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Cp and Cpk for little groups

Discussion in 'SPC - Statistical Process Control' started by Future engineer, Dec 30, 2020.

  1. Future engineer

    Future engineer Member

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    Hello everybody, I'm new here and I'm not native English speaker so I'm sorry for mistakes and describing some concepts instead of using professional vocabulary.
    I'm writing my engineering project and I've got a problem. I want to know how fast a process becames unstable while tools wears away to put new tools. I was trying to make measurement and every thee measurement (five samples in every measurement) count cp, cpk and cm and check how fast they became too low. I know it's a strage method but the company I cooperate didn't let me use any device measuring force at tools etc. So I was thinking that it would be a good idea. I'm not studying quality engineering but mechanical engineering so I don't know quality tools well. I wasn't albe to use laboratory as often as possible and I was doing up to three measurments a day (I don't know if it's an important piece of information so I'd better tell about this). I have no idea why but Cp are uncredibly high, there is no sign of wearing away of the tools (but they WERE really wearing out). I've read that to counting cp and cpk I may use 50, 100 and more groups. If I use very little number of groups, do the indexes increace? Is it possible that in my situation accetable level of Cp should be (for example) 3,6, not 1,67? What stranger, cpk increases instead of lower (the tools are kind of die). Can I still "save" my project or I made unforgivable mistake at the beginning?
     
    Last edited: Dec 30, 2020
  2. Golfman25

    Golfman25 Well-Known Member

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    Not sure Cp or Cpk will really get you what you are looking for. You're probably better off doing a control chart and looking for trends that would indicate tool wear (ie; measurements consistently heading towards the high or low spec limit).
     
  3. Andy Nichols

    Andy Nichols Moderator Staff Member

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    Have you done any studying on Statistical Process Control basics at all? Read any good books/online information on this subject?
     
  4. Future engineer

    Future engineer Member

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    I tried but I did't have much time and much support, my method was accepted but in fact in that company most of employees at engineering posts aren't engineers by education. They use some statistic tools but not always fully understand them. I did't learn a lot about quality tools at the university, too.
     
  5. Andy Nichols

    Andy Nichols Moderator Staff Member

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    You will only obtain full understanding if you devote some time to studying. Anyone can come here and tell you, but that isn't understanding. What you do will be meaningless in the future, as a result.
     
  6. Future engineer

    Future engineer Member

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    Yeah, I know and I'm going to understand it but in fact I have very little time now. I need to know if my data is usefull or useless. I want to be sure if I didn't waste 3,5 years of my life because of false assumption of my engineering project.
     
  7. Bev D

    Bev D Moderator Staff Member

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    PLOT THE DATA (EACH INDIVIDUAL MEASUREMENT) IN TIME SEQUENCE OF MANUFACTURE AGAINST THE SPEC LIMITS. That is all you need to do. You can post the data here and we will help you.

    Cp CANNOT show any trend. Look at the math. It is only a ratio of the within sample variation vs teh tolerance width. Without regard to the average. CP, Cpk, Pp and Ppk are non-sensical summaries. The experts at quality engineering will tell you to plot the raw data in time series first. Then look at the data and THINK about the data.
     
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  8. Bev D

    Bev D Moderator Staff Member

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    I also reiterate what Andy said. Quality engineering tools are as complicated as Mechanical engineering. you must study and practice to understand. You are in college NOW is the time to start a continual life of studying and learning. attached is a complete list of resources to get you started. The links provide access to references that are FREE. As a mechanical engineer you will still need quality engineering tools.
     

    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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  9. Future engineer

    Future engineer Member

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    I know that Cp doesn't show any trend but lowering of Cp may show that the process is going to be unstable, isn't it? If I calculate Cp and Cpk for a strech of time and I calculate Cp and Cpk for other strech of time I should be albe to comparise how stable was that process in those periods. Do I think correctly? If not, how can I calculate how the "quality" of the process changes?
     
  10. Bev D

    Bev D Moderator Staff Member

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    PLOT YOUR DATA IN TIME SERIES. Math is not going to help you when it’s the wrong math. If you want to learn anything forget the mythology and read about statistical process control from the masters not the hacks.
     
