Hello!
Is there any recomendations of evaluating the process normal or non normal?
Any helpfull excel templates or small software to check the process distribution, stability etc. Capability etc is calculated in a software but no normality test?
Any ideas to test/evaluate the process?

We use Minitab, which is a great statistical product, for our capability studies... however, it's not free... I think we paid about $1000 USD for it a few years ago.

You can probably get 80% of the way there by plotting a histogram and visually comparing it to the standard normal curve. For example, it should have a single peak, centered at the mean, and the tails should be similar in size to each other. Many manufacturing processes are not normal, and often there are simple reasons. For example, if you have 2 or more process streams (e.g. 2 different dies or molds), you may get a bi-modal
distribution. If this occurs, you should do your SPC on the two dies or molds separately.

Another problem that may happen is that the distribution may be skewed, if for example it's not possible for a negative dimension to occur. We have this problem when we do SPC for flatness; it's not possible to have negative flatness.

If you're really determined, I think that you could use the chi squared distribution to test the normality of the distribution. The chi square
distribution is built into excel. I've never done this in Excel but it shouldn't
be that difficult.

It is well worth the effort to verify that a distribution is normal... most of SPC is based on the assumption of normality, and if the distribution is not normal,
you will be wasting your time and confusing yourself if you use statistics
when the assumption is not accurate.

Regards,
Brad

Chi Square tests in excel are not too bad to pull off, though you will have to do a fair amount of coding yourself.

Another thing to consider is check if the "skewness" and "kurtosis" are both zero.

SPC is distribution free and empirically based. Normality is not required.....Shewhart and Deming were clear on this point.

My 2 cents;
Chart your process, identify special causes, eliminate them and improve.

Rich DeRoeck

SPC is distribution free and empirically based. Normality is not required.....Shewhart and Deming were clear on this point.

My 2 cents;
Chart your process, identify special causes, eliminate them and improve.

Rich DeRoeck

Rich, Steve, or Anyone who can Help,

I have been told that I am wasting my time on a U-Control Chart because we are trying to monitor a Process that is Not Normal, or at least our attempt to monitor the Order Quoting-Entry-Review-Releasing-Billing (QERRB) Process is not accurate enough. So I have been generating a Histogram with Descriptive Statistics to determine if the number of defects falls in a normal distribution or not. So I have been watching the P Value from the Anderson-Darling Normality Test, to see if and when it would go below .05. In the 42 weeks we have been monitoring these defects, the P Value has fallen from around .9 to .4. Am I way off in this effort? Please see attached file for the various worksheets.

Thanks,
Doug

You are correct, the U-chart is non-normal. It is in fact related to the Poisson. Do not take control charting as an exercise in probability. It is an empirical rule which has some good theory and testing behind it. I don't see what you are referring to with the .9 and .4 p values.

Looking at the U-chart, there is an out of control low point on week 33. It looks to the eye that something may have shifted in week 25. The effect of this shift may be hidden because you are updating the baseline with new data values. If you were happy with the initial baseline you should leave it alone.

What I would do is weeks 1 - 24 into a baseline and lock that baseline (this is based upon knowing that week 33 was low). Then I think you will see a lowered baseline for weeks 25 to 42, with the exception of a significantly high spike in week 34 (it is interesting it comes after a drop in week 33 - could some stuff have been counted in 34 that should have been counted in 33?)

The Pareto is a good idea, but be sure to do it only over a time interval that the control chart shows is stable.

Now, all this is based upon only looking at the chart. What happened with the process? Did something change around week 25?

Do not take control charting as an exercise in probability. It is an empirical rule which has some good theory and testing behind it.

A control chart is nothing if not "an exercise in probability." What's the point in doing control charting if the charts have no predictive value? How can you have predictive value without a basis is statistical probability?

A control chart is nothing if not "an exercise in probability." What's the point in doing control charting if the charts have no predictive value? How can you have predictive value without a basis is statistical probability?

This is a point that was made by Dr. Deming on several occasions. It has taken me a while (as a classically trained Operations Researcher) to get used to this idea, but I think it has merit. A lot of folks teach SPC using the normal distribution and making statements like 99.7% of the data will be between the control limits. There are several things which would cause the 99.7% to be incorrect - such as the data aren't normal (which they aren't in the u-chart) and the calculated baseline may be off (sample vs. reality) and the process data may not be stable. A concern for the 99.7% has sent several people off to mathematically transforming their data, or trying to calculate what the 99.7% limits would be for their distribution. This is not necessary.

Dr. Deming was also against the traditional uses of hypothesis testing.

But we do both agree (and so did Dr. Deming) that the control chart's purpose is prediction.

You are correct, the U-chart is non-normal. It is in fact related to the Poisson. Do not take control charting as an exercise in probability. It is an empirical rule which has some good theory and testing behind it. I don't see what you are referring to with the .9 and .4 p values.

