Operations and Supply Chain Management The Core

316 OPERATIONS AND SUPPLY CHAIN MANAGEMENT
a defect should be very, very low. Motorola made process capability and product design
famous by adopting Six Sigma limits. When a part is designed, certain dimensions are
specified to be within the upper and lower specification limits.
As a simple example, assume engineers are designing a bearing for a rotating shaft—
say an axle for the wheel of a car. There are many variables involved for both the bearing
and the axle—for example, the width of the bearing, the size of the rollers, the size of the
axle, the length of the axle, how it is supported, and so on. The designer specifies limits
for each of these variables to ensure that the parts will fit properly. Suppose that initially
a design is selected and the diameter of the bearing is set at 1.250 inches ± 0.005 inch.
This means that acceptable parts may have a diameter that varies between 1.245 and 1.255
inches (which are the lower and upper specification limits).
Next, consider the process in which the bearing will be made. Consider that many different
processes for making the bearing are available. Usually there are trade-offs that need
to be considered when designing a process for making a part. The process, for example,
might be fast but not consistent, or alternatively it might be slow but consistent. The consistency
of a process for making the bearing can be measured by the standard deviation of
the diameter measurement. A test can be run by making, say, 100 bearings and measuring
the diameter of each bearing in the sample.
After running the test, the average or mean diameter is found to be 1.250 inches. Another
way to say this is that the process is “centered” right in the middle of the upper and lower
specification limits. In reality, it may be difficult to have a perfectly centered process like
this example. Consider that the diameter values have a standard deviation or sigma equal
to 0.002 inch. What this means is that the process does not make each bearing exactly the
same size.
As is discussed later in this chapter, normally a process is monitored using control charts
such that if the process starts making bearings that are more than three standard deviations
(± 0.006 inch) above or below 1.250 inches, the process is stopped. This means that the
process will produce parts that vary between 1.244 (this is 1.250 − 3 × 0.002) and 1.256
(this is 1.250 + 3 × 0.002) inches. The 1.244 and 1.256 are referred to as the upper and
lower process limits. Be careful not to get the terminology confused here. The “process”
limits relate to how consistent the process is for making the bearing. The goal in managing
the process is to keep it within plus or minus three standard deviations of the process
mean. The “specification” limits are related to the design of the part. Recall that, from a
design view, acceptable parts have a diameter between 1.245 and 1.255 inches (which are
the lower and upper specification limits).
As can be seen, process limits are slightly greater than the specification limits given by
the designer. This is not good because the process will produce some parts that do not meet
specifications. Companies with Six Sigma processes insist that a process making a part be
capable of operating so that the design specification limits are six standard deviations away
from the process mean. For the bearing process, how small would the process standard
deviation need to be for it to be Six Sigma capable? Recall that the design specification
was 1.250 inches plus or minus 0.005 inch. Consider that the 0.005 inch must relate to the
variation in the process. Divide 0.005 inch by 6, which equals 0.00083, to determine the
process standard deviation for a Six Sigma process. So, for the process to be Six Sigma
capable, the mean diameter produced by the process would need to be exactly 1.250 inches
and the process standard deviation would need to be less than or equal to 0.00083 inch.
We can imagine that some of you are really confused at this point with the whole idea of
Six Sigma. Why doesn’t the company, for example, just check the diameter of each bearing
and throw out the ones with a diameter less than 1.245 or greater than 1.255? This could
certainly be done, and for many, many parts 100 percent testing is done. The problem is