"Lean Math." Now, there's a name that evokes passion in the heart of every lean practitioner!?
But, the truth is effective lean transformations require some level of math, whether it's the often deceptively simple calculation of takt time, sizing kanbans, calculating process capability, or anything in between. It's hard to get away from math-free lean and certainly math-free six sigma!
Lean Math is not intended to be some purely academic study and it does not pretend to be part of the heart and soul of lean principles. Rather, it's a tool and a construct for thinking. Here we want to integrate lean math theories and examples with experimentation and application.
In the end, we hope the blog, along with its fledgling community, lives up to the tag line, "Figuring to improve."
Life happens. Sometimes it rains on wedding days. Sometimes a supplier misses a ship date, and sometimes there are glitches in our processes. The challenge for lean practitioners is what to do about this – especially since all of these things could happen.
It all started when my colleague and I noted that we had used the same data to calculate Cpk, but ended up with different results. This led us down an Alice in Wonderland-like path of Google searching, Wikipedia reading, and blogosphere scanning. After several days of investigation, we determined that there was no consensus on how to properly calculate estimated standard deviation. Knowing that there must be a misunderstanding and that this should be purely an effort based on science, we decided to get to the bottom of this.
Did first-class passengers on the Titanic get preferential treatment during the evacuation? James Cameron’s movie certainly seems to suggest so, but let’s look at the data.
| Survived | Died | |
| First class | 203 | 122 |
| Third class | 178 | 528 |
Days inventory on hand, also known as a days of supply, along with inventory turns, is a measure of inventory investment. While turns may be one of the most basic measures of an organization’s “leanness,” days inventory on hand perhaps helps lean practitioners better visualize the magnitude of (excess) inventory and its impact on a value stream’s lead time. This is especially applicable when the notion of inventory extends beyond parts and finished goods to transactional (i.e., files, contracts, etc.) and healthcare (i.e., tests, reports, etc.) value streams.
Full time equivalent(s), commonly referred to as FTE(s), represents the number of equivalent employees working full time. One full time equivalent is equivalent to one employee working full time. Typically, FTEs are measured to one or two decimal points. FTEs are NOT people. Rather, FTEs are a ratio of worked time, within a specific scope, like a department, and the number of working hours during a given period of time. As such, an FTE often does not equate to the number of employees actually on staff.
Flow is a key lean principle. We should relentlessly pursue a state in which value flows smoothly, without interruption to the customer. But how can this be achieved? Assuming that we have adequate system stability, repeatability, and other important "ilities," as well as a design and culture that facilitates continuous flow (admittedly, really difficult stuff), the answer is amazingly simple – match capacity to demand. So, if you have 10 customer requests your capacity should be 10 customer requests, and if the demand is 1,172 customer requests the capacity should be 1,172 requests.
In the words of my friend and colleague Larry Loucka, “graphs are math.” Graphs often serve as effective visual process performance tools. Typically, these types of graphs fall into the metric category. As reflected in the supporting concepts of the fourth dimension of the Shingo Prize model, good metrics should: 1. “measure what matters,” 2. “align behaviors with performance,” and 3. “identify cause and effect relationships.” Real lean drives measurable operational and financial performance improvement.
Analysis of Variance (most commonly referred to as ANOVA) is a common statistical test that compares the averages of several sets of data. It is unlikely for datasets to have the same average, and an ANOVA test quantifies how likely those observed differences in occurred by chance. It is a really useful test because we frequently find ourselves comparing averages of different datasets.
Maybe you have a day by hour chart, or sales plan vs. actual sales data and you want an easy way to decide when to take action - consider the simple Cumulative Deviation. First you need some data, two variables that you want to compare. Here in this spreadsheet example we have Plan and Actual for eight time periods.
Value stream analysis is an effective way to identify improvement opportunities within a product or service family’s value stream, envision a leaner future state and develop an actionable value stream improvement plan to achieve the future state. It's bread and butter stuff for the lean practitioner. Most folks are well acquainted with the value stream map’s lead time ladder. And many people are familiar with the concept of rolled throughput yield.
