|
A process that is capable is capable of producing within specification.
Very little of the product will be non-conforming due to being
out of specification. Suppose the specifications call for glue
to be spread at the rate of 27 grams per square meter, plus or
minus 2 grams. The specification limits are 25 and 29 grams. A
process that cannot produce consistently within this range is
not capable. The cause may be any of the usual suspects-- the
machinery, the methods, the material, or the measurements.
Suppose it is known from extensive sampling that a glue application
process is
- in statistical control (Sample means are within control limits,
and without pattern.)
- individual measurements are normally distributed
- the specification limits are 27 plus or minus 2 grams (25 to 29
grams)
- The mean amount of glue applied is 27.8 grams
- the standard deviation (of the individuals) is 1.3 grams.
The normal curve below represents the glue weight distribution.
Glue weights have been placed on the horizontal axis. As usual,
percent of occurrences are represented by area under the curve.
|
|
|
|
In Excel use the normdist function to find the area under the curve to the left of a given value. For example, =NORMDIST( 29, 27.8, 1.3, 1 ) gives 0.82. In this case the result is 82% of values are to the left of (under) 29.0 grams. We are interested in the part over 29.0 grams, which is 18%. For the other tail, =NORMDIST( 25, 27.8, 1.3, 1) yields 2 % is the percentage under 25.0 grams. Thus 18% + 2% or 20% of production is out of specification.
The arguments for NORMDIST are =NORMDIST(x, mean, std.dev., cumulative). The last argument, cumulative, should be set to "true" by entering a 1. |
|
|
