# How can I manage the defective rate in this situation?

Discussion in 'SPC - Statistical Process Control' started by judegu, Jul 16, 2018.

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1. ### judeguWell-Known Member

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I have a big question regarding the management of the defective rate(SPC management for attribute data). For variable data, I know we can use X-bar R Chart to do the SPC management. However when it comes to attribute data, it has become tricky. In my original plan I was going to use P chart to do the SPC management. The question is when using p char algorithm (UCL = p-bar + 3* sqtr((1-p-bar)*p-bar/n)) to calculate the UCL, the UCL is so small, almost 10 out of 35 of the points(defective rates) will be above the UCL. It indicates not only the whole process is not statistically stable, but also it is hopeless to do the P chart management. How can I do it with so many anomalies?! Before I was trying to use P chart to manage the defective rate, normally the algorithm for us to caculate the UCL for defective rate is that UCL = average defective rate + 3 * standard deviation of all defective rates. This UCL is large enough that there are not too many anomalies for us to check. The management on this UCL is doable. I know the algorithm of this UCL lacks the correct statistics support, however it can be implemented.
Please help me on this problem, thank you.

2. ### Bev DModeratorStaff Member

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first doing something because it's 'doable' is not worth doing - you will only fool yourself.

There are several options for appropriate control limit formulas besides the p chart. I would recommend reading Donald Wheeler’s article “What About p-charts?” as a first step in understanding.

One alternative – depending on what type of ‘defect’ you are trending – is to use the c or u chart. However if you have relatively large sample sizes and your occurrence rate is somewhat low (<5%) this approach is inappropriate.

The most common reasons for a p chart failing are:

• The process is actually out of control (even though you can’t find an assignable cause with casual investigation)

• The process doesn’t follow the ‘model’ for the chart formula (categorical or attribute is much more susceptible to ‘model assumptions’ than the traditional continuous data charts.) Models include Poisson and Normal approximation. This happens for occurrence rates less than ~5%.

• The sample size is far too high and the defect rate between samples is too large. The fundamental thing to understand here is that ALL control charts work on the assumption that the within sample variation is related to the total variation by the square root of the sample size. In other words the process is homogenous. Many processes are simply not homogenous.

A control chart actually is designed to detect non-homogeneity. so you are either out of control or you are simply using the wrong formula for your process...using the approach you describe will 'hide' variation and non-homogeneity from you.

A couple of alternative approaches to try are the I, MR chart (See Wheeler’s “The Chart for Individual Values”) and the p’ chart (See Laney’s “Improved Control Chars for Attributes”. You will have to purchase this article. If you are an ASQ member it is \$5 or \$10 for a non-member if you buy it from ASQ

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3. ### judeguWell-Known Member

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g're'a
Sir, it is the greatest answer I ever received regarding SPC management so far. Thank you very much.
"A control chart actually is designed to detect non-homogeneity." You kind of show me the essence of the SPC. Yes, it is all about "homogeneity". Sometime the process just has no homogeneity. The conventional methods simply can't be used in these cases. Or maybe the process being studied is just unstable.
In my case the sample size is always around several thousands pcs and the occurrence rate is definitely below 5%, average occurrence rate is from several thousands to several hundreds of thousands of PPM. We do the full inspection on every production lot by auto inspection machines.
With regards to the method I talked about, yes, I agree it would hide some anomalies and can't detect all the non-homogeneity. However even using this method, there are enough anomalies detected for us to analyse each day. We are not sampling checking some of the production lots. Instead we check each of them... There will definitely be a lot of anomaly lots detected each day, since we process many of them everyday. I want to know what would you do if you are in my situation. Thanks.

4. ### Bev DModeratorStaff Member

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I would do what I said I would do above. try the p' chart and the X, MR chart

5. ### tony sWell-Known Member

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Once you tried Bev D's recommendation, can you post the results of both p" chart and ImR chart here? So we can see the difference.

6. ### judeguWell-Known Member

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I have tried the MR chart. The result is rather undesirable - there are too many OOC points. Regarding the P' chart he mentioned, it needs dollar to see the real content. Although I really want to read it, the payment process is quite troublesome for me and the price is a little beyond my allowance.

I have been working on SPC management for a while (focus on the deffect rate). Well I have to admit that it is a not standard SPC which strickly follows the book.(You can see the algorithm how I MANAGE it. UCL = average defect rate + 3 * standard deviation of all defect rates).

As a quality engineer, I tend to focus more on the data, on the trend. However, in the reality, I also need to take into consideration the processing capacity of the manafacturing line. Normally when the computer-aided quality system identifes an ABNORMAL lot, the system will automatically "HOLD" the lot from going downstream and stop the corresponding manufacturing machine if necessary. I NEED TO CONTROL THE NUMBER OF OOC LOTs. If there are too many of them, the production will be interrupted severely which also poses a BIG quality risk and there is also not enough manpower to deal with them.

