Statistical technique sought for predicting replacement of perishable tooling



Preventive and Predictive tools seem to be taking on greater importance in manufacturing. I am seeking advice as to what appropriate statistical tool to apply to predict the optimum time to replace perishable tooling in a manufacturing process.

Example: a 6 mm drill bit is required to make a hole in a part when nested in a fixture. At present, the maintenance department replaces it when it breaks. Perhaps a means exists to gather data of when the tooling breaks, and then analyse it in order to predict when this might happen again, and proactively schedule a replacement rather than reactively stop the machine to replace the bit.

(example, over 10 replacements, we tabulated the number of parts that the drill bit made before it failed and needed replacing: let’s say:


Any advice appreciated.

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M Greenaway

I would remove as many variables from the process as possible. For example ensure that the drilling occurs using the same drill type, material/part, coolant, speeds/feeds, etc.

Then collate data on time to tool breakage. Count how many occurrences at suitable time periods. Arrange the data in a histogram to check for normality. Calculate mean and standard deviation. Take 3 standard deviations from the mean time, and use this value as your tool change time.

Repeat for other process settings/materials.


Very good advice from Martin.

Consider also the cost in replacing the bit and the time taken to make a replacement. What are the effects if the tool does break? Remember that replacing the bit before it breaks may not always be the best solution. You could change the bit after each part and never have to worry about breaking another one. That wouldn't be any good at all. The trick is to replace the bit just before it breaks. If you could do that every time you would be home.

The numbers you posted show a large variance in tool life and setting a "change" time to the average may be costing you more in "unused" tool life than you are saving.

Depending on the consequence of breakage, you might be better off letting it break. Just because it is "in fashion" doesn't mean it is best for your situation. Consider all sides first, then decide.

Just my opinion.


M Greenaway

True Dave

I would imagine the consequences are potentially the scrapping of an expensive part if the drill breaks and jams in the product. In a previous life we used to have to send stuff out to get broken drills spark eroded from parts where the cost of repair was less than the cost of scrap.

Bill Ryan - 2007

Please understand that I am not a statistical guru but the 10 data points you supplied show me that "you can't get there".

Ave: 8280
StDev: 2705

Just those two numbers "tell" me that you cannot predict tool breakage (which is in line with my experience on our floor). My feeling is that you need to do some Root Cause Analyses if breakage is what you are trying to predict. In that respect I agree with Martin. To paraphrase him, you may want to look at tool material, speeds, feeds, part fixturing, etc. (some type of DOE might be justified).

I only use SPC to predict tool WEAR.

Don't give up hope. There are many other "Covers" (stronger in statistics than me) who may be able to give you some other avenue to pursue (and I'll probably learn something I've not thought of).


Bill Ryan - 2007

Sorry, I didn't see Dave's reply before I posted.

You bring up a great point regarding overall cost. As long as there is something in the "system" to catch a broken tool and the risk of sending an unmachined hole to the customer is, truly, minimal, it may be in the best interest to "let it break".


Dave Strouse

Brfeak Even

Your data are best described by a Weibull distribution with scale factor 9233 and shape 3.37. This is very close to a normal distribution.

If you plot it on normal probability paper, you won't be far off.

I suggest you read "Out of the Crisis" , Chapter 15 on minimum cost to sample. You have an analogous situation here. Should get some good ideas from the good Dr.

You can predict to some degree when a tool is likely to break and optimize that curve with the total cost to replace versus the cost to break as others have suggested.

If you really don't see how to do this and the perceived cost to continue the current situation is large enough, it might pay to consult through a local university for an optimization guy. Most industrial engineering departments will put you on the right track to find the best solution.

Good LUck!



Thanks to all who took the time to reply to my query and for your thoughtful replies. Let me tell you all where I am coming from.

