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In my opinion very few companies apply Lean six sigma completely. Though several lean concepts can be applied in isolation to improve the extent and consistency of quality and production respectively.
These are some of the reasons due to which Lean cannot be implemented completely
a) Not all industries are suitable for lean. Though several Lean concepts can be implemented. Ex- A firm which manufactures40+ SKU's. Leveling the production or following Kanban can be difficult.
b) Capturing the metric is difficult too. For ex- quality in mass production factory with multiple SKU's.
c)Cost- Though some may argue that implementing lean is costly. It definitely requires some investment at the start- to train people.
d) Industries such as Steel, Rubber cannot apply lean as the WIP is too big to control production. And it is very costly to even stop the plant. However few concepts such as SMED, TPM for machines can be used.