Looking at the U-chart, there is an out of control low point on week 33. It looks to the eye that something may have shifted in week 25. The effect of this shift may be hidden because you are updating the baseline with new data values. If you were happy with the initial baseline you should leave it alone.

What I would do is weeks 1 - 24 into a baseline and lock that baseline (this is based upon knowing that week 33 was low). Then I think you will see a lowered baseline for weeks 25 to 42, with the exception of a significantly high spike in week 34 (it is interesting it comes after a drop in week 33 - could some stuff have been counted in 34 that should have been counted in 33?)

The Pareto is a good idea, but be sure to do it only over a time interval that the control chart shows is stable.

Now, all this is based upon only looking at the chart. What happened with the process? Did something change around week 25?

Steve,

Let me see that I have this right. The U-Chart shows that the number of defects monitored over time for our Order QEERB process is not normal. Besides Week 33 being Outside the LCL, we have more than 4 out of 5 points 1 STD above / below the average (wks 13 thru 20), more than 2 out of 3 points 2 STD above / below the average (wks 8 thru 11 again wks 26 thru 32). But it would appear that weeks 35 on are meeting the rules for normalcy, especially if I re-compute the Baseline - right? (see Attached Chart)

I did not know what Poisson meant.

Main Entry: Pois·son distribution
Pronunciation: pwä-'sOn-
Function: noun
Etymology: Siméon D. Poisson died 1840 French mathematician
: a probability density function that is often used as a mathematical model of the number of outcomes obtained in a suitable interval of time and space, that has its mean equal to its variance, that is used as an approximation to the binomial distribution, and that has the form f(x) = e-µµx/x! where µ is the mean and x takes on nonnegative integral values

But the Histogram was looking Bi-Modal. As for the P value, it was with the Descriptive Statistics shown with the Histogram under the Anderon-Darling Normality Test. So even though the P Value was greater than the .05, the number of defects were not representative of a normal distribution.

As for week 33, that was the week before school started and a number of vacations were taken by the people who monitor these defects. It would make you wonder how many jobs were not identified as not conforming to some specification.

I still wonder if I should continue monitoring the Order Quoting-Entering-Review-Release-Billing process in this manner.

Thanks,
Doug

Realized after posting that weeks 36 on looks too trendy for it to even be normal - right!? Then I really wonder if this is helping us to know how our process is running!

Again - Thanks,
Doug

Two observations about the data for the U chart:

1) There seems to be a definite downward trend. According to Minitab...

Regression Analysis: Ave. Number of Defects (U) fo_1 versus Week Number
The regression equation is
Ave. Number of Defects (U) = 0.589 - 0.00542 Week Number

Predictor Coef SE Coef T P
Constant 0.58870 0.04669 12.61 0.000
Week Number -0.005419 0.001732 -3.13 0.004

Congratulations. Overall defects are decreasing. However, that would suggest the process in not in control (in a good way!).


2) Every 4 weeks there is a dip followed by an increase. Regular as clock work (well, there is one time it doesn't come back up). Look at weeks 13, 17, 21, 25, 29, 33, 37, 41. Every one has a higher defect rate the previous week. Every one (except 29) has a higher defect rate the following week. Curious. Is there some root cause?

Tim F

Two observations about the data for the U chart:

1) There seems to be a definite downward trend. According to Minitab...

Regression Analysis: Ave. Number of Defects (U) fo_1 versus Week Number
The regression equation is
Ave. Number of Defects (U) = 0.589 - 0.00542 Week Number

Predictor Coef SE Coef T P
Constant 0.58870 0.04669 12.61 0.000
Week Number -0.005419 0.001732 -3.13 0.004

Congratulations. Overall defects are decreasing. However, that would suggest the process in not in control (in a good way!).


2) Every 4 weeks there is a dip followed by an increase. Regular as clock work (well, there is one time it doesn't come back up). Look at weeks 13, 17, 21, 25, 29, 33, 37, 41. Every one has a higher defect rate the previous week. Every one (except 29) has a higher defect rate the following week. Curious. Is there some root cause?

Tim F

Tim,

Wks 13, 17, 21, and 25 are the end of the month, while wks 29, 33, 37, and 41 are mid-month. I could see where the supervisors, who are evaluating the orders and giving me their defects sheets, would be lax at the end of the month since they are working to get orders out - but that would not explain the shift to mid-month. I'll to to take a closer look!

I presented the information I gathered from Steve's feedback to the Cross-Functional (kinda like our QOS meetings). Those who seem statiscally endowed, who have been saying all along our data gathering is not correlating with the actual data, say drop the U-Chart and work with the Pareto. The others, who do not want to give up on this method of measure, want to try just monitoring the data on a monthly basis. They think that if we track on a monthly basis that we may have a better picture. Since the CEO is in the latter, I will be going that way.

For those who might want to look at it some more and give me recommendation, I have attached the charts through week 43.

Thanks,
Doug