I am presently doing masters in industrial eng. and presently got a doubt with my project. I am taking into consideration of two machines one of which is a traditional lathe and other being a cnc m/c. I would like to develop a sampling plan. Is there a relation between sampling size and machine capability and also does machine capability influence the sampling size. if so how. . also based on defects how is machine capability calculated???
First of all, it is important to determine your distribution. In precision machining, the variations experienced should all be controlled to a statistically insignificant level
except for tool wear. That means you GR&R is less than 10% of your control limits (yes, control limits!), etc. If this is the case, then you are truly doing "precision machining" and your distribution is a uniform or rectangular distribution. To determine the long term sampling plan, you should perform a capability study of approximately 100 pcs
in a row, in order!. If you are doing an OD, the OD should increase over time as the tool wears. You should set up control limits of 75% of the specification. As the dimension reaches the control limit, adjust down to the lower control limit and allow to resume increasing to the upper control limit. With a uniform distribution, the "mean" has no practical value for evaluating the process. To determine the sampling frequency, you need to divide the time or number of parts required to go from the lower control limit to the upper control limit, and divide by 5. As far as sampling number, you only need to sample 1 part per increment. Why? Because in precision machining there is so little difference between consecutive parts that it is a waste of time. You should spend more time measuring that one part, getting the highest and lowest diameter and plotting a X hi/lo-R chart. Then, you are actually controlling the GD&T parameters of a circular characteristics.
Xbar-R chart is the worst possible chart for this distribution - it simply encourages overcontrol.
Also for precision machining, (uniform distribution) the capability is calculated as (USL-LSL)/(UCL-LCL) Note that it is a constant, because (UCL-LCL)=.75(USL-LSL) from using control limits set at 75% of the specification.
For more details on this see thread
http://elsmar.com/Forums/showthread.php?t=20935
HOWEVER - for a "traditional lathe" (if it is one that the operator moves the tool by hand), it may
not fall into the category of "precision machining", and could very well be a normal distribution. When operators become the
key variation of the process, it tends to have a more "natural variation" and fall within normal distribution, especially if they are doing the "backyard garage style control" of "
running to the mean" to control their dimensions.