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Home Forums Old Forums General P/NP CHART

This topic contains 13 replies, has 8 voices, and was last updated by  Darth 13 years, 6 months ago.

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       As we all know a basic requirement for P/NP chart is NP>=5, but which type of chart should we use if NP<5? Thanks for your help!


    Depends on what you are trying to control – what the appropriate underlying distribution is.  NP suggests that you are using constant sample size.  If you are concerned about low defect rates (np<5), a c-chart may be appropriate.  Need more info on what you are controlling.


    You need enough information to monitor your process. More information can be provided by a larger ammount of data or by data intrinsically containing more inmormation. Attribute data is one that provides little information per unit of data, and hence the need of large samples. So:
    a) You can increase n to get, on average, np>=5
    b) You can try to find some characteristic that is measurable in terms of variables, and use one of the charts for variables (such as an Xbar-R, for example). These type of data contains much more information, ans sample sizes are much smaller than those of attributes charts.
    c) You can make 100% poka-yoke type inspection. To see if the process remains in control you can plot the time (or number of good parts) between failures (I never used it but heard it works).
    d) Of course you can use the p or np chart, accepting the risks involved in the lack of performance. Or, again accepting the risks, you can choose to not to chart the process.


    I would like to add one more option to your list and that is to chart the number of units produced between occurance of a defect.  This works particularly well when the occurance is relatively rare and will give you a data point for each occurance.
    Of course this data will be best modeled as exponential so the control chart will have Mean units between occurance (MTBF) as the center line, 6.6*MTBF as the upper limit, and 0.0013*MTBF as the lower limit.


    Of course you made my point in your option C.  I guess I should read more carefully the first time.
    Do you need to change the inspection rate to 100%?  Why couldn’t you stay at the same inspection rate and use number of pass tests between failed test as the metric at any inspection rate?


    You are right, 100% is not needed. The reason why I put that is because I pictured the following scenario in my head:
    1) The guy does not reach to np=5. That means that either n is small or p is small. The typical situation when you have problems to go on with attribute charts is that the process has improved to a level where the chart becomes unusable unless the sample size becomes too big.
    2) A sampling other than 100% makes sence if it is much less than 100% (an order of magnitude less, let’s say). Let’s call r=n/N the sample-to-population ratio.
    3) You will find a failure every 1/(p*r) parts produced. (The produced part must be “failed” AND “sampled”)
    4) For example, if the defectives rate is 0.5% (you would need a sample size of 250 parts to have np=5) and the sample ratio is 5%, you will find, on average, a bad part in the sample every 4000 parts (the MTBF, where “time is” measured in “parts produced” instead of a time unit). Then the LCL would be 5.2 produced parts. The first thing to note is that if I sample 1 part every 20 (that’s 5%) the lowest TBF I can find is 20, so no point will fall below the LCL. But there are other OOC criteria. Lets take 7 points below the MTBF line. Let’s say that the process shifted in a way that it cuadrupled the defectives rate. Then I will find, on average, one defective every 1000 parts produced. That’s about half a day (4 hours) of production in the porcesses I use to deal with in my work. That means that the 7th point will be found 3 days after the process has shifted, if we have luck and all the points are bolw the MTBF line, which is pretty unlikely (the UCL with a MTBF of 1000 is 6600, well above the original MTBF). So being somehow more realistic, let’s say that the OOC signals will be found one week after the special cause. That is pretty unpractical (it would be difficult to recall one week to investigate the special cause, ant the process would have been performing poorly for too long).
    Compare that with the same chart made after 100% inspection. To begin with, you now can find points below the LCL. Also, if the process quadruple the defectives rate, you would be detecting a bad part every 50 (raised from 0.5% to 2%). Seven point in that condition would be found after about 350 hours, or slightly more than one hour of work.
    Of course that that was just a scenario I made in my imagination. If you have a process with 10% of defectives and inspect a sample every 10 parts and the process output is 1000 parts/hour, then the things change. But now you would be inspecting 100 parts/hour, in which you would find on average 10 non conforming, which is greater than 5 so a p or np chart would work fine.
    And, the most important, as I said in the previous post, I never used a MTBF chart as you proposed. So this is all just a sort of well itentioned guessing. I can be wrong with my deductions.


    Agreed. Absolutely.
    A sampling plan that is intended to detect a shift in the process will have to increase in frequency as the occurrence of the defect decreases.  A sampling plan that is intended to prevent defects from continuing to the customer will have to be at 100% so that the sample error is removed leaving only the beta risk of the test.
    You may detect a bias in my thinking.  I tend to think first of the use of control charts as an analytical tool rather than a control tool.  Of course they are used as both.  My question was to the use as an analytical tool for process characterization (assessing process capability and process stability), provide insight into the cause of process shifts, or assess the impact of a process improvement.
    This bias causes me much frustration when I see emphasis on enumerative statistics rather than analytical statistics in much of the BB training material.  As well as the tendency to teach control charts as a tool only for the control phase.  But I know that I have gone off topic.


    Stat man,
    Good day,I’ll like to ask you this question and very quick response to the question will be highly appreciated.


    You are responding to a post that is over a year old.  What do you mean by handling the p chart?  The p chart is used for defective data.  It can be used for sample groups of equal or unequal size.  It represents the proportion defective.  This contrasts with the np chart which reports out the number defective and requires the use of equal sample groups.  The c and u chart are used for defects rather than defective.  Please clarify your question and possibly a more complete answer can be provided.


    I don’t know about you Darth, but I prefer to handle them by the corners only and like to keep them in a sealed plastic cover so that they are pretty when the customer does their cursory check to see if I have SPC.


    Hi Darth,
    We were asked by one of our lecturers that ” what are the various ways of handling P-chart apart from  standardized and proportion which he gave as examples in the class. personally I have searched through textbooks and what I found was TIME PLOT,FLOW CHART,DATA COLLECTION &INDIVIDUAL CHART. What do you suggest.


    Ahhh… but Stan… if you keep them all neat and pretty, the customer will think they were done in a vacuum (office) instead of out in the “real world” of the shop floor.  That’s why you should keep them on your desk and use them for coffe cup coasters, ash trays, etc.  Just before your customer arrives for his dog and pony show, you should have a couple of maintenance guys play some trash can b-ball with them.  Make sure they understand this should be just after replacing a couple of bearings and gears on the machines…. and not to wash their hands before the game.  Then place the charts at the proper work stations.  When your customer comes, he will comment on how you SPC charts are effective shop floor tools……
    OH… be sure to use various color ink pens and pencils… and vary your penmanship when you’re filling them out.  Othewise, the customer will suspect the vacuum thing……
    And one more thing…. make sure the operators can spell SPC……
    Not that I’ve ever done any of this…….
    RubberDude – Certified Gran Master Holiday Inn Express Black Belt


    You obviously have a higher caliber customer than I am used to.


    Back in my old manufacturing days, we did preprint control charts with the aforementioned coffee cup stains, boot marks, frayed corners, etc.  My dead giveaway was if I got stoned on the volatiles emanating from the fresh ink when I walked into the room where they displayed all the control charts.  But, taking a serious stab at the original poster’s question:
    There is only one way to handle the p chart.  Formulas are fixed and computations are standard.  I wonder whether your Instructor was asking more about the different ways to handle defective data.  In some cases, proportion defective data can be displayed on an Individuals and Moving Range chart if np>5.  Maybe you want to clarify what exactly the question is.

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