STATISTICAL
PROCESS
CONTROL
PROCESS CAPABILITY
Process capability is the repeatability and
consistency of a manufacturing process relative to
the customer requirements in terms of specification
limits of a product parameter.
This measure is used to objectively measure the
degree to which your process is or is not meeting
the requirements.
The capability of a process is some measure of the
proportion of in-specification items the process
produces when it is in a state of statistical control.
Process Capability – process spread
Tolerance – difference between specifications
Three Scenarios for
Process Capability
and Tolerance
USL
UCL
USL - LSL 6 X0
LCL
LSL
1st SCENARIO
when the process capability is less
than the tolerance
USL
UCL
USL - LSL 6 X0
LCL
LSL
2nd SCENARIO
when the process capability is
equal to the tolerance
USL
UCL
USL - LSL
6 X0
LCL
LSL
3rd SCENARIO
when the process capability is
greater than the tolerance
Process Capability
cannot be determined until the Xbar and R
charts have achieved the optimal
improvement
Process capability = 6 0 when the process
is in statistical control
Finding Process Capability
Using RANGE
0 = R/d2
Using STANDARD DEVIATION
0 = s /c4
Capability Index
a value indicating how capable a process is of
producing product without many defects
Formed from the combination of process
capability and tolerance
Capability indices should be used to determine
whether the process, given its natural variation,
is capable of meeting established specifications.
It is also a measure of the manufacturability of
the product with the given processes.
Capability Index
Defined as
USL - LSL
Cp =
6 0
The larger the capability index, the better the
quality.
Does not measure process performance.
While Cp relates the spread of the process
relative to the specification width, it does not
address how well the process average, X, is
centered to the target value. Cp is often referred
to as process "potential".
Process Performance
Measurement
Min {(USL – X) or (X – LSL)}
Cpk =
3
Cpk measures not only the process variation with
respect to allowable specifications, it also
considers the location of the process average.
About Cp and Cpk
1. The Cp value does not change as the
process center changes.
2. Cp = Cpk when the process is centered.
3. Cpk is always equal to or less than Cp.
4.A Cpk value of 1.00 is a de facto standard.
It indicates that the process is producing
product that conforms to specifications.
About Cp and Cpk
5. A Cpk value less than 1.00 indicates that
the process is producing product that does
not conform to specifications.
6. A Cp value less than 1.00 indicates that
the process is not capable.
7. A Cpk value of zero indicates the average
is equal to one of the specification limits.
8.A negative Cpk value indicates that the
average is outside the specifications.
6
Process Centered
Cp = 1.33
CpK = 1.33
LSL X0 USL
Case I Cp = (USL-LSL)/ 6 = 8 /6 = 1.33
6
Process Off Center 1
Cp = 1.33
CpK = 1.00
LSL X0 USL
6
Process Centered
Cp = 1.00
CpK = 1.00
LSL X0 USL
Case II Cp = (USL-LSL)/ 6 = 6 /6 = 1.00
6
Process Off Center 1
Cp = 1.00
CpK = 0.67
LSL X0 USL
6
Process Centered
Cp = 0.67
CpK = 0.67
LSL X0 USL
Case III Cp = (USL-LSL)/ 6 = 4 /6 = 0.67
6
Process Off Center 1
Cp = 0.67
CpK = 0.33
LSL X0 USL
EXERCISES
1. An existing process is not meeting the
Rockwell-C specifications. Determine the
process capability based on the range
values for 25 subgroups of size 4. Data
are7,5,5,3,2,4,5,9,4,5,4,7,5,7,3,4,4,5,6,4,7,
7,5,5 and 7.
2. A new process is started, and the sum of
the sample standard deviations for 25
subgroups of 4 is 105. Determine the
process capability.
3. Assume that the specifications are 6.50
and 6.30 in the depth of the keyway
problem. Determine the capability index
before ( 0 =0.038) and after ( 0 =0.030)
improvement.
4. Determine the Cpk for the problem 3
(USL= 6.50, LSL=6.30, and =0.030)
when the average is 6.45. Find the Cpk
when average is 6.38.
