22 terms

Statistical Process Control

Control Chart
-periodically take a sample from a process
-calculate a statistic of interest from the sample
-plot the statistic on a control chart
-determine if the process is in control
-prevent quality problems
signs of a process in control
-no sample points outside limits
-most points near process average
-about equal number of points above and below centerline
-points appear randomly distributed
normal distribution
the empirical rule applies
we set control limits at +-3 sigmas
2.6/1000 observations will fall outside of control limits
common causes of variation
-ever-present factors that contribute to small, random shifts in output
-difficult to track to a source
-inherent in the process
-present when in control
-what we want to see in a chart
special causes of variation
-identifiable factors that induce variation beyond the inherent variation in the system
-can usually be tracked to a source
-process is not in control when present
-want to remove
-driving to school example, car accident
attribute data
product characteristic evaluated with a discrete choice
variable data
product characteristics that can be measured on a continuous scale
real numbers
initial construction of a control chart
-decide what to measure or count
-collect the sample data
-plot the samples on the control chart
-determine if the data is in control
control charts for attribute data
p-chart and c-chart
percentage of defects found in a sample
can only make a proportion is there is a finite number of defects
count the number of defects found in an item
p bar
total number of defects / total number of observations

use 3 sigma
c bar
total number of defects / k (number of samples)
control charts for variable data
x bar chart, r chart
R bar
sum of the ranges / k
x double bar
sum of the means / k
process capability
the natural variation of a process relative to the variation allowed by the design specifications

comparing what we are producing with what we need to produce
design specifications
sets of instructions that say the product will process fine if we follow these rules
3 sigma quality
design specifications are 3 sigma from the process average
6 sigma quality
design specifications are 6 sigma from the process average

6 sigma is the tolerance
then find 3 sigma by dividing the tolerance by 2
then find upper and lower bounds
process capability ratio
if less than 1, it implies that there is too much variation for 3 sigma quality
R bar