Standard Deviation - Doubt and Clarification of my Understanding

[KCIPOH]

Hello Cove members,

I am very new to standard deviation and have doubt to clarify, from my understanding (correct me if i'm wrong):

1. +/-1 Std Dev from the AVERAGE means 68% of our data or 68% of part
fall within this range.
2. +/-1 Std Dev from the AVERAGE means 95% of our data or 95% of part
fall within this range.
3. +/-1 Std Dev from the AVERAGE means 99% of our data or 99% of part
fall within this range.

Questions 1:

Which one (+/-1 Std Dev, +/- 2 Std Dev or +/-3 Std Dev) to use, is it up to us on how tight we want to control our process (min +/-1 Std Dev, max +/- infinite Std Dev) to meet customer specification?

4. The smaller the Std Dev, the bell shape curve will become like a spike
(narrow) which means the data are very close to the AVERAGE.
5. The HIGHER the Std Dev, the bell shape curve will become flatter
(wider) which means the data are spread further away from the
AVERAGE.

Question 2 :

If we take 30 samples from a population of 320 and calculated the Std Dev (sample Std Dev), how do i interpret the calculated Std Dev? is it i take 0 as a reference, the nearer the calculated Std Dev to 0 means the smaller the Std Dev and the samples are nearer to the AVERAGE and if the AVERAGE is close to target, then the samples are consider near to target which is GOOD while the further the calculated Std Dev from 0 means the HIGHER the Std Dev and the samples are further away from the AVERAGE and if the AVERAGE is close to target, then the samples are consider further away from target which is NOT SO GOOD, am i right?

Question 3 :

In usual practice, we always try to get a smaller Std Dev (which is close to 0), am i right?

Need help

[Steve Prevette]

1. +/-1 Std Dev from the AVERAGE means 68% of our data or 68% of part
fall within this range.
2. +/-2 Std Dev from the AVERAGE means 95% of our data or 95% of part
fall within this range.
3. +/-3 Std Dev from the AVERAGE means 99% of our data or 99% of part
fall within this range.

Keep in mind that these percentages only hold for the "normal" distribution. Nothing says that a given set of data has to be normal, most times it is not.

Questions 1:

Which one (+/-1 Std Dev, +/- 2 Std Dev or +/-3 Std Dev) to use, is it up to us on how tight we want to control our process (min +/-1 Std Dev, max +/- infinite Std Dev) to meet customer specification?

It depends. The folks who developed six sigma believe that six sigma is the correct answer. A Boeing manager once stated at an ASQ conference that for passenger airplane parts they are going to nine sigma.

Question 2 :

If we take 30 samples from a population of 320 and calculated the Std Dev (sample Std Dev), how do i interpret the calculated Std Dev? is it i take 0 as a reference, the nearer the calculated Std Dev to 0 means the smaller the Std Dev and the samples are nearer to the AVERAGE and if the AVERAGE is close to target, then the samples are consider near to target which is GOOD while the further the calculated Std Dev from 0 means the HIGHER the Std Dev and the samples are further away from the AVERAGE and if the AVERAGE is close to target, then the samples are consider further away from target which is NOT SO GOOD, am i right?

Within that set of 30 samples, if no samples are outside of three standard deviations from the average and there are no other sequential trend signals if they were plotted on a control chart, then all parts are equal. No sample is better than any other, they are just randomly distributed and "in control". This does not imply that any or all are "acceptable" against customer specs however.

Question 3 :

In usual practice, we always try to get a smaller Std Dev (which is close to 0), am i right?

Yes, generally smaller variation is better. But there is a cost benefit issue there - at some point you are expending a lot of money to reduce variation beyond what is "good enough". Six sigma applied the rule that Six sigma was as a blanket rule, "good enough". Good enough actually varies based upon the risks involved with too high a variation vs. the costs to get a low variation.

[Darius]

In Reply to Parent Post by KCIPOH

Questions 1:
Which one (+/-1 Std Dev, +/- 2 Std Dev or +/-3 Std Dev) to use, is it up to us on how tight we want to control our process (min +/-1 Std Dev, max +/- infinite Std Dev) to meet customer specification?

The control must be done with +/- 3 Sigma, the %, just is what is expected to be on each Sigma "Stage", points outside control limits (+/- 3 sigma) MUST be understood why that happened, and corrected on the root causes if possible. However as Steve said, deppending on the goals, the indicators on how the variable behave could take 3or 6 sigma as a goal (the corresponding ppm), check for process indicators.

In Reply to Parent Post by KCIPOH

Question 2 and 3:
the samples are further away from the AVERAGE and if the AVERAGE is close to target, then the samples are consider further away from target which is NOT SO GOOD, am i right?
In usual practice, we always try to get a smaller Std Dev (which is close to 0), am i right?

The whole idea is nearer the target the better quality and the lower costs, check for Taguchi's ideas

[KCIPOH]

In Reply to Parent Post by Steve Prevette

1. +/-1 Std Dev from the AVERAGE means 68% of our data or 68% of part
fall within this range.
2. +/-2 Std Dev from the AVERAGE means 95% of our data or 95% of part
fall within this range.
3. +/-3 Std Dev from the AVERAGE means 99% of our data or 99% of part
fall within this range.

Keep in mind that these percentages only hold for the "normal" distribution. Nothing says that a given set of data has to be normal, most times it is not.

Hello Steve,

Thank you for your sharing but just to clarify, if the data i plot is not "normal distribution", so the above method is not applicable, then what method should i use to see how many % of my data falls in what range?

Thank you

[KCIPOH]

In Reply to Parent Post by Darius

The control must be done with +/- 3 Sigma, the %, just is what is expected to be on each Sigma "Stage",

Hello Darius,

Thank you for your sharing but i still not quite get with the above sentence, why is it +/- 3 sigma? is it because it covers 99% of the data instead of +/- 2 sigma (95%) and +/- 1 sigma (68%) only?

Thank you

[Steve Prevette]

In Reply to Parent Post by KCIPOH

Hello Steve,

Thank you for your sharing but just to clarify, if the data i plot is not "normal distribution", so the above method is not applicable, then what method should i use to see how many % of my data falls in what range?

Thank you

Generally there really is not a need to know what % of data fall within what range. But if that is truly needed, then a distribution should be fit to the data. Start with the normal and see if it passes a normality test (there are several out there, "goodness of fit" being the easiest). Also, if you know the nature of the data that may help determine which distribution to use, such as if it is from counting independent events, it is likely Poisson.

[Jim Wynne]

In Reply to Parent Post by KCIPOH

Hello Darius,

Thank you for your sharing but i still not quite get with the above sentence, why is it +/- 3 sigma? is it because it covers 99% of the data instead of +/- 2 sigma (95%) and +/- 1 sigma (68%) only?

Thank you

The reason that Walter Shewhart, the originator of SPC, chose +/- 3 standard deviations as control limits is in the title of his landmark work on the subject, Economic Control of Quality of Manufactured Product. The limits were seen as sort of an economic break point, given that in a normal distribution 99.73% of the population will fall within those limits.

[KCIPOH]

In Reply to Parent Post by Steve Prevette

Generally there really is not a need to know what % of data fall within what range. But if that is truly needed, then a distribution should be fit to the data. Start with the normal and see if it passes a normality test (there are several out there, "goodness of fit" being the easiest). Also, if you know the nature of the data that may help determine which distribution to use, such as if it is from counting independent events, it is likely Poisson.

Hello Steve,

I get better idea now, will post again if any doubt.

Thank you