Attributes Controls

Control Limits

This page discusses the calculations of the control limits. The control limit calculations take place at the sample level. The attributes controls of the .Net Analytics package include the following:

c-Chart (cChart)
np-Chart (npChart)
p-Chart (pChart)
u-Chart (uChart)

The series classes of the respective charts are:

and the sample classes are:

The control limits include the following properties:

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

Control Limit Formulas

c-Chart

c =

total count of nonconformities in baseline samples

number of baseline samples

UCL_c = c + 3 * √(c)
CL_c = c
LCL_c = c - 3 * √(c)

np-Chart

p =

total number of nonconforming in baseline samples

total number items examined in baseline samples

UCL_np = np + 3 * √np * (1 - p)
CL_np = np
LCL_np = np - 3 * √np * (1 - p)

p-Chart

p =

total number of nonconforming in baseline samples

total number items examined in baseline samples

UCL_p = p + 3 * √(p * (1 - p)) / n_i
CL_p = p
LCL_p = p - 3 * √(p * (1 - p)) / n_i

u-Chart

a_i is the area of opportunity and u =

total count for the baseline samples

total area of opportunity in baseline samples

UCL_u = u + 3 * √(u / a_i)
CL_u = u
LCL_u = u - 3 * √(u / a_i)

Retrieve Control Limit Values

Below, we will retrieve the control limit calculations from a c-Chart sample (named csSample in the examples below). The control limit calculations for the attributes charts are kept at the sample level. The process is similar for the other charts:

[Visual Basic]

' Retrieve the control limits of the sample
Dim fUCL As Double = 
                  csSample.UCL

                  Dim fCL As Double = csSample.CL

                  Dim fLCL As Double = csSample.LCL

[Visual C#]

// Retrieve the control limits of the sample
double fUCL = 
                  csSample.UCL;

                  double fCL = csSample.CL;

                  double fLCL = csSample.LCL;