# How to determine the correct Sample Frequency for SPC Features

R

#### Ravven

Hello evryone,
My company is trying to launch SPC on our production lines and I've been appointed SPC coordinator. I have only got basic theoretical knowledge on SPC and could use some help.

My question is;

How do I determine a correct Sample frequency for SPC features?

The process is a Automated Turning Process and material is cast iron which leads to significant material variation (hardness, Tool wear etc.)

The process produces between 80 and 100 parts per hour under normal conditions.

Any suggestions are greatly appreciated.

#### bobdoering

Trusted Information Resource
Re: How do I determine a correct Sample frequency for SPC features?

My question is:
How do I determine a correct Sample frequency for SPC features?

The process is a Automated Turning Process and material is cast iron which leads to significant material variation (hardness, Tool wear etc.)

The process produces between 80 and 100 parts per hour under normal conditions.
Although you may have significant material variation (which is a special cause), the key variation in machining is tool wear. If your process is in control, and your measurement system is adequate for SPC, you should be able to observe tool wear. If so, you will get a sawtooth curve. Let's say you are doing an OD. As the tool wears, the OD of consecutive parts will become larger. At some point you will have to adjust down to you lower control limit. If you take the number of parts it takes to get from the lower control limit to the upper control limit and divide by 5, that should be the minimum sampling frequency. Could be every 5 parts, could be every 100 - depends on the wear characteristics of the tools you have chosen.

Most important, if your process is in control and you have predominately tool wear on a part to part basis - do not use a X bar-R chart. It is the wrong chart. By the way - the sample data on the link is from machining forgings...pretty close to machining castings.

D

#### David DeLong

Re: How do I determine a correct Sample frequency for SPC features?

Hello evryone,
My company is trying to launch SPC on our production lines and I've been appointed SPC coordinator. I have only got basic theoretical knowledge on SPC and could use some help.

My question is;

How do I determine a correct Sample frequency for SPC features?

The process is a Automated Turning Process and material is cast iron which leads to significant material variation (hardness, Tool wear etc.)

The process produces between 80 and 100 parts per hour under normal conditions.

Any suggestions are greatly appreciated.
I have found that the sample size depends upon the process and also the time it takes to measure the feature (characteristic).

I remember one time, I was working with a screw machine company and we placed a 5 pc sample size on a process that had 12 stations. What a mess. The X bar and R results were all over the ball park. Once we switch the sample size to 12, the results became stable.

In another situation, the truck frame had to be physically moved and it took about 15 minutes to complete the measurement. We certainly couldn't run 5 pcs/hour here so we ended up with a sample size of 1 using a X bar and moving range chart.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: How do I determine a correct Sample frequency for SPC features?

In general, your frequency take into account the cycle of natural change in your process. Typically we start out taking samples too frequently then we start to back off as we understand the natural cycles. A general rule of thumb is 5 sequential pieces every 2 hours. BUT teh applicability of this is conditional on the largest component of variation being piece to piece (a homogenous process stream) and that real process changes are occuring in slighly less than two hour tiem periods (shift changes, operator changes, raw material changes.)

I always start with a basic multi-vari chart with 3 sequential pieces every hour or so (might be more or less dependign on what i know for sure about the process). Once I have a good picture of the variation I determine the 'best' rational subgroup, subgroup size, chart type and sampling frequency...

#### bobdoering

Trusted Information Resource
Re: How do I determine a correct Sample frequency for SPC features?

A general rule of thumb is 5 sequential pieces every 2 hours. BUT the applicability of this is conditional on the largest component of variation being piece to piece (a homogeneous process stream) and that real process changes are occurring in slightly less than two hour time periods (shift changes, operator changes, raw material changes.)
A rule of thumb I use is 5 data points between adjustment or expected special causes (raw material changes, shift changes, operator changes, tool changes, etc.) That could be 2 hours or 10 minutes. Otherwise you will not have enough data to see what your process is doing, only what the effect of special causes are. I think it is best to know both.

One thing that is VERY bad is adjustments between chart sampling - such as adjusting every 15 minutes, but charting every 2 hours. That approach renders your chart useless. Your chart should be telling you when to adjust (or overadjust, if you use X bar R), and until then you should not touch the process (unless a special cause requires attention).

S

#### swarbur4

Re: How do I determine a correct Sample frequency for SPC features?

