Short-term vs. Long-term Variation

[Ramizz]

Hi all,

I want to know the difference between the short-term and the long-term variation practically (StDev within and StDev between).

Where is the short-term and the long-term in the following 3 scenarios, assuming that the data is normal and the process is stable?

1- Suppose that we are collecting a subgroup of 5 parts once per shift for a month period of time.

2- What if we are collecting only 1 part once per shift for a month period of time.

3- What if we decide to do the analysis weekly, and we need to collect 1 part every hour (the 1 week period is short relatively).

Thanks to all.

 

[Bev D]

are you taking a six sigma class or preparing to sit a CQE or Six Sigma exam?
I will answer these questions but they really are very simple if you take the time to think about them:

Where is the short-term and the long-term in the following 3 scenarios, assuming that the data is normal and the process is stable?

1- Suppose that we are collecting a subgroup of 5 parts once per shift for a month period of time.

short term is the variation of the 5 parts in each subgroup. long term is the variation of all of the parts across all of the subgroups for the entire month

2- What if we are collecting only 1 part once per shift for a month period of time.

long term is the variation of all of the parts over the month. short term is the 'moving range' beteeen the parts.

3- What if we decide to do the analysis weekly, and we need to collect 1 part every hour (the 1 week period is short relatively).

when you do the analysis has no bearing on the short or long term variation. the answer is the same as for 2.


These really are non-sensical questions. and so there are only generic answers. If you aren't sitting an exam or studying, it is much more helpful to your understanding to post real world situations with actual data.

 

[Ramizz]

Re: Long-term Variation

Thank you,

I am working in a quality department in a manufacturing company, and currently we are having a green belt training.

I always thought that long-term variation is a result of long-term data collection (monthly or more). I realized now that there will be always long-term variation if the data was taken in a timely manner. Maybe the only case which might not involve long-term variation is when we are collecting data sample from a population (one time), right?

thnx

 

[Bev D]

Re: Long-term Variation

Thank you,



I always thought that long-term variation is a result of long-term data collection (monthly or more). I realized now that there will be always long-term variation if the data was taken in a timely manner. Maybe the only case which might not involve long-term variation is when we are collecting data sample from a population (one time), right?

thnx

how frequently or how often or when you collect the data has nothing to do with the determination of long or short term variation. The phrases long term and short term refer to the type of variation in your process and both the data collection frequency. So even if you collect the data ONCE for a population (assuming that you sampled it randomly and representitively) you can still calculate the long term variation of the process. Additionally if you collect and subgroup your data appropriately you can calculate the short term variation of teh process as well.

there are numerous threads in this forum covering the nature of these calculations and how the data is best collected. you can search fo rthem to do further study.

What does your instructor say about this?

 

[Ramizz]

Re: Long-term Variation

He didn't bring up the subject except that we can calculate the Within variation from an individual data set by considering the moving range values.

I also remembered him saying that it's impractical to consider the long term variation and indices if the data collected represent a short time frame.

Attached is what we have in the material about the subject.

Thnx

 

[bobdoering]

Re: Long-term Variation

Attached is what we have in the material about the subject.

I find what is even more entertaining is that the distributions - especially for the long term data - presented in your chart are wrong. They would be continuous uniform distributions, not normal. I have attached a more representative illustration. I left the short term distribution as normal, in that most variation detected from short term measurements from a process shown in your illustration are gage and measurement error - not process variation - and tehy tend to be normal. However, the chart does illustrate that you can not reliably predict long term process variation from short term variation. If so, you will develop an incorrect distribution model, as well as induce overcontrol.

 

[New to statistics]

Re: Long-term Variation



I find what is even more entertaining is that the distributions - especially for the long term data - presented in your chart are wrong. They would be continuous uniform distributions, not normal. I have attached a more representative illustration. I left the short term distribution as normal, in that most variation detected from short term measurements from a process shown in your illustration are gage and measurement error - not process variation - and tehy tend to be normal. However, the chart does illustrate that you can not reliably predict long term process variation from short term variation. If so, you will develop an incorrect distribution model, as well as induce overcontrol.

Question...What was that you said that data comes from uniform distribution?

 

[Bev D]

Tool wear

 

[John Predmore]

I looked at the attachment to the post from @New to statistics. I honestly don't see any difference in the attachment from @bobdoering. Fifteen years ago, maybe he attached the original by mistake. But I understand the point he was explaining. There is a yellow bell-shaped curve to the left of the vertical axis of the short-term segment, implying a normal distribution. There is a green bell-shaped curve to the left depicting a normal-shape distribution of the entire segment. But just because someone drew a shape, doesn't mean that is an accurate depiction.

Consider what we mean by a normal distribution. We are talking about the frequency of data points as they lie across the range. With your naked eye, looking at the aforementioned attachment, you can see there are 9 points inside the yellow rectangle "The Short term". The range of 9 points inside the yellow rectangle actually extends wider than the yellow bell-shape on the left margin - there are 2 points above the top yellow line and a third point below the bottom yellow line. Between the yellow horizontal lines, there are 6 points. Three of the 6 are near the midpoint of the range; the other 3 points are closer to the upper yellow line. So the yellow bell-shape is not a very good summary of the true lopsided frequency distribution. But in theory, if we inspected all short segments of 9 points in an extended run of an actual dataset, and averaged the frequency counts of all the various samples, on average we might expect a bell-shaped distribution.

Now repeat this exercise on the 38 total points in the entire dataset. In the attached copy of the illustration, I added five (red)horizontal lines (by hand, so spacing is a bit rough) to construct 8 equal sub-ranges between the upper and lower green lines. The frequency of points lying in each sub-range varies between 2 and 6, so not literally equally distributed. I sketched in (by hand, not actually plotted data) a brown ragged line on the left margin, depicting what the frequency distribution might look like {if we had a sufficiently huge number of narrow sub-ranges). Notice there is no concentration of points in the center, as is implied by the green bell-shaped curve, approximating a normal distribution. Instead, the frequency distribution of the 38 points across this range more closely resembles a uniform distribution, where the number of points in each segment is closer to being uniform across the entire range.

Another way to quickly summarize a frequency distribution of data is to imagine the data points are bread crumbs and you use a mental crumb-scraper to move all the crumbs to the sub-range axis. In this graph, that is the vertical axis. This mental exercise will produce small piles of crumbs in each subrange. With only a small bit of imagination, you can visualize the crumb-scraper view of the frequency distribution is closer to the brown line (roughly uniform distribution) than the bell-shaped green curve (depicting a normal curve). [Credit to Dorian Shainin for popularizing the crumb-scraper model.]

 

[NotMe]

Where is the short-term and the long-term in the following 3 scenarios, assuming that the data is normal and the process is stable?

If the process is actual stable, then both point estimates (short and long term) will be equal -- at least within their uncertainties. Thus, there is no point in distinguishing them. The purpose to distinguish these two standard deviations estimates is to account for the inevitable systematic drifts and/or jumps of the process. Hence, "short/long term" is not defined by your data collection plan, but by your process.

Let's take your first example and assume that the process is unstable:

1- Suppose that we are collecting a subgroup of 5 parts once per shift for a month period of time.

Although we usually associate "short term" with the "within subgroup" standard deviation and "long term" with "between subgroup", it is incorrect so say that the short term variation is the standard deviation within a single shift. Although it is correct to say that each shift defines a subgroup, calculating this within subgroup standard deviation is not "short term", if the process changes much quicker than 1/5th of the shift. What matters is "short term" with respect to change of the process. The same argument explains why "long term" is not (!) the standard deviation of the data collected over one month.