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FICCI CE
Process capability
Process
A combination of equipment, materials, people, methods and
environment that act together to produce an output. The
quality of the process is judged by the quality ( characteristic )
of the output.
FICCI CE
Process capability
Process capability
The inherent variability of a quality characteristic that the
process is capable of maintaining, when in a state of statistical
control under a given set of conditions.
Assuming normal distribution of the quality characteristic
Process Capability = +/- 3 SD = Total spread of 6 SD.
FICCI CE
Process capability
Process capability is judged by comparing process
performance with process requirements. Since meeting
specification limits is one of the most basic requirements of
a process capability study, it is extremely important to
accurately verify and define the specification limits.
FICCI CE
Need for process capability
For meeting customer requirements/ specifications.
To compare actual performance of equipment with
manufacturer’s claim.
To compare the performance of two processes.
To provide more realistic tolerances for component
dimensions.
Provide a basis for process control.
FICCI CE
Factors influencing process capability
1. Condition of machine/ equipment.
2. Type of operation and operational conditions.
3. Raw materials.
4. Skill of operators.
5. Measurement method / instruments.
6. Inspector’s skill.
FICCI CE
Estimation of process capability
• Visual from run chart.
• Frequency distribution and histogram.
• Control charts.
• Analysis of variances.
• Probability papers.
Note : Reduction of variability can be achieved through use of SPC
tools and Design of Experiments.
FICCI CE
The empirical rule
We have seen in the earlier chapter that almost all (to be
accurate 99.73%) the process output from a normally
distributed process lies between (process mean - 3 SD)
and (process mean+ 3 SD).
The total spread of the process can thus be described as 6 SD
FICCI CE
99.73% population between process mean +/- 3 SD
LSL USL
- 3 SD + 3 SD
2 3 4 5 6 7 8 9 12 10 16 15 14 13 11 1
FICCI CE
Process capability indices : The Cp index
A major reason for quantifying process capability is to
compute the ability of a process to hold product tolerances.
A measure of this relationship is process capability ratio or
Cp. Process capability is also known as potential capability.
The Cp index is given by:-
Cp = Tolerance
6 SD
Where Tolerance = USL - LSL
SD = Standard Deviation
FICCI CE
Process capability indices : The Cp index
Interpretations of Cp
Cp > 1 : The process is quite capable
Cp = 1 : The process is just capable
Cp < 1 : The process is incapable
The recommended value of Cp is 1.33 ( minimum)
In order to achieve Six Sigma quality in the organization, we
must reduce the variation in the process so as to achieve the
value of Cp=2.
FICCI CE
Calculating defective PPM at various levels of sigma.
Refer normal distribution table for finding defective parts per
million ( PPM ) for corresponding z values.
Quality level Cp z Defective PPM
2 Sigma 0.67 2 22750
3 Sigma 1.00 3 1350
4 Sigma 1.33 4 32
5 Sigma 1.67 5 0.3
6 Sigma 2.00 6 0.001
FICCI CE
Impact of process capability
For individual parts, the ideal design is Cp = 2; in other words,
the design specification is twice as “wide” as the true capability
of the process. This is where the phrase “Six Sigma Quality”
originated. Since the process capability is +/- 3SD, a design
specification twice as wide would be +/- 6 SD.
FICCI CE
Impact of process capability
However, it is learnt from the industry experience across the
world, that the processes rarely stay centered on their targeted
nominals, shifts of 1.5 SD to either side of the mean are
common, even in well controlled processes.
Therefore in practice, an ultimate z-value of 4.5 is considered
Six Sigma Quality. Consulting the z-table, we find that the
probability of producing non conformities associated with a z-
value of 4.5 is 0.0000034. If this value is obtained, then only
3.4 out of every million parts manufactured will be defective.
FICCI CE
Calculating defective PPM with permissible shift of 1.5 SD
at various levels of sigma. ( practical situation )
Refer normal distribution table for finding defective PPM for
corresponding z values.
Quality level Cp z Defective PPM
2 Sigma 0.17 0.5 308538
3 Sigma 0.50 1.5 66807
4 Sigma 0.83 2.5 6210
5 Sigma 1.17 3.5 233
6 Sigma 1.50 4.5 3.4
FICCI CE
Drawbacks of Cp
Cp however is not a very reliable measure as it does not tell us
all.
Consider the following four processes producing the same
output X with specification 20+/- 4. Each of these processes
have the Standard deviation of 1.
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LSL USL
X=20
SD=1
Cp=1.33
Process 1
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LSL USL
X=22
SD=1
Cp=1.33
Process 2
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LSL USL
X=15
SD=1
Cp=1.33
Process 3
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LSL USL
X=25
SD=1
Cp=1.33
Process 4
FICCI CE
Calculation of Cpk index
Cpk = Min [ USL - x , x - LSL ]
3SD 3SD
Cpk is a measure of process performance capability
The process performance index Cpk is given by:-
Example :
Specification : 20 +/- 4, SD = 1
Cp = Tolerance/6SD = 8/6 = 1.33
FICCI CE
x = 20, Cpk = Cp = 1.33
x = 22, Cpk = 0.67
x = 15, Cpk = -0.33
x = 25, Cpk = -0.33
Example :
Specification : 20 +/- 4, SD = 1
Cp = Tol/6 SD = 8/6 = 1.33
Calculation of Cpk index - Example
FICCI CE
In the previous slide we observe that, although the Cp
value = 1.33 in all the four cases, but because of the shift
in the process setting level we are getting Cpk values as
0.67 in 2nd case and hence the non conformities. Similar
observations are noticed in 3rd and 4th case where we get
the Cpk as -0.33.
Calculation of Cpk index
FICCI CE
The Cpk index
Thus Cpk = Cp means the process is centered.
Cpk < 1 means non- conformances are being produced.
Cpk < 0 indicates that the process has been set beyond either of
the two specification limits.
Note : Cpk is always less than or equal to Cp.
FICCI CE
Therefore, the first step is to bring Cpk=Cp by proper
centering of the process. The second step should be to
improve the Cp value by decreasing the variation.
Cp and Cpk indices
FICCI CE
One-sided Tolerances - The Cp and Cpk indexes are used
for characteristics with two-sided tolerances - that is,
processes with both upper and lower specification limits.
Since many characteristics have only one-sided
specifications, it is also convenient to have one-sided
capability indexes.
Process capability indexes for one sided tolerances
FICCI CE
For processes that have only a Lower specification limit, LSL,
the lower capability index Cpl is defined by:-
Correspondingly, when only an Upper specification exists,
we define an upper capability index by:-
Process capability indexes for one sided tolerances
Cpl = x - LSL
3 SD
Cpu = USL - x
3 SD