Web Handling & Converting

From the previous post we noted that nearly everyone has an idea of the costs of maintenance.  (We used cover grinding as an example, but the application is much wider than this).  The more frequently you grind the greater the maintenance costs.  If that is the only cost management has to work with, the result will be predictable; pushing things till they are obviously broke.  More importantly from the previous posts we noted two things.  First is that we can for many situations quite easily tabulate the costs of NOT grinding as an increase in defect rate.  Second, that if you grind more frequently that the costs of NOT grinding decrease.

We can put these two ideas together to do an economic optimum analysis.  We plot these two costs against maintenance interval (MTBS from the previous post).  The costs of grinding go as 1/r; in other words concave upward going to infinity.  The costs of NOT grinding are also concave upward going to infinity, but the high costs are seen when you push component lives.  The economic optimum regrind inteval is the minima of the sum of the costs of grinding and not grinding.  (This is not, as some think, where the curves intersect but rather where the slopes are equal but of opposite sign).  Those of you who follow my work will recognize this as just another application of the most important paper I’ve ever written, Optimization by Integrating Engineering and Business Models.

So, while this might seem to be a daunting bit of calculus, it is not.  Sometimes you can get an approximate answer with a back of an envelope calculation.  I had on one occasion helped troubleshoot corrugations on a paper machine; their number one defect and one that approached $1M/yr (not uncommon in the paper industry).  Here, as not unexpected, corrugations increase as the calender roller wore.  A quick calculation indicated they should regrind more frequently.  I asked them why they pushed life so long.  They said that the cycle time was limited by how quickly the spare roller could be shipped to a precision grinding shop, reground, returned and returned to service.  A quick calculation showed they could easily pay for a third roller AND increase the regrinding frequency by a reduction of corrugations whose costs and parentage was well known.