1. DMAIC Define and Measure6
DMAIC Define and Measure
GEOP 4316

2. Define The initial phase of the DMAIC process
Understand the problem(s), reasons, measures, individuals involved, the effects of it
Create plans and determine needed resources
Justify the need for the project
Projects may not progress beyond this phase

3. Define Project Definition Projects must
Have a financial impact or significant strategic value (e.g. solidify relationships with key customers)
Results significantly exceed effort and investment
Addresses a complex problem
Aims at an improvement change of at least 70%
Project must solve a business problem that hurts a key performance related to:
Costs, Cycle time
Customer satisfaction
Revenue Potential
Process Capability/ Capacity

4. Define Use of case writing tools for project justification
As a company, our _____________ performance for the ____________ area is not meeting _______. Overall this is causing _______ problems., which are costing as much as $_____ per ________.
Example
As a company, our on time delivery performance for the health product area is not meeting the goal of 95% on time delivery. Overall this is causing customer satisfaction problems, which are costing as much as $2Milion in lost orders and revenue per year.

5. Define 1.1 Determine what needs to be improved.
What is the problem ( a high level effect); e.g. high inventory levels consuming space and assets.
Where is the problem occurring; e.g. the Westland Warehouse
Timeframe of the problem; e.g. Since Product Family ds was introduced in 2017.
Customers or business are affected by this problem; Production planning, sales given higher costs.

6. Define 1.2 Determine the outputs (CTQs = y’s)
Characteristics or process outputs affected (the specific y’s); e.g. inventory levels.
Identify the primary metric for each y; e.g. inventory days
Identify tradeoff metrics to monitor for negative impact; e.g. orders filled.

7. Define 2. Determine associated processes and location
a. List the major process steps and location (top level processes); e.g. PO generation, order replenishment, inventory reconciliation, production planning.
b. Develop a top level flowchart
3. Determine the baseline performance of the y’s
a. Estimate the magnitude of the problem using the primary metric; e.g. between 31.2 to 40.5 days of inventory with a mean of 37.4 days.

8. Define 4. ID the cost and impact of the problem
a. Identify the cost centers affected by problem
b. Based on a baseline improvement level, what is the financial impact of the project.
Soft versus Hard Savings
Soft: increased customer satisfaction > this increases loyalty and customer orders. Estimates included but hard to trace
Hard: reduced inventory in warehouse = reduced assets and increased cash available.

9. Define 5. The problem Statement
A description of the problem and the metrics
Where its occurring and in what processes
Timeframe and Magnitude
Should not simplify it: audience will not know the problem and the processes.
Inventory levels are too high.
Inventory levels at the Westland warehouse are consuming space, taking up management time, and creating cash flow issues. Inventory levels are averaging 31.2 days with a high of 45 days. These levels exceed the 20 day target on 99% of the days since October We could save $400,000 if at the target level.

10. Define The level of improvement
Based on current performance, entitled performance, and the team leader goals
Entitled performance: the best performance that a process as currently designed has demonstrated in operation.
Long term performance of a line: 90% on time delivery
Mar 4 – Mar 23, 98% on time performance.
98% is the entitled performance
So what x’s caused the 98% performance level.
Breakthrough improvement: 70% change

11. Define 6. The Objective Statement 7. ID and recruit the team
Based on the Problem Statement
Improve some metric from baseline in t amount of time with an impact towards a corporate goal or strategy.
Reduce Inventory levels
Reduce inventory levels from an average of 31.2 days to an average of 20 days with a maximum of 25 days. This will be completed by August This project will save $400,000 per year in interest, space, and management effort. These savings are in support of our corporate goal of improving asset management and ROI.
7. ID and recruit the team
8. Obtain approvals and launch

12. Measure During the Define phase
the critical process variables were identified
targets were identified
The Measure phase captures and analyzes process/ system data
What is the gap between target and actual performance?
Analysis of the gap is based on statistical analysis. Statistics is the key to understand variability.
Data may not be available, and this phase includes data collection.

13. Measure Process/ Product Measurement
Identification of error opportunities (for the product)
Possible missing or wrong parts, information, delays in completing a task, …
Defects per Opportunity
Opportunities are the critical dimensions / characteristics of the product (unit)
Directly related to the complexity
Issue: overestimating the ops. with trivial elements. This will lead to over assessing the process capabilities

14. Measure Process capability Based on data and on specifications
Specifications: performance values of a process or product characteristic that are acceptable to the customer.
Specifications should not be arbitrary: unless they have a real reason (separate the good from the bad) they are a stumbling block to progress
Too tight: spend more resources/ effort than necessary, too loose: customer will not be satisfied

