Stability, Linearity, Discrimination

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About this lesson

These three attributes of a measurement system are inherent in the design and management of the system. When not managed well they will prevent effective measurements. Each of these is discussed and principles for managing them are introduced.

Quick reference

Stability, Linearity, Discrimination

Stability, linearity, and discrimination are categories of measurement system error that are based on the design and maintenance of the measurement system. These errors can be reduced and eliminated by the selection of the measurement system to be used.

When to use

Stability, linearity, and discrimination are aspects of the measurement system that should be addressed when designing or selecting a measurement system for use. Once the system is selected, linearity and discrimination cannot be changed and as long as the measurement system is managed well, stability should not be an issue.

Instructions

Stability, linearity, and discrimination are normally aspects of the measurement system that are outside the control of the operator. These are inherent in the design of the selected system and must be monitored or controlled by the management of the measurement process.

  • Stability is the most volatile of these three. Stability of a measurement system is the extent to which the measurement distribution stays the same over time. A stable system does not drift or deteriorate. The stability of the system is significantly impacted by how the system is managed. Many measurement systems use regularly scheduled calibration and encourage the use of golden standards by operators to identify stability problems when they are small and can be easily corrected. There are three categories for causes in of instability in measurement systems:
     
    • Standard Operating Procedures – Well designed procedures that are followed by all operators will minimize stability errors due to the operators modifying the measurement process over time. Operators should be trained and periodic certification or audits can be used to ensure continued compliance.
    • Noise factors – these are aspects of measurement system use that cause distraction or confusion. These factors are often related to the environment in which the measurement system is used. If the environment changes over time, these factors may take on a larger or smaller role in the normal distribution of the measurement system error. The selection of the measurement system can minimize these factors by using systems that have Poka Yoke features to reduce variation.
    • Controllable factors – these are factors that the operators or manager can monitor and control. An effective procedure and trained operators will monitor these and take the appropriate action to ensure that the target settings or controls are maintained. This may mean adjusting settings for changes in environmental factors, monitoring the system for wear and tear, and the use of golden standards to detect when the system performance is starting to change.
       
  • Linearity is also known as bias shift.  This is an attribute of the design of the measurement system and normally cannot be changed. This refers to the condition that the measurement system bias begins to change once it is near the edge of its ideal operating range. As the system attempts to measure very small or very large items, the performance degrades and the bias shifts. This is common in electronic systems with sensors or systems that rely on springs. In both cases there is an ideal range of performance. If the system is not linear throughout the normal range of measurement, a different system should be selected.
  • Discrimination refers to the resolution of the system metric. A system with poor discrimination is not able to measure small differences in the items being measured. Discrimination is affected by the desired precision in the measurement. The measurement system should always be able to go one decimal further in resolution than the required specification value. Ideally a measurement system has a minimum of 10 gradations in the normal range of item variation – and more is definitely better. Poor discrimination leads to a uniform distribution which cannot be used with many of the statistical analyses done in Lean Six Sigma projects. If the measurement system does not have adequate discrimination, a different system must be selected.

