Quality and Reliability Methods - SAS

Chapter 5 Shewhart Control Charts 89
Shewhart Control Charts for Attributes
Control Limits on U-charts
The lower and upper control limits, LCL and UCL, are computed as follows:
LCL = max( u – k u ⁄ n i
, 0)
UCL =
u + k u⁄
n i
The limits vary with n i .
u is the expected number of nonconformities per unit produced by process
u i is the number of nonconformities per unit in the i th subgroup. In general, u i = c i /n i .
c i is the total number of nonconformities in the i th subgroup
n i is the number of inspection units in the i th subgroup
u is the average number of nonconformities per unit taken across subgroups. The quantity u
computed as a weighted average
n 1
u 1
+ … + n N
u N
c
u -------------------------------------------- 1
+ … + c N
= = -------------------------------
n 1
+ … + n N
n 1
+ … + n N
is
C-Charts
N is the number of subgroups
C-charts are similar to U-charts in that they monitor the number of nonconformities in an entire subgroup,
made up of one or more units. C-charts can also be used to monitor the average number of defects per
inspection unit.
Note: When you generate a C-chart, and select Capability, JMP launches the Poisson Fit in Distribution
and gives a Poisson-specific capability analysis.
Example: C-Charts
In this example, a clothing manufacturer ships shirts in boxes of ten. Prior to shipment, each shirt is
inspected for flaws. Since the manufacturer is interested in the average number of flaws per shirt, the
number of flaws found in each box is divided by ten and then recorded. To replicate this example, follow
these steps or submit the JSL below.
• Open the Shirts.jmp data in the Quality Control sample data folder.
• Choose the Analyze > Quality And Process > Control Chart > C command.
• Choose # Defects as the Process variable.
• Choose Box Size as the Sample Size.
• Choose Box as the Sample Label.