Six Sigma Metrics Caalculations

The options for formulas and metrics that could be used during the Measure phase of the DMAIC cycle are endless. However, there are some common ones that are used in the world of lean six sigma and some that are part of Six Sigma Green Belt certification. In this assignment, you will practice working with the following variables:

• Takt time
• Throughput rate
• Total cycle time
• Throughput yield
• Defects per unit
• Parts per million
• Defects per million opportunities
• Sigma level

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Assignment Template is attached.

Metrics Calculations

Student Name

Instructions: You are currently working on an improvement project to address the problem that customer demand for widget output is not being met. Your company is growing quickly, customers love your widgets, and you are having trouble keeping up with demand. You will measure the extent of the problem, make improvements, measure again, and repeat improvements and measurements until customer demand is met. Fill out the yellow areas to complete the assignment.

Your first task is to figure out Takt time. Takt time is expressed as production time divided by average

customer demand during that production time. You know that the customer wants 1600 widgets per day and the production facility has one 8-hour shift per day. You want to figure out Takt time in minutes per unit so that you can more easily do other calculations to measure the extent of the problem and make improvements. I.e. how many minutes per unit would be allowed for the facility to be able to meet customer demand?

TAKT TIME
Customer demand in units per day CD (given):	CD = _____ UNITS/DAY
Production time in minutes per day:	PT = _____ MIN/DAY
Takt time in minutes per unit:	Takt Time = _____ MIN/UNIT

Next you will figure out the current widget output rate to see how it compares to Takt time. This rate is known as the throughput rate. You know that the production facility is currently putting out

30

0 acceptable units per day. You will use the Little’s Law formula to figure out the throughput rate in units per minute. Then take the inverse of the throughput rate to get total cycle time per unit to compare to Takt time.

ROUND 1 TOTAL CYCLE TIME PER UNIT
Daily acceptable output in units per day DAO1 (given):	DAO1 = _____ UNITS/DAY
Throughput rate in units per minute (Little’s Law):	TR1 = _____ UNITS/MIN
Total cycle time in minutes per unit:	T CT1 = _____ MIN/UNIT

Your mission is to get the TCT to be lower than the Takt time. Right now it is higher. Your project team will make iterative improvements to reduce the TCT. The most obvious change that is feasible to make is to switch from online setup (ST) to offline setup as the first improvement to reduce the TCT. Offline setup is setting up Widget #2 for production without using up the production machine and while Widget #1 is still running on the machine. Switching to offline setup has reduced the online setup time (ST) by 89% from 0.9 minutes per unit (ST1) to 0.1 minutes per unit (ST2). One production machine (MC) is currently being used to make the widgets. Calculate the cycle time (CT1) per unit after setup, then calculate the new TCT2 based on offline setup.

ROUND 2 TOTAL CYCLE TIME PER UNIT WITH OFFLINE SETUP
Total cycle time in minutes per unit formula:	——-
Number of machines MC1 (given):	MC1 = _____
Old setup time in minutes per unit ST1 (given):	ST1 = _____ MIN/UNIT
Cycle time in minutes per unit (rearrange TCT formula):	CT1 = _____ MIN/UNIT
New setup time in minutes per unit ST2 (given):	ST2 = _____ MIN/UNIT
			New total cycle time in minutes per unit:	TCT2 = _____ MIN/UNIT

Your TCT2 is still higher than the Takt time. Your project team decides to invest in another production machine to further reduce the TCT. Calculate the new TCT3 based on 2 production machines and the recently improved setup time ST2.

New total cycle time in minutes per unit:

ROUND 3 TOTAL CYCLE TIME PER UNIT WITH 2 MACHINES
New number of machines MC3 (given):	MC3 = _____
TCT3 = _____ MIN/UNIT

Your TCT3 is looking much better but could still use some improvement to meet customer demand. Your project team decides that better tooling will machine the widgets faster and reduce the cycle time (CT) per unit after setup. Switching to better tooling has reduced the CT to 0.53 minutes per unit (CT4). Calculate the new TCT4 based on the improved CT4, 2 production machines, and the recently improved setup time ST2.

New total cycle time in minutes per unit:

ROUND 4 TOTAL CYCLE TIME PER UNIT WITH BETTER TOOLING
New cycle time per unit after setup CT4 (given):	CT4 = _____ MIN/UNIT
TCT4 = _____ MIN/UNIT

Your TCT4 is getting close to meeting customer demand. Your project team decides that defect reduction would be the best way to get the TCT under Takt time. You will do that by upgrading components on the production machines so there will be fewer machine failures that damage the widgets in process. Calculate the latest daily acceptable output DAO4 based on TCT4. Right now the facility is producing DAO4 acceptable units/day + 200 units with defects per day. Calculate the current total output (TO4) and current throughput yield (TY4) considering the defects.

ROUND 4 THROUGHPUT YIELD
Daily acceptable output in units per day:	DAO4 = _____ UNITS/DAY
Total output:	TO4 = _____ UNITS/DAY
Throughput yield without defect reduction:	TY4 = _____%

The defect reduction improvement results in a new throughput yield of 97% (TY5). Calculate the new daily acceptable output DAO5 based on TY5 and the existing total output TO4. Then calculate the TCT5 based on DAO5.

New total cycle time in minutes per unit:

ROUND 5 TOTAL CYCLE TIME PER UNIT WITH DEFECT REDUCTION
New throughput yield TY5 (given):	TY5 = _____%
New daily acceptable output in units per day (rearrange TY formula):	DAO5 = _____ UNITS/DAY
TCT5 = _____ MIN/UNIT

Congratulations! Your TCT is less than your Takt time, which means that you can now meet the customer demand of 1600 units per day. Your initial calculations (Round 1) and four rounds of improvements (Rounds 2-5) including implementation of offline setup, adding another production machine, switching to better tooling, and reducing defects, have paid off.

97% throughput yield is not bad, but how good is it in the grand scheme of things? Let’s do some quality performance calculations to figure out where your organization’s performance stands. Some of your units have more than one defect. As a result, there are 78 defects total in one day. There are 3 opportunities for a defect to occur in one unit, meaning the hole could be messed up, the length could be wrong, and/or the width could be wrong. Calculate the following quality metrics below.

ROUND 5 QUALITY PERFORMANCE
Number of defects DF (given):	DF = _____
Number of opportunities per unit OP (given):	OP = _____
Total output TO4:	TO4 = _____
Number of units with defects:	# Units with Defects = _____
Average number of defects per unit (uses total output rather than # units with defects):	DPU = _____
Parts (defects) per million units PPM:	PPM = _____
Defects per million opportunities DPMO:	DPMO = _____
Sigma level (use the table below to find the right sigma level based on your calculated DPMO):	Sigma Level = _____
DPMO	SIGMA LEVEL
308,500	2.0
158,700	2.5
66,800	3.0
22,700	3.5
6,200	4.0
1,300	4.5
230	5.0
30	5.5
3.4	6.0