Hints & tips

  • Determine the measurement needs in terms of the range or measurement and the fidelity or precision of the measurement. Then select or design a system that has adequate discrimination and is not subject to linearity problems.
  • Many organizations have a metrology department (or at least an individual who is responsible for metrology) that manages and monitors measurement system stability. This department establishes a calibration schedule for each measurement system and creates and maintains any golden standard that operators are to use as part of their procedures.
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  • 00:04 Hi, I'm Ray Sheen.
  • 00:06 Let's now consider the other three components of measurement system error,
  • 00:10 stability, linearity and discrimination.
  • 00:13 Again, we'll describe each of these and
  • 00:15 understand its impact on the measurement system error.
  • 00:19 I'll start with stability.
  • 00:21 Stability is the extent to which the measurement distribution
  • 00:24 stays the same over time.
  • 00:26 A stable system continues to have the same levels of accuracy and
  • 00:29 precision as the weeks and months go by.
  • 00:33 An unstable system will have changes to either accuracy, precision or both.
  • 00:38 And by accuracy, we mean a shift in the bias or the mean of the distribution.
  • 00:42 And precision, we mean a change in the spread or
  • 00:45 standard deviation of the distribution.
  • 00:48 One way to measure stability is to constantly recalibrate
  • 00:51 the measurement system.
  • 00:53 But if you have to send your system out for calibration, this can be expensive and
  • 00:56 time consuming.
  • 00:57 A far more common technique is to use Golden Standards.
  • 01:01 This is normally an item that is measured whose measurement characteristic is known
  • 01:05 precisely.
  • 01:06 This item is kept near the workplace for the measurement operators to use.
  • 01:10 When using the Golden Standard, the measurement system measures
  • 01:13 this known item and the measuring results are compared to the known value.
  • 01:17 If the measuring results start to drift,
  • 01:19 it's an indication of a stability problem.
  • 01:22 At that point, either the system is recalibrated or the characteristics of
  • 01:26 the measurement system that caused the shift is repaired or replaced.
  • 01:31 A lack of stability means the measurement system does not provide a standard
  • 01:34 distribution over time, therefore, we cannot trust the measurement.
  • 01:39 In my experience, many, in fact probably most,
  • 01:42 measurement systems will eventually have a stability problem.
  • 01:45 Let's look at some of the reasons.
  • 01:47 One category of causes is operating procedures.
  • 01:51 If the procedures are vague or not used consistently, there's likely to be a drift
  • 01:55 as one operator falls into habits that are easy for them,
  • 01:58 but not conducive to good measurements.
  • 02:01 Some questions to consider in this area are,
  • 02:03 do procedures exist, are they current, do operators follow them?
  • 02:08 The next one is important when dealing with turnover among measurement system
  • 02:11 operators.
  • 02:12 Do they understand them?
  • 02:14 Two ways to minimize the effective procedures on stability
  • 02:17 is to do operator certification with periodic recertification and
  • 02:21 to conduct audits of that process.
  • 02:24 Next are what I call the noise factors,
  • 02:26 now this doesn't mean that noise is in a very loud sound or
  • 02:29 noise as in fluctuations of the power supplied to the measurements system.
  • 02:33 What I mean are factors that confuse or
  • 02:35 distract an operator while they are doing the measurement.
  • 02:39 Do these factors exist, are they monitored, and
  • 02:42 do the operators know to be aware of these factors and compensate for them?
  • 02:46 Often, these factors can change over time,
  • 02:49 and this leads to a stability concern in the system.
  • 02:52 Questions to ask when diagnosing or selecting the measurement system is
  • 02:55 whether the system is robust enough that these factors don't matter by using
  • 03:00 a poka-yoke or other mistake proofing principles.
  • 03:03 Or if they can't be avoided or controlled, can they at least be acknowledged and
  • 03:06 if appropriate compensated for in the measurement?
  • 03:10 The third category is controllable factors, this is usually either
  • 03:14 settings in the measurement system or items of wear and tear on the system.
  • 03:19 In either case,
  • 03:20 the operators can minimize their impact if they are paying attention to them.
  • 03:23 That is why the questions here are along the lines of, are they monitored?
  • 03:27 Are they verified?
  • 03:28 Are the readings or settings recorded?
  • 03:30 And in those cases, is there an optimum target value and a tolerance for
  • 03:34 allowed variation set?
  • 03:36 If these factors are monitored or recorded, the operator or
  • 03:39 measurement system manager can take appropriate action
  • 03:42 when they see that these items are inconsistent or drifting.
  • 03:46 The next cause of error is linearity, which is often called bias shift.
  • 03:51 Well what that means is that the bias in the system, in other words its accuracy,
  • 03:55 changes as the measurements go up and down the measurement range.
  • 03:59 If the bias does not change, the system is said to have good linearity.
  • 04:03 If the bias shifts, it is said to have poor linearity.
  • 04:07 In the illustration shown on the slide, the bias is smaller to the left for
  • 04:11 items measured in the low end of the measurement system range.
  • 04:15 But the bias is larger, and to the right, in the high end of the range.
  • 04:19 The measurement system has poor linearity.
  • 04:23 Linearity problems normally cannot be solved with calibration
  • 04:25 system maintenance or operator training.
  • 04:28 The linearity characteristics of a measurement system are inherent
  • 04:31 in the design of the system.
  • 04:33 Every measurement system has an optimal range for
  • 04:35 measurement in which there's virtually no linearity problems.
  • 04:39 If using a measurement system outside of its optimal range or
  • 04:42 even when approaching an extreme, check for a linearity problems.
  • 04:46 If you have some,
  • 04:47 you must pick a different system whose range fits your measurements.
  • 04:52 Our last category of measurement error is discrimination.
  • 04:55 This category is a little different from the others.
  • 04:58 It doesn't create wrong information,
  • 05:00 rather it creates information that is not meaningful.
  • 05:03 Discrimination is the resolution of the measurement system.
  • 05:07 That means the degree to which it can detect small changes in
  • 05:10 the measured value.
  • 05:11 As a rule, you should never use a system that has less than 10 gradations
  • 05:15 in the typical range of the items being measured, and more is definitely better.
  • 05:20 You can see on the diagram that the top measurement has poor discrimination.
  • 05:25 The only possible choices for values are 0, 1, and 2.
  • 05:28 The lower diagram has much better discrimination.
  • 05:32 There are 18 possible values.
  • 05:35 Let's look at another illustration.
  • 05:37 The top graph on the right of the slide is the actual distribution of the items
  • 05:41 being measured.
  • 05:42 If there is poor discrimination, the measurement system would
  • 05:45 likely measure those items and give us this uniform distribution that
  • 05:49 means approximately the same values for all items.
  • 05:52 In other words, there's about the same number on the low side as on the high
  • 05:55 side, you can see that in the middle diagram.
  • 05:58 Well, many of our statistical analysis tools require a normal distribution, so
  • 06:02 the uniform distribution is a problem for us.
  • 06:05 By increasing the discrimination, we can measure the same items and
  • 06:09 get a normal distribution as you can see in the diagram at the bottom.
  • 06:13 So those are the other three categories of measurement error,
  • 06:17 stability, linearity, and discrimination.
  • 06:20 Now as you can see, these errors can be managed through the selection and
  • 06:24 maintenance of the measurement system.

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