# Category Archives: Math

Posts including calculations and formulas.

# The Kingman Formula – Variation, Utilization, and Lead Time

The lead time of a system is heavily influenced by both the utilization and the variation. There are approximations available to estimate this relation, and one of them is the Kingman formula. In this post I would like to introduce you to this equation and describe the fundamental understanding of it. Luckily, you don’t really need the formula for your daily dose of lean. The equation itself has little practical use. However, this relationship is important for understanding the behavior of your production system. While you won’t use the Kingman formula to evaluate your production system, understanding the equation will help you in tweaking your system in the right direction.

# On Running Changeovers

Changeover times and their reduction are popular topics in lean manufacturing. In this post I would like to introduce the idea of running changeovers for production lines. The idea behind it is simple, and probably many of you do it already. Nevertheless, I have found little info on it online. I also would like to go into more detail on the benefits of a running changeover in comparison to the alternatives. Continue reading On Running Changeovers

# The Many Different Flavors of the OEE

If imitation is the sincerest form of flattery, the OEE (Overall Equipment Effectiveness or Efficiency) is indeed one of the most appreciated measures in lean. I counted at least eight different variants and adaptions of the basic OEE – although let me tell you that I am not impressed with all of them. Many of them seem to be theoretical academic constructs with little meaning for your shop floor. Also, identical acronyms and similar terms are often used in a completely different way, adding quite a bit to the confusion. On top of that, I think the OEE is used way too much in industry where it does not make sense, and many OEE numbers are heavily fudged. Anyway, let me show you the many different flavors of the OEE. Continue reading The Many Different Flavors of the OEE

# Good and Bad Ways to Calculate the OEE

There are different ways to calculate an OEE. I know of at least three different ways. However, some of them are easier and more practical than others.

Maybe you have seen a formula similar to OEE = A x P x Q. I see this formula often, but for me it is a very impractical way to calculate the OEE. Let me show you why by comparing the three different ways to calculate an OEE.  Continue reading Good and Bad Ways to Calculate the OEE

# How Product Variants Influence Your Inventory

The sales & marketing department often aims to create more and more product variants to target even the smallest niche in the market. Yet, it is common wisdom that more variants also mean more inventory.

However, the relation is not quite as clear cut. In my last post I wrote about the Relation between Inventory, Customer Takt, and Replenishment Time. The relation is similar for variants, and it all depends on the ratio of the customer takt to the replenishment time.  Continue reading How Product Variants Influence Your Inventory

# The Relation between Inventory, Customer Takt, and Replenishment Time

Inventory is helpful for a fast delivery of goods. If you have it in stock, you can deliver to the customer right away. In that respect, more inventory is better. Yet, at the same time, inventory creates cost, some visible, some more hidden. Hence, one of the goals of lean is to reduce inventory and therefore reduce cost. During my research I stumbled on a very interesting relationship between inventory, customer takt, and replenishment time. Let me elaborate … Continue reading The Relation between Inventory, Customer Takt, and Replenishment Time

# Cycle Times for Manual Processes

In my last two posts I described how to measure cycle times. However, for manual processes measuring cycle times is quite different, since the humans that are measured usually strongly dislike being measured. Therefore, it is difficult to measure it directly. There is an alternative to calculate it, but this also has lots of pitfalls. Let me explain you a bit about human psychology, and how to measure manual cycle times. Continue reading Cycle Times for Manual Processes

# How to Measure Cycle Times – Part 2

This is the second post on how to measure the cycle time of a process. Again, the cycle time is the fastest repeatable time in which you can produce one part. Hence, as part of a series on manufacturing speed measurements I continue with more details on what cycle times really are. This is the second post on how to measure cycle times (post 1 here), with an additional third post focusing on the details of manual cycle times coming up next. Continue reading How to Measure Cycle Times – Part 2