Time Series Controls

Control Limits

This page discusses the calculations of the control limits. The control limit calculations take place at the limit range level. The time series controls of the Silverlight Analytics package include the following:

IndControl (IndControl)
MovRngControl (MovRngControl)
XbarControl (XbarControl)
RangeControl (RangeControl)
StdDevControl (StdDevControl)

The series classes of the respective controls are:

The control limits include the following properties:

UCL - upper control limit
CL - centerline
LCL - lower control limit

Control Limit Formulas

Individuals and Moving Range

Individuals calculations (X is the average and mR is the moving range)

UCL_X = X + 2.660 * mR
CL_X = X
LCL_X = X - 2.660 * mR

Moving range calculations

UCL_mR = 3.268 * mR
CL_mR = mR
LCL_mR = 0

Xbar and Range

Xbar calculations (X is the grand average and R is the average range)

UCL_X = X + A₂ * R
CL_X = X
LCL_X = X - A₂ * R

Range calculations

UCL_R = D₄ * R
CL_R = R
LCL_R = D₃ * R

Xbar and Standard Deviation

Xbar calculations (X is the grand average and s is the average standard deviation)

UCL_X = X + A₃ * s
CL_X = X
LCL_X = X - A₃ * s

Standard deviation calculations

UCL_s = B₄ * s
CL_s = s
LCL_s = B₃ * s

Retrieve Control Limit Values

Below, we will retrieve the control limit calculations from an Individuals series (named isSeries in the examples below). The process is similar for the other charts:

[Visual Basic]

' Retrieve the control limits of the series
Dim fUCL As Double = 
                  isSeries.LimitRanges(0).UCL

                  Dim fCL As Double = isSeries.LimitRanges(0).CL

                  Dim fLCL As Double = isSeries.LimitRanges(0).LCL

[Visual C#]

// Retrieve the control limits of the series
double fUCL = 
                  isSeries.LimitRanges[0].UCL;

                  double fCL = isSeries.LimitRanges[0].CL;

                  double fLCL = isSeries.LimitRanges[0].LCL;