Is Cpk calculation of dBA (noise level) valid?

As the sound noise level dba is a log function, can we calculate the cpk using the traditional method ?
- First, can we add them up and make an average ? Remeber that 1dba+1dba is not equal to 2 dba.
- Secondly, can we calucate the standard deviation ?
- Can we use the formula cpk = ..... ?
I've struggle with this problem for a long time. Hope that someone can help me.

Re: Is Cpk calculation of DBA (noise level) valid ?

raymondsmlui said:

As the sound noise level dba is a log function, can we calculate the cpk using the traditional method ?
- First, can we add them up and make an average ? Remeber that 1dba+1dba is not equal to 2 dba.
- Secondly, can we calucate the standard deviation ?
- Can we use the formula cpk = ..... ?
I've struggle with this problem for a long time. Hope that someone can help me.

Click to expand...

As common adding method does not apply to sound level measurement. Cpk calculation can not be applied. A run chart can be used to record trends. An histogram for db observed can also be misleading.

V.J.Brahmaiah

raymondsmlui said:

As the sound noise level dba is a log function, can we calculate the cpk using the traditional method ?
- First, can we add them up and make an average ? Remeber that 1dba+1dba is not equal to 2 dba.
- Secondly, can we calucate the standard deviation ?
- Can we use the formula cpk = ..... ?
I've struggle with this problem for a long time. Hope that someone can help me.

Click to expand...

Since Db(a) is a relative measurement, can you determine (or calculate) the power (in mW) and use that for a capability calculation? (removing the log)

Can you post some data?

I would not be so quick to change from dB to mW.

There is a reason that A log scale is used for sound levels. Human perception of sound is more closely related to dB than to mW. At least approximately, 50 dB is perceived as "half way" between 40 dB and 60 dB. With a calculation based on power, 57 dB is the "average". (In fact, 57 dB would ALSO be the average of 0 dB and 60 dB! based on power.) If you want to know the spread in sound as perceived by people ,then working with dB would seem to be fine. If you want ot know the actual power levels, then mW may be better.


Or think of it another way. A very common technique in capability analysis is to apply a Box-Cox transformation to data. In a sense, using a dB scale is like applying a Box-Cox transformation to the data. Without seeing the data is is hard to know if that transformation will make the data closer to normal or not.

Tim

Tim Folkerts said:

Or think of it another way. A very common technique in capability analysis is to apply a Box-Cox transformation to data. In a sense, using a dB scale is like applying a Box-Cox transformation to the data. Without seeing the data is is hard to know if that transformation will make the data closer to normal or not.

Tim

Click to expand...

gently posing an alternative view: - just because it's common, doesn't mean you should. This is one area where I certainly disagree with current commonly held statistical practices; I'm a bit old school. my heroes are Tukey, Ott, Seder, et al. Everyone should read Wheeler's article* in the August issue of Quality Digest: "Do you have Leptokurtophobia?" bobdoerring posted the link yesterday...

my answer to the OP's question would be slightly different: he is absolutely correct that a standard calculation of Cpk with dB data would be mathematically incorrect. Because the data isn't Normally distributed AND it's a log scale...HOWEVER, one can assess still assess capability either by determining the proportion of out of tolerance values and working thru the Z table "backwards" [Cpk = Z/3; Z = Normsinv(p)], alternatively you can simply calculate the ratio of the spread of the process to the spread of the tolerance...it depends on what the Cpk value will be used for. Is it defect rate or variation that you are concerned with?

There is no magical correctness to the standard way of calculating Cpk; even with a Normal distribution, the answer is still a point estimate. Processes are rarely static and even slight variations form homogeneity or Normality will yield fairly large differences in the estimate. The intent is to understand capability; It is not to hit some magical value. Towards that end the run chart plotted against the spec limits is the best first start - it will tell you the most with the least amount of mathematical worries.

If you post your data we can help further...

*"When you transform the data to achieve statistical properties you deceive both yourself and everyone else who is not sophisticated enough to catch you in your deception. When you check your data for normality prior to placing them on a process behavior chart you are practicing statistical voodoo. Transforming the data prior to using them on a process behavior chart is not only bad advice, it is also an outright mistake." Donald Wheeler, Do you have Leptokurtophobia?, Quality Digest, August 2009

I've included some data for discussion.

Re: Is Cpk calculation of DBA (noise level) valid ?

This is one of the fundamental source of the problem.
What indicator should be used to reflect the ability of the products meeting the specification ? Cpk should be considered as this is a well known indication, but it seems the calculation should be modified.
If we just focus on the center-tendency, it seems medium is better than the average.

what are the two columns? did you measure the dB level of each event twice or is each value from a unique event? wha ti sthe event that you are measuring?

Hi Rev D

The original data measurement is noise level of 2 different rotation directions. I've pool the data for the capability calculation.