Process output monitoring: What does Process capability index > 1.33 mean

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 140-145 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 :-

  1. The data should be a variable data ( refer to my blog dated 5 Oct 2017
  2. The data must be normally distributed
  3. The data must derive from a stable process which is free from special cause.  (refer to my blog  dated on 8 Sep 2017

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.

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.

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