  11. Future engineer

    Future engineer Member

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    Of course everything is ploted in time series etc. but if not by Cp and Cpk, how can I find a moment, when the process BECAMES unstable, before number of scraps increases? I'm reading some of your sources.
     
  12. Bev D

    Bev D Moderator Staff Member

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    When I was in university the professors I disliked the most expected me to study and think and extrapolate on what they had lectured. Their homework and tests always had questions that they hadn’t yet lectured on directly. The nerve of them! They were the best educators I ever had. I have now become much like them in my instruction. When we don’t learn to think we can only remember and apply tools and methods by rote. We never learn if we don’t think and practice and understand.

    Cp and Cpk are mathematical summaries of variation – but they are not complete pictures of variation. (It is nonsensical to try to express and then understand variation with a single number). Any professional quality engineer worth their title will answer any question regarding Cp and Cpk interpretations by asking to see the time series data. There is no more powerful, unambiguous, analysis that cannot be misinterpreted. You can SEE the trends, shifts, cycles and all components of variation.

    Cp and Cpk were never intended to be calculated on small samples. They were intended (and mathematically designed) to be calculated on very large sample sizes that represented a long stream of process data. (weeks, months or even years of data) to calculate Cp/Cpk on individual small subgroups is a gross misuse of the formulas. It is like trying to trim your toe nails with a chain saw.

    Cp and Cpk cannot and do not reveal any instability in the data. Only a time series plot of the data can do that. A Control chart (assuming that you have a rational subgroup scheme and appropriate sampling frequency) can show you when a process becomes “unstable”. And actually, a control chart only detects non-homogeneity. “Stability” is a human “operational” definition; it is not a law of physics.

    If you have tool wear, then you have a non-homogenous process. A non homogenous process is one where the factor(s) that control the location (average) are not the same factor(s) that control the variation (standard deviation). Tool wear is a systemic (yet ‘stable’ = predictable) cause. It will exhibit a predictable pattern: a ‘drift’ or steady increase – or decrease, depending on the feature – until the parts are out of specification. SO, PLOT THE RAW DATA IN TIME SEQUENCE. PUT THE SPECIFICATION LIMITS ON THE CHART. LOOK AT THE PLOT.

    If this confuses you then you can post your data here along with the specifications and a description of your sampling scheme and we will look at it.
     
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  13. Future engineer

    Future engineer Member

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    I agree with you but if you extrapolate your knowlage too much, you may come to wrong conclusion. Sometimes direct asking is necessary to verify own logic.

    Okay, so I won't use Cp and Cpk in my analyse. I'm surprised that the company agreed at my interpretation of it. When I was reading your sources, I got know some tools. I'll use moving average and CUSUM chart. Will it be okay? Wearing out of the tools is quite slow process and parameters change lightly, too. Have you got any tips for me? I was reading some instructions but I'm not sure of some things. I was measuring ten pieces in every sample. I put all the measurments in the calculating sheet and counted average. When I count average moving range, should I count it from averages of samples or from "previus" measurments? And why can't I use "tarditional" standard deviation, why have I use "simpled" formula? And is it good that I use "quantity of pieces" instead of "time" in charts? The process isn't constant, changing of tools is very often.

    Willingly but if somebody in the company would see it, I'd have serious problems. I'm not allowed to show widely any data from the firm and my engineering project will have to be accepted by the company before marking.
     
  14. Andy Nichols

    Andy Nichols Moderator Staff Member

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    Right, but you must, first, understand the subject to be able to apply "logic" and make your case. Simply asking a question without any background to how you arrived at a conclusion - putting the effort in to study first, then derive a question - isn't "logic".
     
