Capability Studies

A fundamental question should always be asked when reviewing production processes, “Is the process capable of consistently producing good parts?” If the process is capable then you must decide what statistical controls you wish to place on the process.  If the process is not capable then you must either improve the process or implement 100% checking of the processed parts.  

Machine Capability 

This is a study conducted at each machine under controlled conditions to determine the natural variation that occurs.  The person operating the machine is not allowed to alter any machine settings during the study.  Material quality is checked beforehand to ensure consistency and the measuring equipment is correctly calibrated and confirmed to be repeatable (i.e. capable to consistently recording the same measurement of one specific dimension on one specific part).

Process Capability

This study is conducted to determine total variability and process stability.  The study includes person, machine and material influences over a period of time.  Time is an important factor as quality will be influenced by material changes, and the person making corrective adjustments to cope with this and other variables such as tool wear etc.

Procedure

The first steps required for conducting both studies are as follows- 

·        Understand the part; determine critical dimensions and what measuring instruments are needed.  Consider part material and how it could influence the results.

·        Understand the process; part location, machine settings and adjustments (manual or automatic), cycle time, other factors such as coolants required or temperature control needed for process and measurement and is process carried out on a single multiple work station.  This final factor is very important because if there is more than one workstation it may be necessary to study each station.

·        Understand the incoming part quality used in the process.

·        Understand the inspection equipment to be used.

·        Understand the operating procedure that the person will use during the process.

·        Review any other relevant information from Engineering, Production and Inspection sources that might influence the study.

·        Record: machine number; operation number and description; tooling numbers and machine settings etc.

The capability of the process or machine is expressed as a “summary” of the test results of the characteristic checked compared to the specified tolerance of that characteristic.  The results are first converted to a predicted range of variation of “6 standard deviations” (called 6 sigma) using normal probability distribution.  There are a number of ways that this can be expressed –

Capability Ratio % = (6 sigma / dimension tolerance) x 100 or this expression can be inverted to represent Cpk (which is another way of expressing the same thing).

Machine Capability Study

·        Conducted at machine suppliers and later on site.

·        Use in-coming raw material or parts from the same batch.

·        Use one person to operate the machine.

·        Set machine and do not adjust it during the course of the study.

·        Calibrate measuring device, if required, and then do not recalibrate during study unless it is a normal requirement.

·        Record the machine details and settings as outlined previously.

·        Produce a minimum of 50 sequential parts from the process, recording the order of each part.  The number of parts studied is a matter of applying common sense.  If the machine produces 4 parts per minute (240 pieces/hour) or more, you should aim for about 200 pieces.  If the machine produces less than 4 parts per minute, it is OK to use 50 parts in the study.

·        From the data generated calculate the predicted spread of 6 sigma and compare this with the total tolerance of the particular dimension under review.

·        For the machine to be considered capable it should be able to produce a predicted spread of 6 sigma that represents no more than 67% of the total tolerance in the case of a new machine and 75% in the case of an existing machine.  The spread should also be centrally located within the tolerance, not pushed to one end of the tolerance.

·        The calculations are best left to specialized computer programs that can significantly speed up the review of results.  This is particularly important if the part requires a number of features to be measured and subsequently studied.

Capability Ratio % Total = 6 sigma / Total Tolerance

Cm = Total Tolerance / 6 sigma

The above chart represents a graphical look at the normal curve representing the results of a capability study.  If you wish to construct your own capability study work sheet then it is reasonably straight forward using an excel worksheet with the statistical special functions to establish the estimated sigma value.  The acceptable Capability Ratio % of 75% Total converts to a Cp value of 1.333.  From the diagram it is easy to recognise that you need to have a centrally positioned curve.  The easiest way to do this is to calculate the ratio for the top and bottom limits as follows.

