Page 218 - The Handbook for Quality Management a Complete Guide to Operational Excellence

204 P r o c e s s C o n t r o l Q u a n t i f y i n g P r o c e s s Va r i a t i o n 205

Interpreting Capability Indexes
Perhaps the biggest drawback of using process capability indexes is that
they take the analysis a step away from the data. The danger is that the
analyst will lose sight of the purpose of the capability analysis, which is to
improve quali ty. To the extent that capability indexes help accomplish this
goal, they are worthwhile. To the extent that they distract from the goal,
they are harmful.
The quality engineer should continually refer to this principle when
interpreting capability indexes.
C Historically, this is one of the first capability indexes used. The
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“natural tolerance” of the process is computed as 6s. The index simply
makes a direct comparison of the process natural tolerance with the
engineering requirements. Assuming the process distribution is normal
and the process average is exactly centered between the engi neering
requirements, a C index of 1 would give a “capable process.” However,
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to allow a bit of room for process drift, the generally accept ed minimum
value for C is 1.33. In general, the larger C is, the better. The C index
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has two major shortcomings. First, it can’t be used unless there are both
upper and lower specifications. Second, it does not account for process
centering. If the process average is not exactly centered relative to the
engineering requirements, the C index will give misleading results. In
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recent years, the C index has largely been replaced by C (see on the
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next page).
C The C index is algebraically equivalent to the C index. The
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index simply makes a direct comparison of the process with the
engineering requirements. Assuming the process distribution is
normal and the process average is exactly centered between the
engineering require ments, a C index of 100 percent would give a
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“capable process.” However, to allow a bit of room for process drift,
the generally accepted maxi mum value for C is 75 percent. In gen-
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eral, the smaller C is, the better. The C index suffers from the same
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shortcomings as the C index.
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C The C index is generally used to evaluate machine capability
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stud ies, rather than full-blown process capability studies. Since varia-
tion will increase when normal sources of process variation are added
(e.g., tooling, fixtures, materials, etc.), C uses a four sigma spread
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rather than a three sigma spread.
Z The Z index measures the process location (central tendency) rela-
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tive to its standard deviation and the upper requirement. If the distribu-
tion is normal, the value of Z can be used to determine the percentage
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above the upper requirement by using the table in Appendix 2. In gen-
eral, the bigger Z is, the better. A value of at least +3 is required to
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