5.2.2. Check standard for assessing two levels of variability
Check standard procedure. Measurements on a single check standard are recommended for studying the effect of sources of variability that manifest themselves over time. Data collection and analysis are straightforward, and there is no reason to estimate interaction terms when dealing with time-dependent errors. The measurements are made at two levels which should be sufficient for characterizing most measurement systems. Three levels (sec. 5.2.4.) are recommended for measurement systems where sources of error are not well understood and have not previously been studied. The following levels are based on the characteristics of many measurement systems and should be adapted to a specific measurement situation as need be.

Level-1 measurements taken over a short term to estimate gauge precision

Level-2 measurements taken over days to estimate longer-term variability

A schedule for making check standard measurements over time (once a day, twice a week, or whatever is appropriate for sampling all conditions of measurement) should be set up and adhered to. The check standard measurements should be structured in the same way as values reported on the test items. For example, if the reported values are averages of two repetitions made within 5 minutes of each other, the check standard values should be averages of the two measurements made in the same manner. One exception to this rule is that there should be at least J = 2 repetitions per day, etc. Without this redundancy, there is no way to check on the short-term precision of the measurement system.

Model. The statistical model that explains the sources of error being studied is

where the subscripted terms in the model represent random errors in the measurement process that fluctuate with days and short-term time intervals. The purpose of the experiment is to estimate standard deviations, denoted by s2 and s1 respectively, which quantify these sources of variability.

Time intervals. The two levels discussed in this section are based on the characteristics of many measurement systems and can be adapted to a specific measurement situation as need be. A typical design is shown below where there are J = 4 repetitions per day.

  • Level-1 J (J > 1) short-term repetitions to capture gauge precision
  • Level-2 K (K > 1) days (of other appropriate time increment)
Data collection. It is important that the design be truly nested as shown in the diagram above so that repetitions are nested within days. It is sufficient to record the average and standard deviation for each group of J repetitions along with the following information:
  1. Month
  2. Day
  3. Year
  4. Operator identification
  5. Check standard identification
  6. Gauge identification
  7. Average of J repetitions
  8. Repeatability standard deviation from J repetitions
  9. Degrees of freedom
  10. Environmental readings (if pertinent)

Measurements on the test items are designated:

where the first index identifies day and the second index identifies the repetition number.

Calculation of standard deviations A repeatability standard deviation is computed for the each day as follows:

where the mean for the kth day is


The level-1 standard deviation for gauge precision is computed by pooling these standard deviations over the k days so that there are v = K(J - 1) degrees of freedom in the estimate

.
The level-2 standard deviation is computed with v = K -1 degrees of freedom as:

where


Component for days. The standard deviation that explains day-to-day variability is computed from

if the difference under the radical is positive. If the difference is negative, the standard deviation is assumed to be negligible.

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