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Full Question:

During a Lean Six Sigma review, a Green Belt stated that the population of motors meeting a certain acceptance criteria had been improved by 6%. Last year, we tested 1,200 motors and 800 of them met the acceptance criteria. This year we tested 1,100 motors and 855 of them meet the acceptance criteria. What is the X? What is the Y? What is the appropriate analysis tool to use?


The “X” in this example is the year, so you’ve got last year and this year as the two values of X. The “Y” is the yield or % of motors deemed “good”. If you just looked at the proportions, last year there were 66% deemed good and this year there is 77% deemed good. That looks like they did a bit better than the goal of a 6% improvement. But your second question refers to the right analysis tool to use. For that you’ve got two options.

  1. The is discrete data (pass/fail). If you want to see if there is a statistically significant improvement over last year, one option is to conduct a 2-proportion test. The 2-proportion test would tell you if there is “no difference” between last year and this year, or if “there is a difference.” If you are using Minitab, you can enter the total count of the motors and the total count of the “good motors” for both the baseline and the improvement. If you have a P-value less than .05. that means that there is a statistically significant improvement.
  2. Another option is to use the Chi Square test, and for that you would create a two by two matrix of Good units/Bad units over Last year/This year in Minitab or QI Macros, etc.. Again, if the P value is below .05 then the improvement is statistically significant!

Tracy O'Rourke

Tracy is a Managing Partner at She is also a Lean Six Sigma Green Belt Instructor at UC San Diego and teaches in San Diego State University’s Lean Enterprise Program. For almost 20 years, she has helped leading organizations like Washington State, Charles Schwab and GE build problem-solving muscles.

Elisabeth Swan

Elisabeth is a Managing Partner at For over 25 years, she's helped leading organizations like Amazon, Charles Schwab and Starwood Hotels & Resorts build problem-solving muscles with Lean Six Sigma to achieve their goals.