Hello Everybody,

I've made a comparison between XmR and p chart.

I used data from % non conforming items per month with variable sample sizes.

In both charts I removed points outside control limits (CL) and I have recalculated averages and CLs. These points are still plotted in graphs and are circled in RED.

NOTE for XmR chart: I first analyzed the mR chart, removed out of control points from the average mR (but NOT from the X average on the X chart), recalculated the control limits on both X and mR charts, analyzed X chart, removed out of control points from X average, plot new control limits until no signals are present.

Some points are exactly on the CLs but my interpretation of the rule is that they must be greater than the CL in order to be considered signals.

At the end, in my opinion both charts give the same messages, in short:

1. Process was unpredictable between end 2006/beginning 2007 than some improvements brought it under control.

2. a stable average of around 12%-14% defects can be considered.

The p-chart show me that one additional point should be considered as a signal (Jan 2008) and I agree this is worth to investigate.

As you can see I used a Z chart together with the p-chart in order to be able to recognize 2/3 points above 2sigma and 4/5 points above 1sigma trends. Do you agree with this "method"?

Generally, any comments on my analysis? Thank you for your views on this.
Ciao.
Giuseppe

Any feedback from the specialists?

none of the three methods diverge significantly from the answers they provide.

Techncially the p chart is probably the best choice. I, MR does not allow for changes in sample sizes and so signals can be missed. And the data has enough sample size variation to warrant the use of variable control limits.

The Z chart is also refered to as the p' chart (ref: Laney, David B., “Improved Control Charts for Attributes”, Quality Engineering, 14(4), 2002, pp. 531-537) but is typically used when the process has very high volume 10,000+ and the largest component of variation is time to time. I do use it in my current position but typically for field failure rates when the usage volume is on the order of 25,000 to 50,000+ events and the failure rates are fairly small (under 5%). It works like a champ. However, in this case the poster's unit volume is very low and so I wouldn't recommend the Z chart. Stick to the basic p chart.

I also think the poster may be stuck in admiring the different charts: remember it is the economical control of quality. Some out of control points are just the extremes of the natural variation and not due to an assignable cause. and the opposite can occur with a poor chart choice or a convergence of two factors offsetting each other: a single point may appear to be the result of common cause when it is not. This is why there is more than one rule concerning detection of possible assignable causes. We can only know which chart was the most accurate by having done the appropriate investigation into assignable causes for the detected points.

The chart never indicates truth; the physics of the actual situation do. Or as George Box said: all models are wrong; some are useful.

Dr. Deming does provide an interesting scenario in his Out of the Crisis, which makes a pitch for the p-chart. A shoe manufacturer was sampling 225 pairs of shoes per data point, and coming up with 9.5% defective rate. The plant management felt that was too high and did call in Dr. Deming.

Dr. Deming looked at the data and determined the three standard deviation spread for 225 samples at an average of 9.5% should be about 5% to 15% variation, using the binomial p-chart calculations. Yet, the actual data varied from 9% to 10%. If you did a ImR of the actual data, you would find it to be statistically stable and "in control". Yet, the variation was much less than the p-chart predicted.

Dr. Deming interviewed workers and the QC inspector. He determined that the common conception amongst the workers was that if the percent defective exceeded 10%, management would shut down the factory. The QC inspector "knew" this also. Basically, when 22 defective product out of 225 were counted, the count would stop, and the defect rate for the day would be reported as slightly less than 10%.

What was the "true" percent defective? Certainly more than 10%. What were the costs of defective product shipped? Also unknown and unknowable, but certainly greater than $0.

The key is that Dr. Deming was able to determine that something must be amiss by comparing the actual variation in the data to the binomial predicted data. This would have been missed if he had chosen to use ImR.

Thank you for the really valuable comments.

Giuseppe

none of the three methods diverge significantly from the answers they provide.

Techncially the p chart is probably the best choice. I, MR does not allow for changes in sample sizes and so signals can be missed. And the data has enough sample size variation to warrant the use of variable control limits.

The Z chart is also refered to as the p' chart (ref: Laney, David B., “Improved Control Charts for Attributes”, Quality Engineering, 14(4), 2002, pp. 531-537) but is typically used when the process has very high volume 10,000+ and the largest component of variation is time to time. I do use it in my current position but typically for field failure rates when the usage volume is on the order of 25,000 to 50,000+ events and the failure rates are fairly small (under 5%). It works like a champ. However, in this case the poster's unit volume is very low and so I wouldn't recommend the Z chart. Stick to the basic p chart.

I also think the poster may be stuck in admiring the different charts: remember it is the economical control of quality. Some out of control points are just the extremes of the natural variation and not due to an assignable cause. and the opposite can occur with a poor chart choice or a convergence of two factors offsetting each other: a single point may appear to be the result of common cause when it is not. This is why there is more than one rule concerning detection of possible assignable causes. We can only know which chart was the most accurate by having done the appropriate investigation into assignable causes for the detected points.

The chart never indicates truth; the physics of the actual situation do. Or as George Box said: all models are wrong; some are useful.

So, while using a p chart for sample size with low volume and big difference between sample sizes (my examples) I would avoid the 2/3 out of 2sigma and 4/5 out of 1sigma rule due to difficulties in caluclating these lines.
I would stick to the interpretation of out of control points and trends above/below average.

Do you agree? Any more suggestions?

Thank you.

So, while using a p chart for sample size with low volume and big difference between sample sizes (my examples) I would avoid the 2/3 out of 2sigma and 4/5 out of 1sigma rule due to difficulties in caluclating these lines.
I would stick to the interpretation of out of control points and trends above/below average.

Do you agree? Any more suggestions?

Thank you.

No, I don't agree. You can easily calculate sigma, it equals the square root of pbar x (1 - pbar) divided by the sample size. In extreme cases, you can run into the UCL and LCL are greater than 100% and less than 0%, and in that case, I would really try to role the data into larger sample groups.

If you really are concerned, it is possible to calculate the "exact" control limits using binomial confidence intervals. But they aren't really going to be that much different than just using the p-chart control limits and likely won't give any different signals.

See http://www.hanford.gov/rl/uploadfiles/VPP_18_P_Chart.ppt and http://www.hanford.gov/rl/uploadfiles/VPP_pchart.pdf for my writings on p-charts.

Dr. Deming does provide an interesting scenario in his Out of the Crisis, which makes a pitch for the p-chart...
The key is that Dr. Deming was able to determine that something must be amiss by comparing the actual variation in the data to the binomial predicted data. This would have been missed if he had chosen to use ImR.

Yes. The really powerful thing about control charts is how the control limits for the subgroup to subroup variation is calculated using the within subgroup variation: if the process as you have decided to sample it and analyze it is stable, then the chart will 'look' right; if it indicates an out of control condition then you either have an out of control process or you selected the wrong subgrouping scheme, frequency or type of chart. Its' a real safety net. It will drive you to LEARN something about your process. As Dr. Ott said (I am a (an?) Ott disciple): plot your data and think about your data.

This is why you should determine what type of data your process is generating then first pick the chart type that fits the data type. The p chart is for defective data (binomial or bernoulli trials). An I, MR chart is for single unit subgroups of continuous data. It can be used as a chart of last resort for other odd situations but that should be rare compared to its' intended use.

The dilemma I see is that so many people are only interested in making the chart look right or submitting their PPAP or whatever, not in improving their processes.