By now my reader should have a better understanding that
what is variations, process, its input and output. In order to achieve consistent good
quality product from a manufacturing process, it is imperative to manage and
control all process inputs – man, machine, method, material, measure and
environment. The next question is, after
we control all process inputs, how do we know if we have produce consistently
good quality part per customer specification or requirement. The only way to know is to measure the output
produced and collect measurement data for analysis.
One of the widely use measurement data analysis method to
determine product quality is process capability. In this method process output are measure for
its quality characteristic such as dimension and compare the distribution of data
with a predetermine specification. Specification
is either given by customer or derived base on customer requirement.
A simple example would be the molding process of hand
phone plastic cover. The quality metrics
in this case would be dimension such as length or width of the cover to ensure
it can fit properly to the LCD assembly to become a complete hand phone
assembly. If the length specification provided
by the design team is 140 145 mm with 142.5mm is the target, the molding
process need to produce part which is between 140 to 145 mm. Since it is not practical to measure every
part length, therefore a sample which must represent the population need to be measured
to check if the length dimension between 140145 mm. The recommended sample size is at least
30. Once data is collected then a histogram
chart is plotted base on the data, which usually will form into a bell shape
curve known as normal distribution per figure 1. Assume that the current process is able to
produce most part center to the target value of 142.5 mm, therefore will be peak around 142.5 mm. The peak where most of the
data are center is known as central tendency in descriptive statistic. Then we will compare the 6 sigma process
spread with the specification tolerance.
Figure 1 Normal distribution of measurement data length 
If the process spread is less than specification
tolerance in per figure 2 then there are higher chances hwere most of the parts
will meet specification. The comparison
of specification tolerance with process spread is known process capability index,
Ppk or Cpk. If the process spread is
more than product specification as in figure 3, then anything outside the
product specification is consider as reject.
The reject rate will be higher in this case compare to figure 2.
Figure 2. Process spread width is smaller than specification
width,
almost all parts are in specs

Figure 3. Process
spread width is bigger than specification,
there
are parts that are out of spec

The process capability can be used to estimate the
manufacturing process reject rate. The
universal accepted process capability index ratio between specification
tolerance and process spread is 1.33. Below are more commonly used process
capability and their corresponding potential
reject rate for the measured quality metrics.
Commercial statistic software will be able to compute the estimate total
reject rate once the process capability is generated.
In order for the process capability index number to give
a meaningful estimate of the population reject rate there are 3 conditions
which must be full fill :
 The data should be a variable data ( refer to my blog dated 5 Oct 2017 http://www.360qualitymanagement.com/2017/10/essentialdatacollectionforquality.html)
 The data must be normally distributed
 The data must derive from a stable process which is free from special cause. (refer to my blog dated on 8 Sep 2017 http://www.360qualitymanagement.com/2017/09/understandingprocessvariationsin.html)
In most cases it is impossible to measure every single
production part which gives an accurate reject rate, therefore we need to use
the ratio of specification tolerance to actual process spread, Ppk to estimate
the total production output reject. There
are many organizations set the goal of process capability, Ppk goal of 1.33 for
product output parameter, however a lot of them do not know the actual meaning
of Ppk 1.33 and much less able to full fill the 3 conditions above to give
meaningful estimation of reject rate for a process.
I have recorded a full course on process capability analysis and share with my student for free @ Udemy, You can click on the below image or this link to enroll in the course
This is for limited time only.
Note:
Please note that this article does NOT give the technical
or calculation of process capability.
There are many sources which is able to furnish this information. The intent of this article reiterates the
translation of process capability number into a practical conclusion which
management understands.