calibration provider. Very few times are we asked about the uncertainty calculation and what contributors are considered in the total estimated uncertainty. Yes, the auditor at the accreditation company will always ask about the uncertainty budgets and make sure the minimum requirements are met. But why don’t customers ask about this more often, maybe it’s because they aren’t sure why it’s important. This guide is designed to educate those looking to understand more about the uncertainty value reported on certificates. This paper will help someone understand the general process for creating uncertainty budgets and then using the budgets to produce the estimated uncertainty value at the time of calibration.

Understanding Uncertainty of Measurement

Uncertainty of measurement is defined as a parameter associated with the result of a measurement that characterizes the dispersion of values that could reasonably be attributed to the measurand. In simpler terms, it quantifies the doubt that exists about the result of a measurement. This doubt can arise from various sources, including the instruments used, the environment, the operator, and the method of measurement itself. The uncertainty budget is what will be used to detail each of these sources and quantify them. We will discuss this later.

Understanding and quantifying this uncertainty is crucial for several reasons:

• Decision Making: Accurate measurement is vital for making informed decisions in manufacturing, research, and regulatory compliance.
• Traceability: Uncertainty quantification ensures that measurements are traceable to international standards.
• Comparison: It allows for the comparison of results between different laboratories, or comparison of results over time
• Confidence: It provides confidence to clients and stakeholders in the reliability of the laboratory’s results.

How to Get started with Uncertainty – Defining the Process

Before we dive into how to calculate the uncertainty using an uncertainty budget, let’s take a look at the process as a whole. There are three main steps involved with uncertainty calculation that include:

1. Collect Data – This step is used to collect any repeatability and reproducibility data that will be needed for the uncertainty estimation. This data is sometimes called Type A Data, or Type A Data Study.
2. Build the Uncertainty Budget – this is the framework and the tool that will be used to calculate the uncertainty for each calibration in the future
3. Calculate the Estimated Uncertainty during Calibration – using the uncertainty budget to calculate the uncertainty estimation at the time of calibration

Step 1 – Collecting Data

In this step we are going to go through the best practices for collecting the repeatability and reproducibility data. But first let’s define what these two types of data are.

Repeatability – is the amount of deviation between individual measurements in a measurement set usually quantified by the standard deviation of the measurements. Repeatability data will indicate to the lab how repeatable the measurements within a method are.

Reproducibility: is the amount of deviation between two different measurement sets when one or more variables are changed between sets. For example, one common way to measure reproducibility between measurement sets is to have a technician perform a repeatability test (that will have its own standard deviation), and have a different technician perform the repeatability test with the same equipment set up (and this will have another standard deviation value). The reproducibility is the comparison of the variances and standard deviations from the resulting data sets.

Now that we know what reproducibility and repeatability are, let’s take a look at how we are going to measure them. A typical name for the data that is collected in repeatability and reproducibility experiments is Type A data. So, we will refer to this data collection in this paper as Type A data.

First, when collecting Type A data, you will want to have a standardized form where you can record the measurement results. This form will be customizable to the method or measurements you are currently working on. You can see the example below is for someone taking repeatability for a pipette at 100uL using ISO 8655 as the method of measurement.

If you are taking Type A Data for Reproducibility the only thing you would need to do is make a duplicate of the repeatability form and then have another technician take the same measurements using the same equipment set up. See the example below.

Another way to do reproducibility is to send the pipette (in this case) to another lab and have them give you the Type A data that they record. There are other ways as well. For example, if you only have 1 tech, you could have them perform this method twice on different days or with a different scale. Then you compare the data between the two. The point of reproducibility is to measure how consistent the method is when the technician changes, the performing lab changes, the day of calibration changes, or another variable. It measures how robust the method is.

There are ways to further investigate the reproducibility beyond preparation for uncertainty budgets. Which we are going to get to next. Reproducibility between technicians and/or performing labs is an excellent way to see if the variance between the two runs is acceptable or not. It’s a great tool to see if your method works consistently no matter who is performing it. One way to check this is to run ANOVA in excel with the Type A data from both technicians. This is not covered in this white paper because it could be a white paper by itself. But this is an excellent tool to check the performance between labs or technicians.

Step 2 – Filling in Uncertainty Budgets

An uncertainty budget is a way to combine and organize all the contributors to your uncertainty. It is also a way to estimate the overall uncertainty of a measurement method by calculating the individual uncertainties and then combining them. The uncertainty budget is really a template that should be used when evaluating uncertainty for all methods and measurements. The uncertainty budget is the best way to keep organized and calculate the uncertainty.

What is included in an uncertainty budget? Below is an example of an uncertainty budget that involves the following:

• Uncertainty Budget example for pH Probe Calibration
• Equipment Used – Standard pH solutions, DUT pH Probe

It’s important to note that this uncertainty budget will have contributors that pertain to the method used for calibrating pressure gauges. Every uncertainty budget will be unique with its own contributors. This paper is not intended to give you an example of an uncertainty budget to copy, it’s intended to provide guidance on understanding of uncertainty and how labs are calculating the number on their reports.