Actually the parts we make are relatively low cost, high volume automotive plastic parts. The consequence of a single part in several thousand having an absent or wrong sized hole are well known to anyone supplying Tier Ones and OEMs. Lacking a hole on a single $2 part means a quality rejection, with sorting costs and administration costs of about $5000 in debit memos issued to us by our customers. So the charges are there regardless of whether your PPM is very low (ours is very low), or whether the customer found the inconvenience to be major or minor in nature. The customers are demanding 0 PPM. Zero. Not 10, not 5, not 1. Zero. And whether that is statistically or physically achievable is not open to debate. So we are finding that many robust manufacturing processes are failing due to special causes, like a cutting tool drifting or wearing, and inspection process catches it most of the time , but sometimes it “escapes”.
Perhaps I was naïve and optimistic for thinking that there might be a reasonably simple means of predicting failure simply by gathering cycle data. – by the way, the numbers I gave were made up , and I deliberately invented a large spread to show the perception of unpredictability of the process. So my quest was for analytical tools that were relatively simple to implement – i.e. report the number of cycles elapsed when replacing a wearing tool….then hopefully having enough data to plug in and come up with a better means of prediction. Unfortunately, we do not have the resources to analyse each individual fly cutter or drill bit and identify the sources of variation leading to tool wear. My hope was to introduce a predictive tool to strengthen the maintenance department - who like most maintenance depts are stretched very thin, and any training they would receive on numerical methods would need to be tailored to their level of understanding and appreciation.

I have read some buzzwords: Weibull analysis, MTBF, so I know such tools exist…Being an engineer by training, but by no means a PhD or expert in Stats, I sought out textbooks, but I found the explanations baffling. Yet supposedly some Stats packages can do this analysis. Maybe there is something that I am missing. Am I in a hopeless situation? Or can someone throw me a lifeline?

Thanks to Dave …. I will go and see what Dr. Deming said in Chapter 15.

Rick Goodson


There is a danger in throwing 'made up date' at Cove people. We tend to take it as real and try to do something with it. i hope Dave and Bill didn't spend too much time analyzing it.

Yor mention picking up on some 'buzz words'. Actually those 'buzz words' are very useful and powerful statistical and analytical tools when used properly. I would caution, no strongly caution you against just looking for a software package that can do the analysis for you. Without understanding the underlying theory you can do more damage than good. Dave S. mentioned the Weibull distribution because he knows that it is a tool often used in reliability engineering to predict failure, and that for the most part the distribution does not care what the parent population looks like. (Not to put words in your mouth Dave but I have read enough of your posts that I think I know where you are coming from). The software is not much help however if you don't understand what a Beta equal to 1 is versus a Beta equal to 3.3.

Your second post helps us to understand your situation. If you are in a situation where you can not tolerate any defects you probable should not be trying to predict when the prrocess will fail. I would suggest you address mistake-proofing so that the process can not pass a defective unit. There are automated methods for detecting the presence or not of a hole in a material. Based on the extremely high costs you incur for a defective you should be able to justify the equipment. I also suggest you look at the other ideas mentioned to control the useful life of the drills and that you look at a DOE to determine the factors that affect drill life and then start improving the process.

Dave Strouse

Still Possible


I still think you are on a good track. It is just that you will need to do the analysis of the cost of letting an "occasional" breakage/wear occur versus the cost of changing at some preset time.

For example, I believe that many faciulity maintainence groups in large installations routinely change light bulbs at a preset time. They base this on the data from their failure rates and the cost of doing the replacement as predictive maintainence rather than reactive. It's usually cheaper to send out a crew to do this on a given day when they are close to the time the bulbs will fail rather then responding as they burn out. Somebody in facilities engineering could probably shed some light on this.

The analysis I did was through a software package -MINITAB. I just cut and pasted your data into it and the numbers were generated in about 30 seconds that told me the distribution model with the best fit. Then I could make a graph with confidence intervals on the failure times. For youir cribbed date, less than 15% of the population will fail before 4000 hours. So the economic question becomes"Is it cheaper to replace a bit as it hits 4000 hours (and absorb the sorting etc costs to rectify the lot on the 15% of those that will fail before that) or let each go to failure and get the costs on each bit?" You can solve the problem once you collect the real data.

These problems interest me, so I took a little time to do it. You are correct that using a software package is almost a neccessity. It would have taken me 30 minutes rather than 30 seconds to do this problem by hand. However, Rick;as usual, is correct in that you must know what the numbers mean that you generate.

Good luck in your quest for qulaity.

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