  15. Bev D

    Bev D Moderator Staff Member

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    The EWMA "might" work. But without seeing the time series data we cannot say for sure. I really don't think it's the right tool as it will most likely show the drift in tool wear long before you actually need to change the tool. The articel you want to read about tool wear is:
    Sarkar, Ashok; Pal, Surajit, “Process Control and Evaluation in the Presence of Systematic Assignable Cause”, Quality Engineering, Volume 10(2), 1997-1998.
    Unfortunately you will have to purchase it as there is no free version.
    an alternative free article that describes systemic drifts in general is: "
    Wheeler, Donald, “Can I Have Sloping Limits?”, Quality Magazine, May 1999 https://elsmar.com/elsmarqualityforum/attachments/can-i-have-sloping-limits-doc.2845/

    You persist in trying to get math to solve your problem. It can't without knowledge of the actual physics of what is happening.
    I'm sure that your company approved the use of Cp and Cpk. These process capability ratios are mathematical myths and they probably don't understand it either.
    the moving average is calculated by taking the average of subgroup 2 - the average of subgroup 1. then the average of subgroup 3 - the average of subgroup 2 and so on.
    the reason for not calculating the standard deviation directly is that IF the process is homogenous THEN the within subgroup standard deviation will predict the total standard deviation. This is the fundamental essence of statistical process control. (and there is a LOT to understanding why this is so. you can either blindly accept it or do the research and practice to understand it yourself. some of the articles in the list I provided cover this topic.) teh x-axis doesn't have to be clock or calendar time as long as the plot is in sequential order of manufacture with the oldest parts on the left and the youngest parts on the right...

    But more importantly, you have stated the crux of your Problem: "Wearing out of the tools is quite slow process and parameters change lightly, too" yet "The process isn't constant, changing of tools is very often" and "number of scraps increases". The first question you need to answer is do you actually have tool wear driving scrap? is the scrap of the tools or the parts? are they changing the tools because the parts are out of spec? it is illogical to say that tool wear is very slow but changing of tools is frequent...
     
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  16. Miner

    Miner Moderator Staff Member

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    You can anonymize the data by adding or subtracting a constant from all the original values.
     
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  17. Future engineer

    Future engineer Member

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    Thank you Bev D, you helped me so, so much, you're so engaged and patient! You're an angel! And your sources (including the newest source) are fantastic! Are you an academic teacher?

    I don't know if I want to be a quality engineer after my internship and project but I WANT TO understand SCP but now I can see that I've learnt many things wrongly :( It's hard to learn everything in my own but I have to. I'm mad that my university of technology reduces teaching about quality to teaching ISO 9000 norms and how to try to look for potential problematic production processes. No SCP! No quality tools! Um...

    Ew, it depands on scale :D Problematic tools wear out much faster than simmilar tools in the company used to machining other matherials so that tools have to be repaired and replaced much more often that in simmilar processes. This wear is quite fast (in scale of the factory) but not sudden, dimentions of the tools (and so made parts) change subtly between measurments so that one day number of scrap of parts becames bigger ang bigger. Dimension tolerance is low. Okay, now I can see how my descriptions were looking like :D

    Thank you all again, especially you, Bev D.
     
  18. Andy Nichols

    Andy Nichols Moderator Staff Member

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    How did we get here, from your original question about employing SPC and group size? Of course tools wear differently - it's a function of all manner of factors. What are you trying to do? Applying SPC without a framework of related process analysis tools, is unlikely to be beneficial. Doing SPC just by itself isn't going to work.

    What is your goal here?
     
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  19. Future engineer

    Future engineer Member

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    To write my engineering project and not to disturb and embarrass people with my stupid questions anymore. Really.

    I've got one more, maybe not as stupid as at the begginning question. When I make a cumsum chart and a malfunction happen, I can "restart" the chart because disturbance in dimentions or other parameters aren't caused by process but technical problem. Can I do something simmilar with moving average chart?
     
  20. Andy Nichols

    Andy Nichols Moderator Staff Member

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    OK, so let me help you. We are here because some of us actually ENJOY answering people with their questions! Secondly, as the old saying goes, there's no such thing as a stupid question! We do, however, want you to learn so that you can go away without the need to keep coming back and asking the same questions over - that IS stupid. Hence some of our replies require you to put in some effort on your part. "No pain, no gain".

    Someone will be along to answer the tech stuff...
     

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