Standard Deviation Charts for Blanks, Standards and Spikes

Standard deviation charts are plots of standard deviations of values of blank, standard or spike QC samples within a group of observations over time, used to evaluate the stability of the variability within the analytical process, that is, how the spread of results changes over time. For example, if a tight spread is followed by a much wider spread, then some process has changed in the testing. If there are many individual points, a CuSum chart shows the bias or errors accumulated, but the standard deviation chart show the change of 'noise' or 'spread' over time. An X chart with a group size of 4 potentially shows this spread, but the standard deviation chart shows it as a numeric representation of the spread or reproducibility of the blank, standard or spike.

Input Variables

  • Chart Type—SDV—Standard Deviation Chart
  • Group Size

    The group size is used to determine group standard deviations, and the mean and standard deviation of those group standard deviations, as follows.

    For a number of observations, the Group Size is applied to group the observations:

    Number Of Groups = Number of observations / Group Size

    For example, if there are 100 observations and a group size of 4, then 25 groups are formed.

    For each group of observations, the group standard deviation is determined:

    1stGroupSD = square root (((1stObsInGroup—meanOf1stGroupObs) + (2ndObsInGroup—meanOf1stGroupObs) + ... + (nthObsInGroup—meanOf1stGroupObs))^2 / (Group Size—1))

    2ndGroupSD = square root (((1stObsInGroup—meanOf2ndGroupObs) + (2ndObsInGroup—meanOf2ndGroupObs) + ... + (nthObsInGroup—meanOf2ndGroupObs))^2 / (Group Size—1))

    ...

    nthGroupSD = square root (((1stObsInGroup—meanOfNthGroupObs) + (2ndObsInGroup—meanOfNthGroupObs) + ... + (nthObsInGroup—meanOfNthGroupObs))^2 / (Group Size—1))

    The mean of those group standard deviations is determined:

    meanOfGroupSDs = (1stGroupSD + 2ndGroupSD + ... + 2ndGroupSD ) / Number of Groups

    The standard deviation of those group standard deviations is determined:

    SDOfGroupSDs = square root (((1stGroupSD—meanGroupSDs) + (2ndGroupSD—meanGroupSDs) + ... + (nthGroupSD—meanGroupSDs))^2 / (Number of Groups—1))

  • Chart Title—'Standard Deviation Chart ' + (<standard's Name > + ' ' + <scheme's Name > + ' ' + <scheme version's Version Number> + ' ' + <scheme version analyte's Name > + ' ' + <unit's Name for the related specification scheme version analyte's Unit Code>)

    Note: A known defect is that even when a different chart type is selected, the limits are not being cleared until the limit source drop-down is clicked.

  • The data points are the standard deviations calculated for each group, based on the QC history record's Numeric Final Value and the given Group Size.
  • Limit Source, where selected as Sample Mean, the target value and limits are calculated as follows:

    Target Value = meanOfGroupSDs

    Upper Failure Limit = 3.09 x SDOfGroupSDs

    Upper Warning Limit = 1.96 x SDOfGroupSDs

  • Limit Source, where selected as Specified, the Target Value, Upper Failure Limit and Upper Warning Limit are specified by the user.

Axes

The X-axis displays the range from 1 to the number of observation groups, sorted by the QC history reading's Analysed Date. Since grouping is in place, the sort is applied on the first analysed date within the group.

The X-axis label includes:

  • 'First Date: ' + the date of the first analysis
  • 'Last Date: ' + the date of the last analysis
  • 'Target: ' + <set from the Target Value input variable>
  • 'Lower Limit: ' + <set from the Upper Warning Limit input variable>
  • 'Upper Limit: ' + <set from the Upper Failure Limit input variable>
  • 'Mean: ' + <mean of all observations returned from the search>
  • 'StdDev: ' + <standard deviation of all observations returned from the search>
  • 'Observations: ' + <number of observation groups>
  • 'Group Size: ' + <set from the Group Size input variable>.

The Y-axis displays the range from 0 to the standard deviation of the group.

The Y-axis label includes:

  • 'Group Average StdDev' + <unit's Name for the related specification scheme version analyte's Unit Code>

Data Points

A point on the chart is calculated as:

Standard deviation of the group = square root of (sum of ((observations's value—mean value of the group) ^2 / (number of observations—1))

Target, Warning and Failure Lines

If no upper warning or failure limits are defined, the graph shows no warning and failure lines, and is shaded entirely green.

If an upper warning limit is defined, but an upper failure limit is not defined, the graph shows a warning line but no failure line, and is shaded green below the warning line and yellow above the warning line.

If an upper failure limit is defined, but an upper warning limit is not defined, the graph shows a failure line but no warning line, and is shaded green below the failure line and red above the failure line.

If upper warning and failure limits are defined, the graph shows warning and failure lines, and is shaded green below the warning line, yellow above the warning line and below the failure line, and red above the failure line.

The target line is given by the Target Value input variable.

The upper and lower warning lines are given by the Upper Warning Limit and Lower Warning Limit input variables, respectively.

Data Point Details

When the mouse pointer is hovered over a point on a standard deviation chart with a group size greater than 1, the following details are displayed:

  • Observation group number
  • Standard deviation of the group
  • Standard name (or standard code if standard name is not defined)
  • Creation date of the first QC history record in the group.