Why this level matters
In Level 1 you met Lean and Six Sigma as two separate traditions. Lean focuses on flow and the removal of waste. Six Sigma focuses on reducing variation and defects with data. This level shows how a single project uses both, and introduces the idea that links them: Y = f(X).
Running example for this course: a parts distributor promises customers that every order will be dispatched within 3 working days. You will come back to this order-to-dispatch process at every stage of the course.
Task 1: Understand Y = f(X)
Y = f(X) is read as "the output is a function of the inputs."
- Y is the output or result the customer cares about, such as order-to-dispatch time in days.
- X stands for the inputs that drive Y: staffing, stock availability, how orders are entered, approval steps, picking method.
- f is the relationship between them. You often do not know it at the start. Finding out how it works is the purpose of the project.
The practical point: you cannot change Y directly. You can only change the Xs. Shouting "dispatch faster" at a team does nothing. Fixing the stock check that holds orders back does.
Two more ideas to keep in mind:
- Controllable Xs are inputs you can set, such as the number of pickers on a shift or the order-entry template.
- Noise Xs affect Y but are hard or impossible to control, such as weather that delays inbound deliveries.
Usually only a few Xs have most of the effect on Y. Later stages of the course show you how to find them with data. For now, just list the candidates.
Task 2: Write your own Y = f(X) statement
DO this for a process you know well:
- Name the output the customer experiences. Make it measurable: "time from order received to dispatch, in working days", not "good service".
- Brainstorm 5 to 8 inputs that could affect it. Cover people, methods, materials, equipment, information and environment.
- Mark each input C (controllable) or N (noise).
- Write the statement in this form:
Dispatch time (Y) = f(stock availability, order-entry errors, credit-check delay, pickers per shift, carrier collection time, inbound supplier delays [N])
Check: every Y must be something you can measure, and every X must be something that happens before or during the process, not a result of it.
Task 3: See why speed alone or consistency alone fails
The customer feels the whole distribution of results, not the average. Compare three teams handling 10 orders each (dispatch days):
| Team | Dispatch times (days) | Pattern |
|---|---|---|
| A | 1,1,1,1,1,1,1,1,6,6 | Fast on average but variable |
| B | 4,4,4,4,4,4,4,4,4,4 | Consistent but slow (waiting and extra approvals) |
| C | 1,2,1,2,1,2,1,2,1,2 | Fast and consistent |
Spreadsheet task (Excel; Minitab gives the same statistics):
- Enter each team's 10 values in one column (A2:A11, B2:B11, C2:C11).
- In row 13, calculate the mean:
=AVERAGE(A2:A11). - In row 14, calculate the spread:
=STDEV.S(A2:A11). - In row 15, count late orders:
=COUNTIF(A2:A11,">3"). - Copy the formulas across to columns B and C.
Check your results:
| A | B | C | |
|---|---|---|---|
| Mean | 2.00 | 4.00 | 1.50 |
| Standard deviation | 2.11 | 0.00 | 0.53 |
| Late (>3 days) | 2 | 10 | 0 |
What the numbers show:
- Team A looks good on average (2 days), but 2 customers in 10 still get late orders. That is a variation problem, and it is where Six Sigma tools are strongest.
- Team B is perfectly predictable, and every order is late. The cause is waiting and steps that add no value. That is a flow and waste problem, and it is where Lean tools are strongest.
- Team C is fast and consistent. That is the aim of Lean Six Sigma.
Waste and variation are also linked. Variable arrivals and variable task times create queues, and queues are waiting, which is a waste. Waste such as rework adds variation. Fixing only one often leaves the other in place.
Task 4: Decide which toolkit a project needs
Use the symptoms to choose a starting point:
- Mainly Lean when the problem is long lead times, queues, handoffs, excess inventory or obvious non-value-adding steps, and the cause is fairly clear once the process is mapped.
- Mainly Six Sigma when the problem is inconsistent results or defects, the causes are unclear, and you need data and statistics to find which Xs matter.
- Both (most projects) when the process is slow and unpredictable, like a mix of Teams A and B. Lean removes the waste so the flow is clear, and Six Sigma reduces the variation that remains.
DO: for your Y = f(X) statement from Task 2, write one sentence saying whether the main pain is speed, consistency or both, and which toolkit you would start with.
Key takeaways
- Y = f(X): the output (Y) is driven by inputs (Xs). Improve Y by finding and changing the few Xs that matter most.
- Separate controllable Xs from noise Xs.
- Judge a process by its average and its spread. Use AVERAGE, STDEV.S and COUNTIF in Excel.
- A fast but variable process still lets customers down, and so does a consistent but wasteful one.
- Lean targets flow and waste, and Six Sigma targets variation and defects. Most real projects need both.