So for me balancing the number of OOCs and the actual capacity is also a key of SPC management. Sometimes I just doubt that whether there is a need for a decent SPC management in my factory. ㅜ.ㅜ

7. ### MinerModeratorStaff Member

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You can find a lot of information about the Laney P' chart on Minitab's site. There are a number of pages on this topic available through the menu bar on the left side of the page. The formulae for the chart may be found by selecting the link enclosed by the red box in the attached image.

#### Attached File(s): 1. Scan for viruses before using. 2. Report any 'bad' files by reporting this post. 3. Use at your own Risk.:

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8. ### Bev DModeratorStaff Member

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Thanks Miner!

Can you clarify what you mean by “controlling the number of OOC lots”?

Your formula for the UCL is simply incorrect - not unusual as a lot of training and some software get it wrong. SPC is not as simple as some want to think it is. The formulas are specifically selected so that the within subgroup variation is used used to calculate the control limits. IF you have a stable (homogenous not Normal) process then the variation of subgroup averages will be described by the within subgroup variation which is an estimate of the total variation. If you dont’ have a homogenous process then the subgroup averages will fall outside the control limits. If you are having too many lots fall outside the control limits there are really only two reasons: the control limits are incorrectly calculated or your process is actually unstable.

If you have a stable yet non-homogenous process then you will need to create “rational subgroups”. These are sampling schemes that deliberately utilize teh non-homogeneity to determine the subgroups. This is somewhat complicated but we could post links to some articles if this is the case.

If you are using the incorrect formula as you indicate, your control limits are most likely too wide. This means you are actually more unstable than you think. It is possible that your limits are too narrow if you are using very large sample sizes (hence the suggestion to use the I, MR chart (use the real formulas not the one you indicated) or the p-prime chart).

It is possible that your process is simply unstable and the only way to ‘control’ that is to find the cause(s) of instability and eliminate or control them.

Short of determining the correct chart type and sampling scheme,

If you post your data with some explanation of how it is subgrouped and collected (sample size and frequency) we could provide further help.

Short of thsoe suggestions I strongly recommend that you start reading Donald Wheeler’s columns in the Quality Digest. These are available for free and his articles are easy to search for on the website (www.qualitydigest.com)

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9. ### judeguWell-Known Member

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Thank you for your help. I will do some serious study on the content you recommend.

I'd like to share some data, however my company have done a really good job on the protection for "corporate" intellectual property. And I also has a doubt that there is a huge fundamental misunderstanding towards the usage of SPC in my company.

I will take some time to think through it and hopefully to make a post to illustrate the detailed situation where I am.
PS: Sometimes I just hate the rigidity of the huge organization.

10. ### judeguWell-Known Member

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The following is the reason why I need to control the quantity of OOC lots.
(a really long message, please be patient to finish it.)

First I need to talk about the usage of SPC in my company.

As the Manual mentions, SPC control charts, both for attributes and variables, are the tools to determine whether the manufacturing process is stable or not by identifying whether there is out-of-control point(s) or abnormal trends. If there is such thing identified, the action shall be taken to stabilize the whole process and achieve the continuous improvement.

In my company, the output (i.e. products) from the process on which we are doing the SPC is subjected to full inspection, and the purpose is to identify the out-of-control point(s) which is OOC lot(s). The engineers will check these lots to:
1) see whether there is any underkill product (defective product which is not screened out by the full inspection) in this lot. If there is any, mark them out and scrap them to prevent nonconforming products shipment.
2) find the cause for the abnormality, do the correction to prevent more from happening. (Bring down Quality failure cost)

In my company every production lot will go through SPC control. Furthermore, we do the SPC control on all the main defect types (such as overflow, underflow, foreign material etc.) of each lot in each inspection station, not just on the nonconforming rate. Plus, though our production capacity is far below the average capacity of the competitors, still we produce more than 800 lots per day, and each lot wil go through at least two full inspection stations , and there are several main defect types in each station. It results in a lot of SPC charts and each chart has a lot of points.

As the manual said, the environment must be responsive. We actually establish this responsive environmnet by integrating the SPC into the MES. If OOC lot happens, the lot will be contained by the MES, and CAN NOT go downstream. And based on the setting, the corresponding manufacturing machine will be also stopped. The engineers need to go through the "RELEASE" process to resume production of the machine and let the lot FLOW again. IF THERE ARE TOO MANY OOC LOTs, the production may be literally stopped or severely interrupted.

That is why I need to control the quantity of OOC lots.

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11. ### Bev DModeratorStaff Member

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OK that makes sense. The only real way to do this is to improve the process. Stop making so many defects. You may have the wrong limits but we’d have to see you data to determine that.