Takt time seen from a six sigma point of view

Lean Manufacturing concepts and Six Sigma statistical tools are complementary techniques. Together Lean Six Sigma as we tend to mention for a few years now, they form a very powerful and holistic approach to problems solving and process continuous improvements. However they are some incoherence in their joint application which if we take into consideration may change the entire perspective of a value stream.

Let us highlight the incoherence we mentioned. In lean when we talk about pull system the first thing that comes in mind is kanban. Now kanban has rules and formulas. The size of the kanban or in plain English the number of parts to have available in the replenishment system is calculated from a formula which take into consideration fluctuations of demand because we all know that demand is not stable on a daily basis. The basic formula is:

Kanban size = average daily demand * replenishment time * (mean average deviation of demand +1)

And this is perfectly fine as we all know in Six Sigma that mathematical mean or average is not a good indicator of a set of samples. For example 0 and 100 has a mean of 50, but so do 49 and 51, and as you may see they are two completely different set of numbers. Therefore sig sigma belts uses central tendency to characterize a set of measurements of numbers. Central tendency is given by mean and standard deviation.

Having said that lean calculates its most fundamental value stream and line balancing indicator, called Takt Time, using and average concept only.

Takt time = available daily time / average daily demand

So in one formula, the kanban formula, as demand varies in time, we factor in the variation. However in the other formula, the Takt Time, the same demand variation is not being taken into account. From a six sigma point of view, especially when we talk about lean six sigma, this is unacceptable.

Should the correct formula in a lean six sigma environment:

Takt time = available daily time / average daily demand * (demand coefficient of variation + 1) ?

What would the effect of the new formula be on processes? The answer is that the process would need to produce much faster to comply with delivery time, because the denominator of the fraction will be a greater number as it is multiplied by another factor greater than 1.lets illustrate everything.

Suppose 10 consecutive days with the actual demand:
500      425      560      515      450      550      500      475      500      590
The average daily demand here is 506.5 parts. No rounding off.  Therefore conventional Takt time for a daily available time of 8 hours or 480 minutes would be:
Takt time = 480/506.5 = 0.95 min = 57 seconds
That is the process must produce a part every 57 seconds to be in compliance with delivery time as requested by the customer.

But in a six sigma environment, these 10 demands with mean of 506.5 parts also has a standard deviation of 50.28 parts that can be observed from minimum and maximum demands    In such a case the Takt should of been:
Coefficient of variation = (standard deviation/mean)*100 = (50.28/506.5)*100 = 9.93%
Takt time = 480/506.5*(0.0993+1) = 0.86 min = 51.7 seconds

One thing is a production part rate of 57 seconds and another is a part rate of 51.7 seconds. This is 518 parts difference at the end of the 10 days. Basically 1.02 extra day every 10 days.

However and indeed lean Manufacturing as a stand alone improvement philosophy and method, states that balancing a line according to Takt is not good practice because on the days demand increases, production will not be able to meet delivery requirements, therefore they introduce a new concept called the target cycle time which claims that production should produce x% below Takt that is x% faster. In other words it creates a cushion for the higher days. The concept is fine. The problem is that this % is not objectively defined, it only states between 10% and 15%. What is the scientific method to arrive to an objective percentage?

This is what, in seeking to solve an incoherence situation in lean Manufacturing from a six sigma stand point, we have just done.  Should we call the Takt time calculation which considers the coefficient of demand variation, target cycle time?  It is up to you. Names are not the critical point here. The critical matter is that Takt time should never be calculated with mean demand only if we want to talk about lean six sigma.

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