Analyze the differences between accuracy and precision when assessing a measurement system, and explain why both are important in a Six Sigma project.

In a Six Sigma project, assessing a measurement system for both accuracy and precision is crucial, and although these terms are sometimes used interchangeably in common language, they represent distinct characteristics that must be understood and evaluated to ensure reliable data collection and analysis.

Accuracy refers to how close a measurement is to the true or accepted value of what is being measured. A measurement system with high accuracy yields results that are, on average, very close to the actual value. It speaks to the correctness or truthfulness of the measurements. For instance, if the actual weight of an object is 100 grams, a measurement system with high accuracy will consistently return measurements that are close to 100 grams, say 99.8, 100.1, or 100.2 grams. Conversely, a measurement system with poor accuracy will show measurements that are consistently off from the actual value, such as measurements that center around 105 grams, consistently overestimating the true value. Accuracy therefore is a reflection of systematic error or bias that are characteristics of an inaccurate measurement system.

Precision, on the other hand, describes the repeatability or reproducibility of measurements. A precise measurement system yields results that are very close to each other when the same thing is measured repeatedly. High precision indicates low variability and does not necessarily imply that the measurements are close to the true value. For example, a scale that consistently reports the weight of the same 100-gram object as 105, 105.1, and 104.9 is considered precise, even though its results are not accurate. It is showing low variation from one measurement to the next, but the measurements are far from the true value. A lack of precision, in comparison, might give varying measurements, such as 102, 108, and 98 when trying to measure the same item.

The significance of both accuracy and precision in a Six Sigma project stems from the need to collect reliable and valid data that can be used to make informed decisions about process improvement. If the measurement system lacks accuracy, the data will be systematically skewed, leading to incorrect conclusions about process performance. For instance, if a project is aimed at reducing the weight of a product to 100 grams but the measurement scale is consistently reading 5 grams more than the actual weight, the project may erroneously believe the process is meeting the goal, while it may not be the case in reality. In this case, the inaccuracy of the system is masking the true process output, making decision making difficult.

Similarly, if a measurement system lacks precision, the data will be too variable to reliably identify patterns or changes in the process. If the variability of a measurement is too large, it can mask any subtle changes in the true performance of the process and hinder the capacity to detect or control special cause variation. For instance, if a measurement system of the diameter of manufactured pipes has high variation, it might be impossible to tell if small shifts in diameter are caused by a true change in the process or just the measurement system itself, hampering efforts to understand the root causes of the problem and make process improvements. In this case, the imprecision of the system is creating a 'noisy' measure, making analysis difficult.

Both accuracy and precision are required for a measurement system to be fit for use. A measurement system that is accurate but not precise will provide, on average, a correct estimate of the true value, but will not be reliable enough for detecting small variations in the process. Conversely, a system that is precise but not accurate will yield repeatable measurements that are consistently incorrect, potentially leading to wrong conclusions about the true state of a process. To illustrate, a dart player can be accurate if his darts are mostly close to the bullseye on average, but if they are very spread out, their precision is poor. Alternatively, a player can be precise if their darts are very close to each other but off-center consistently, and this means that player is not accurate. The best player would be accurate and precise, meaning their darts would be consistently near the bullseye and also close to each other.

Therefore, in a Six Sigma project, the measurement system must be evaluated for both systematic error (accuracy) and variation (precision). Both parameters are necessary to ensure that decisions made about process improvements are based on reliable, high-quality data. Tools such as Gauge R&R studies are used to assess both accuracy and precision of a measurement system to ensure the data collected is suitable for analysis. The goal is to use a measurement system that is both accurate and precise, so that project teams are working with data that represents the true characteristics of the process being studied.