Time Series Controls

Control Limits

This page discusses the calculations of the control limits. The control limit calculations take place at both the series level and the limit range (multiple/split limit) level. However, the series level calculations are actually the first limit range calculations. The time series controls of the .Net Analytics package include the following:

Individuals (IndChart)
Moving Range (MovRngChart)
Moving Average (MovAvgChart)
Xbar (XbarChart)
Range (RangeChart)
Standard Deviation (StdDevChart)
RMS Deviation (RMSDevChart)

The series classes of the respective charts are:

The control limits include the following properties:

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

Control Limit Formulas

Individuals, Moving Range, and Moving Average

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

Moving average calculations (mA is the moving average)

UCL_mA = X + 1.88 * mA
CL_mA = X
LCL_mA = X - 1.88 * mA

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

Xbar and RMS Deviation

Xbar calculations (X is the grand average and s_n is the average RMS deviation)

UCL_X = X + A₁ * s_n
CL_X = X
LCL_X = X - A₁ * s_n

RMS deviation calculations

UCL_{s_n} = B₄ * s_n
CL_{s_n} = s_n
LCL_{s_n} = B₃ * s_n

Retrieve Control Limit Values

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

[Visual Basic]

' Retrieve the control limits of the series
Dim fUCL As Double = 
                  isSeries.UCL

                  Dim fCL As Double = isSeries.CL

                  Dim fLCL As Double = isSeries.LCL

                  

                  ' Retrieve the control limits of the second limit range

                  fUCL = isSeries.LimitRange(1).UCL

                  fCL = isSeries.LimitRange(1).CL

                  fLCL = isSeries.LimitRange(1).LCL

[Visual C#]

// Retrieve the control limits of the series
double fUCL = 
                  isSeries.UCL;

                  double fCL = isSeries.CL;

                  double fLCL = isSeries.LCL;

                  

                  // Retrieve the control limits of the second limit range

                  fUCL = isSeries.LimitRange[1].UCL;

                  fCL = isSeries.LimitRange[1].CL;

                  fLCL = isSeries.LimitRange[1].LCL;