Ravven,
As Bob has stated if your process can be classed as precision machining then you need to use XHi/Lo R charts with a frequency of a minimum of 1 part, 5 times between tool adjustments, though if you dont fully inderstand your process then you might want to start with a higher frequency.

If your process is not classed as precision machining and the process has a distribution very close to normal then you can use Xbar R charts. These charts are capable of detecting a shift away from mean. You just need to determine what size of shift yoiu would need to detect and how quickly you need to be able to detect the shift. This all depends on the process capability, how many parts you make and how quickly they get delivered to your customer and many other factors.

attached is a little spreadsheet I put together for training of my engineers and also suppliers (and some customers) on how to determine the sample size and frequency in the control plan using data instead of a guess and operator whinning (as Bob would say). It is really just to be used as an indicator to give you some idea as all statistics, performance indicators are only as good as the data inputted and a full understanding of the processes which produced the data is needed to make sense of the results.

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#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: How do I determine a correct Sample frequency for SPC features?

If your process...has a distribution very close to normal then you can use Xbar R charts.
To clarify: SPC (including Xbar, R charts) does NOT rely on the process being Normal or even close to Normal. (Simple subgrouping - measuring sequential pieces - does rely on a homogenous process stream. If the process stream is not homogenous, then rational subgrouping must be employed.)

These charts are capable of detecting a shift away from mean.
Xbar, R / Xbar, S and I, MR charts will also detect a change in the variation not just a mean change...

#### Paul Simpson

Trusted Information Resource
Re: How do I determine a correct Sample frequency for SPC features?

Firstly I'd suggest you do your capability study and determine if the process is in control. From what you have posted it may not be. If the process is capable and in control then I'd suggest your doing a trial with periodic samples and determine if the process meets the 'SPC rules' over time for trends / above and below the line etc.

This work will give you a good idea of how frequently you need to sample. In the end the sampling rate is risk based. If you leave it longer and the process results in non conforming product what is the cost to the business?

S

#### swarbur4

Re: How do I determine a correct Sample frequency for SPC features?

To clarify: SPC (including Xbar, R charts) does NOT rely on the process being Normal or even close to Normal. (Simple subgrouping - measuring sequential pieces - does rely on a homogenous process stream. If the process stream is not homogenous, then rational subgrouping must be employed.)

I agree rational sampling must always be used especially when you know you are introducing special causes of variation such as, tool change, material change, start-up ect...
They work best on a normal distribution as all of the calculations are based on a normal distribution, for some other distributions that are not affected by the CLT they do not work as well - an example would be a continous uniform ditribution.

Xbar, R / Xbar, S and I, MR charts will also detect a change in the variation not just a mean change...
-

Yes the Xbar chart detects a change in mean and the R chart detects a change in variance.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: How do I determine a correct Sample Frequency for SPC features?

swarbar4: Sorry, but I do need to correct this misperception about the Normal distribution and the central limit theorem. Unfortunately its very common as recent authors have misunderstood and misrepresented Shewharts work but their publications are often refered to as they are 'newer'. This is compounded by the large nunber of people 'teaching' SPC or writign SPC manuals for their companies who also haven't taken the time to truly understand how SPC works. You are not alone in this misperception.

SPC does not require the underlying disstribution of individual values to be Normal. It can be any shape including uniform.

The distribution of subgroup averages does not have to follow the Central Limit Theorem. The subgroup averages don't have to be Normal or even roughly Normal.

The only distributional requirement is that the subgrouping scheme presents the data to be plotted in a random manner. Without a discernable pattern. Homogenous.

In Shewhart's day in Shewhart's industry, most process streams were naturally homogenous. This means that the largest component of variation was piece to piece. A homogenous process stream presents sequential parts in a completely random fashion: the first piece have the largest value and the second piece might have the smallest value. Even if the distribution is Uniform, SPC on the subgroups will still work as long as teh process stream is homogenous.

The example often used here in the forum for the Uniform distribution is not a homogenous process stream. A process stream that has a systemic pattern such as tool wear is not homogenous. That is why Xbar R charts will nto work; it has nothing to do withthe Non-Normality of the underlying distribution or the lack of compliance to the the Central Limit Theorem. It has a systemic causal factor influencing the pattern of the process stream; piece to piece variation is not the largest component. In this case - as in all cases of non-homogenous process streams, we must use rational subgrouping - or other monitoring/control schemes - to control the process.

In today's world there are many processes that are not homogenous streams. Rational subgrouping brings us to a homogenous stream of the subgroups. [*]Within Piece Variation
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