A useful ( but not commonly mentioned) tool in Lean Six Sigma is called Little's Law.  

Little's Law describes the fundamental long-term relationship between Work-In-Process, throughput and flow time of a production system in a steady state:   As an equation Little's Law can be written as :

Inventory =Throughput × Flow Time

Little's law is both fundamental and simple and should be understood all all practitioners of Lean Six Sigma.  It is fundamental to the creation of steady flow and reduction of inventory and WIP.    Because it relates three critical performance measures of any production system, it is a basic Lean principle.  Let's look at an example : If we observe a milling machine that cuts 100 parts per hour with a queue of 800 parts in front if it, we say that it has "8 hours of WIP".  In speaking of WIP in terms of time, we are making use of Little's law, which can be thought of as a conversion of units.  Inventory is measured in pieces, flow time in hours, and throughput in pieces per hour.  Hence, if we divide inventory by throughput we get flow time.  So, to convert 800 pieces to the time it will take to process them, we divide by the throughput (100 pieces per hour) to get 8 hours.  This conversion is useful when diagnosing a plant.  If we see what physically looks like a large amount of inventory in the system, we cannot tell whether this is a signal of trouble until we know how much time is represented by the inventory.  For instance, if we see 2000 pieces of WIP in a system that produces 10 per day, this is probably a disastrous system, while 2000 pieces in a system that produces 1000 per hour is probably extremely lean.  Little's law applies to single stations, production lines, factories, and entire supply chains.  It applies to systems with and without variability.  It applies to single and multiple product systems.  It even applies to non-production systems where inventory represents people, financial orders, or other entities.  Generally speaking, there are only two requirements for Little's law to hold: WIP and Inventory Reduction:  Since Little's law implies that for a line Flow Time = WIP/Throughput, it is clear that reducing WIP while holding throughput constant will reduce flow time.  One might be tempted to conclude that WIP reduction will always reduce cycle time.  However, we must be careful.  Reducing WIP in a line without making any other changes will also reduce throughput.  For this reason, simply reducing inventory is not enough to achieve a lean manufacturing system.  An integral part of any lean manufacturing implementation is a variability reduction effort, to enable a line to achieve the same (or greater) throughput with less WIP.

News this week from the UK government is a classic lesson in Six-Sigma.  The government wants to be the first in the World to make more information about surgeon (doctor for an operation) "success rates" available to the general public in order that they can make "better decisions" about who to choose as their surgeon.   The specific information they have chosen to release to the public is the number of "successful" operations.   How do they want to define a "successful operation" ?
Their definition of success is whether the patient lives or dies as a result of the operation.  ( I am not making this up).     See these two newspaper reports if you want to see for yourself

http://www.theguardian.com/society/2014/nov/19/nhs-chief-surgeons-moral-responsibility-publish-death-rates

http://www.telegraph.co.uk/health/nhs/11240241/PIC-AND-HOLD-Just-three-surgeons-named-as-having-high-death-rates.html

Following the problem solving methodology of Six Sigma we first understand and define the problem we are trying to solve.  This is done in the "Define" phase of the six sigma problem solving methodology DMAIC.  ( D = define )

A summary of the output of the Define phase is a "Problem Statement" ....what is the problem we are trying to solve.
In this case the problem statement is something like " The citizens of the UK presently do not have enough information available to them to make good decision when given the choice as to which surgeon to choose,  in order that they make the choice of surgeon is has the greatest probability of curing their illness".   What we are trying to do is understand which of the INPUTS that we measure have a statistically significant effect on the OUTPUT (  success of curing of illness)

OK, so that sound like a reasonable problem for us to try to solve, right?

INPUTS are anything that could could have an effect on the OUTPUT (  success of curing of illness).

The next phase is DMAIC is the  Measure phase ( M = measure ).

This is where we decide which IMPUTS need to be measured  in order to provide he information we need to be able to lead us,  after ANALYSIS  (  A = Analysis )  to the  IMPROVEMENT (  I = Improvement ).


In this case, INPUTS would be items such as the following ( these are just a few examples ):

Years of experience of surgeon
Age of patient
Did the patient smoke
What was the severity of the operation
Blood pressure of patient before operation
Hospital that the operation took place in
Number of nurses in the operating theatre
Number of minutes taken for the operation
University where the surgeon was educated
etc etc   ( there are obviously hundred or thousands of possible INPUTS that could effect the OUTPUT of "success of curing illness".

So, out of all of all the thousands of different measurements that could have been made on the surgeons and their operations...how many did the UK government decided upon for measurement and to move to the ANALYSIS phase ?       They chose only ONE (1).  They focused on ONE input which is "Did the patient die during the operation"

So now the analysis ( A = Analysis) of this one measurement that we are provided with!  You see that this one input does not tell us the full story about the behavior of the output.

The IMPROVEMENT is where decide to implement in order to correct the problem statement that was developed in the DEFINE stage.    Since we do not have enough of the correct measurements, we cannot do the correct analysis and therefore cannot make the correct decision on how to implement the improvement.

The moral of this story is that if the UK government,  or the UK National Health Service ( NHS ) had understood the methodology of Six-Sigma and the problem solving framework of DMAIC then they would never have made this fundamental mistake.

What are the fundamental differences between Lean Six-Sigma and other process improvement /quality improvement programs ( TQM, TQI, ISO, EFQM etc) ?  
Lean Six Sigma overlaps with many other quality programs in many areas however there are two keys areas in which it stands unique and alone.

1.  Single Piece Flow (SPF):  
 The restructuring of business processes to get away from the "Batch-and-Queue" system and differences in rates of production of connected activities which results in "queues"  of work-in-process (WIP) and "buffer inventory".

With SPF work activities change their throughput rate depending on the demand rate for the product or service by the customers.   This one rate of production by all activities to match customer demand is called the Takt Time.  Items are started and finished one at a time by Work Cells instead of once part of the product being completed by one department and then passed on downstream to a different department.

Single Piece Flow is counter-intuitive and also can be more difficult to manage (with traditional management tools)  which are two reasons why it is still not implemented in many organizations   However when the right management tools and techniques are used (  Visual Factory,  Work Cells, Takt Time, Pull, Just-in-time, Kanban, 5Ss, Poke Yoka )  then Single Piece Flow can reduce cycle times by as much as 90%, is more flexible so can respond more effectively to the voice of the customer.

2.  Measure,  Analysis and Understanding the Standard Deviation of all aspects of production:
We all know about AVERAGES for our business processes ( average production per hour,  average number of defects per shift,  average time per call ...etc ) but that is only half of the picture.   What we also need to measure and analyze is the Standard Deviation (SD) of values in all aspects of our business.    With the tracking of standard deviation together with the knowledge that  68% of all values fall within plus/minus 1 SD, 95% within plus/minus 2 SD, 99.75% within plus/minus 3 SD ...etc is a breakthrough management tool for any business to implement.

Defining the goal of Lean Six Sigma in 4 sentences :  Identify and understand the true value that the customer needs from a product of service and optimize the efficiency and effectiveness of the processes needed to produce that product or service. The optimization is achieved by reducing or eliminating waste in each process and creating steady flow and flexibility of production.  Production of product or service should match customer demand.  Reduce variation in the outputs of each process so that the products and services are free of defects and consistently satisfy the requirements of the customer.