Measurement Errors

Quick reference

• 00:05 Hi, I'm Ray Sheen.
• 00:06 Well, I've talked about the importance of measurement system error.
• 00:09 It's now time to take a look at the factors that could cause measurement
• 00:13 system error.
• 00:14 So let's talk about what goes into a measurement.
• 00:18 When you record an observed measurement,
• 00:20 you're recording a combination of three effects.
• 00:22 On the one hand, there is the true value of the item that is being measured,
• 00:27 how big, or how fast, or how hot it is.
• 00:29 However, there is also the measurement error associated with
• 00:33 the measurement system, the uncertainty in the people and the equipment being used.
• 00:37 And there is the calibration standard of whatever measurement approach you
• 00:41 are using.
• 00:42 I want to focus in on the measurement system error and its sources.
• 00:46 We're going to look at each of these in more detail.
• 00:48 But one thing I want you to realize is that there are many potential sources of
• 00:52 errors or error effects.
• 00:54 Some of these can be easily measured or analyzed,
• 00:57 but some will need a sophisticated statistical analysis.
• 01:02 The first one to discuss is accuracy, which is sometimes referred to as bias.
• 01:07 Accuracy is whether the average of the measurements of an item agree with
• 01:11 the true value of that item.
• 01:13 The question you're answering is whether or
• 01:15 not you're getting the right answer at least on average.
• 01:18 If the answer to that question is yes, you are getting the right answer on average,
• 01:23 then we would say that the system is accurate.
• 01:26 What that means is that the difference between the actual value and the average
• 01:31 of the observed values as measured by the measurement system is very small.
• 01:35 When there are problems with accuracy,
• 01:37 we generally try to fix those by recalibrating the measurement system.
• 01:41 Now, I'd like to talk about precision.
• 01:44 Accuracy dealt with the center point on average of the observed measurements.
• 01:48 Precision deals with the variability of those measurements.
• 01:51 In essence, the width of that bell-shaped curve is determined by taking multiple
• 01:55 independent measurements of the same item and recording the results.
• 02:00 This analysis is at the heart of most measurement system analysis, and
• 02:04 this error is often based upon both the design and use of the system.
• 02:08 The error can be divided into two categories based upon two primary causes
• 02:12 for error.
• 02:13 First is repeatability.
• 02:15 This is looking at whether the same person measuring the same item with the same
• 02:19 equipment and in supposedly the same way, gets the same or different answers.
• 02:23 It's essentially looking at the variability of the equipment in
• 02:26 the process.
• 02:27 High repeatability would be a bell-shaped curve that is very narrow,
• 02:31 low repeatability is a wide curve.
• 02:34 The other category is reproducibility.
• 02:36 Can different people using the same measurement system and
• 02:39 measuring the same item get the same result?
• 02:42 This is looking at person-to-person variability.
• 02:44 If there's high reproducibility,
• 02:46 each individual's bell-shaped curve is almost identical with the others.
• 02:50 If low reproducibility, then each individual's curve is decidedly different.
• 02:55 Determining repeatability and
• 02:57 reproducibility is a statistical analysis known as a Gage R&R study.
• 03:02 It's very practical and important one.
• 03:04 In our course on measurement system analysis,
• 03:07 we show you how to conduct the analysis and interpret the results.
• 03:10 Next, we will look at discrimination as a contributing factor to error.
• 03:14 Discrimination is the resolution of the measurement system.
• 03:17 That means the number of measurement intervals within the nominal range of
• 03:21 the item value.
• 03:22 It represents the ability of the system to determine small changes in the value of
• 03:26 the item that is being measured.
• 03:28 Think of this as the difference between being able to choose only black or
• 03:32 white versus different shades of gray.
• 03:34 At a minimum, for variable data, we should have at least ten gradations available in
• 03:39 the normal range of the item being measured.
• 03:41 And personally, I would like to have 25 to 30 gradations.
• 03:45 In this illustration, you can see that the measurement scale on the left only
• 03:50 has three potential values for the distribution, 0, 1, or 2.
• 03:53 However, with the measurement scale on the right, we have much better discrimination
• 03:58 since there are now 14 potential values in the range of the distribution.
• 04:02 The last two categories are stability and linearity,
• 04:05 both of which look at factors that change the accuracy or bias of the system.
• 04:09 The first is stability, and it looks at whether the bias value stays the same
• 04:13 while using the measurement system or whether it drifts over time.
• 04:17 In our diagram, if we, again, let the gold bar represent the true value of the item,
• 04:22 the system starts with a negative bias in January.
• 04:25 It becomes more accurate, and by March, there is virtually no bias.
• 04:29 And then it begins to drift even higher, and in September,
• 04:33 the system inaccuracy is twice as high as it was low in January.
• 04:37 This could be due to wear and tear or
• 04:40 some aspects of the measurement system that's being used up over time.
• 04:44 Linearity is also a bias shift, but this is not a shift over time,
• 04:48 rather this is a shift over the dynamic range of the measurement.
• 04:52 That means that the bias is one value when measuring small items, and
• 04:56 another value when measuring large items.
• 04:59 If the bias stays the same over the full range of measurements,
• 05:02 then we say the linearity is good.
• 05:04 In this diagram, the bias is a small bias on the high side with small items,
• 05:09 and a larger bias on the low side with large items.
• 05:12 This is not good linearity.
• 05:15 Accuracy, discrimination, linearity, and stability are measurement system
• 05:18 attributes that are normally based upon the design and maintenance of the system.
• 05:22 The precision element of repeatability and
• 05:25 reproducibility is based both on the design and use of the system.
• 05:30 Understanding your measurement system errors allows you to determine if
• 05:34 the overall measurement error is small enough that you can trust your data.
• 05:38 If the error is too large,
• 05:40 you probably need to change to a different measurement system.

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