Capacity Ratio % Bottom = 3 sigma / (Process Mean – Bottom Limit)   [CmL]

Capacity Ratio % Top       = 3 sigma / (Top Limit – Process Mean)         [CmU]

The minimum CmL and CmU value would be 1.333. You may also see a value called Cmk.  The Cmk of the process is simply the smaller of the two CmL and CmU values.  Therefore if the Cmk value is acceptable, you know that the machining process is OK and it is positioned sufficiently central to be acceptable. 

There are a number of other factors that you should be aware of when calculating capability studies and analyzing the results.

There are two standard deviation functions in excel STDEV and STDEVP, use STDEV.  This is the sigma value estimated from the sample that you have taken, the other is the sigma calculated if you were examining the actual study results of the whole population.

Everything in the study depends upon the curve being “normal” for the prediction to accurate.  Rarely however is the curve exactly “normal”.  To see how far the curve deviates from this two checks are often applied.  One is the measure of Kurtosis and the other is Skew.  Kurtosis is the measure of the “sharpness of the peak of the curve.  If the curve is “narrow and pointed” it is called “Leptokurtic” and the Kurtosis value would be > 3.  If the curve is “normal” the Kurtosis value would be = 3.  If the curve is “flat” it is called “Platykurtic” and the Kurtosis value would be < 3.  Skew is the measure of the symmetry of the curve i.e. is it lop-sided.  

The measure of skew is = (Mean-Mode) / sigma.  If Skew = 0, the curve is symmetrical.  Most of the studies are conducted can safely assume that the curve is close enough to “normal” so the information can be used with confidence.  An example where the curve would be skewed would be checking permitted leak rates of products where you would only have a positive leak so the result would be positive skew. 

The above examples have covered two sided tolerances, however you will frequently encounter one-sided tolerances.  Capability studies are conducted in the same way, but the calculation of capability ratio is slightly different. 

If we look at a Bottom Limit only, the Capability Ratio % is = 3 sigma / (Process Mean – Bottom Limit), similarly if we look at a Top Limit only the Capability Ratio % is = 3 sigma / (Top Limit – Process Mean).

Once again the Cm would be the inverse of the capability ratio.

One final point to consider on machine capability study is the influence of tooling.  If you are to use more than one tool to carry out the same operation conduct a study on each.  If the machine has two or more stations it is wise to conduct a study on each station.  If you study the combined results from a machine that has two stations and the calculated mean from each is different the curve will have two peaks.  When you set up subsequent average & range charts to monitor this process you would see a certain pattern emerging.  This has been covered in Statistical Instability.    

Process Capability Study

·        The steps in the process study is similar to that outlined above, but varies in the length of the study.  Process studies are conduced through the course of a day and take into account varying material batches, different people and many other factors that can influence the part quality.  In practice the study work is time consuming.  I have found that you will get most information from the machine capability study.  Only do the extended study after conducting the machine study and then only if you suspect the process is subjected to unstable elements.  The same calculations are used and the Cmk used in machine capability would be replaced by Cpk.

Parts per Million

Many companies now measure defects in parts per million.  Going back to our first look at statistics in the Quality-1 section we will recall that 3 sigma deviations each side of the process mean will encompass 99.73% of the population.  We have been looking at Process Capability using +- 3 sigma so we are really looking at 99.73% of the population.  To give us some safety, we wanted the +- 3 sigma to fall within 75% of the tolerance.  This equates to +- 4 sigma at 100% of the tolerance. If the +- 3 sigma had covered the total  tolerance 0.27% would not be encapsulated in the spread that we were using.  This would equate to 2,700 defective parts per million, 1,350 exceeding top limit and 1,350 failing to reach bottom limit.  Many companies now try for figures much less than this.  If you use +-5 sigma instead of +- 3 sigma in your calculations you will be fairly close to 1 part per million defects provided the process remains centralised and in control.

Many Statistical Process Control software packages are available that calculate capability and also produce average and range charts etc.  If however you simply wish to calculate capability then it is possible to construct an Excel work sheet using statistical functions.  If you are still unsure e-mail me for further information.