15. Measure DC1 data: xave = 21 hours; s = 1.1 hours
Six Sigma assumption: variables are normally distributed.

16. Measure DC1: xave (m) = 21 hours; s (s) = 1.1 hours
Thus there is a 68.3% chance that the time to fulfill the order is between 19.9 and 22.1 hours …
A 95.4% that is between 18.8 and 23.2 hours
17.7
19.9
22.1
24.3
18.8 21
23.2

17. Measure DC2: xave (m) = 19 hours; s (s) = 3.4 hours
Thus there is a 68.3% chance that the time to fulfill the order is between 15.6 and 22.4 hours …
A 95.4% that is between 12.2 and 25.8 hours
8.8
15.6
22.4
29.2
12.2 19
25.8

18. Measure DC1: xave (m) = 21 hours; s (s) = 1.1 hours
What is the probability the fulfill time would be less than 22.1 hours? =
= 84.13%
What about less than 24.3 hours? =
= 99.86% 21
22.1
23.2
24.3

19. Measure
Sigma score (level): relates the process performance to the CTC limit
Sigma score is how many standard deviations can you fit within the mean and the specification level
Z = ( SL – xave ) / s s
xave SL

20. Measure SL = 24 hours. DC1 data: xave = 21 hours; s = 1.1 hours
Z = ( SL – xave ) / s = ( 24 – 21 ) / 1.1 = 2.72
2.72 s s 21 24

21. Measure SL = 24 hours. DC2 data: xave = 19 hours; s = 3.4 hours
Z = ( SL – xave ) / s = ( 24 – 19 ) / 3.4 = 1.47
1.47 s s 19 24

22. Measure Key question. What is the probability of not meeting the CTX?
In other words, what is the failure level for each DC? 19 21 24

23. Measure Relating Z to the long term defective level
Get the Z value from the data.
Find P(X ≤ Z) from the cumulative normal table
Percent Defective = 1 –P(X ≤ Z)
Defects Per Million Opp = (1 – P(X ≤ Z)) x 1M
The discussion in this presentation will assume no process shift (the process mean does not move). For a discussion about the 1.5 shift see

24. Measure Relating Z to defects
Another version is to assume the mean will shift (move)
Get the Z value from the data.
Get Zshift = Z – 1.5
Find P(Zshift) from the cumulative normal table
Percent Defective = 1 –P(Zshift)
DPMO = (1 – P(Zshift)) x 1M

25. Measure No shift DC1. Z = 2.72 P(X ≤ Z) = 99.67 Defective = 0.33%
DPMO = 3,300
If they fill 1,000 orders per week, about 4 will take more than 24 hours
0.33%
No shift 19 21 24

26. Measure No shift DC2. Z = 1.47 P(X ≤ Z) = 92.92 Defective = 7.08%
DPMO = 70,800
If they fill 1,000 orders per week, about 71 will take more than 24 hours
7.08%
No shift 19 21 24

27. Measure Processes can have USL, LSL or both. Sigma Score (Z)
ZU = (USL – xave ) / s
ZL = (xave – LSL ) / s
Z = min. (ZU, ZL)
Capability index (Cpk) = Z score/ 3.
A capability index of 1 or more indicates a capable process.
A Cpk = 1 is equivalent to a 3 Sigma process

28. Measure Example 1 Customers are complaining about pedal problems.
CTQ = Part strength in psi of a bike pedal
Data from 956 bike pedals resulted in an average of 255 with a standard deviation of 6
To meet the bike design specification (based on customer expectations), the LSL = 240.

29. Measure Z score (Sigma score) = (255 – 240) / 6 Z = 2.5 No shift
LSL = 240 psi xave = 255 psi s = 6 psi
Z score (Sigma score)
= (255 – 240) / 6
Z = 2.5
No shift
P(Z) = or about 0.62% defective
6,200 DPMO 15 6 6
xave
= 255
LSL = 240

30. Measure Z score (Sigma score)
2.5
LSL = 240 psi xave = 255 psi s = 6 psi
Z score (Sigma score)
If the mean shifts towards the LSL by 1.5
Zshift = 1
P(Zshift) = or about % defective
158,650 DPMO 15 6 6
xave
= 255
SL = 6
LSL = 240

31. Measure Example 1. Conclusions
Process is not capable as Cpk = 2.5/3 < 1.
Assuming not mean shift, process would produce less than 1% defective.
Assuming a mean shift, process would produce about 15% defective.

32. Measure
Example 2
A bag of aguacate dip must weigh between 3.5 and 3.95 ounces.
CT Quality = No fewer than 3.5
CT Cost = No more than 3.95
Data from 300 containers resulted in an average of 3.79 ounces with a standard deviation of 0.07 ounces
LSL = 3.5; USL = 3.95.

33. Measure Z = min. (ZU, ZL) = 2.29 With no shift; P(Z) = 0.989
sigma score
Zu = (3.95 – 3.79) / = 2.29
Zl = (3.79 – 3.5) / = 3.85
Z = min. (ZU, ZL) = 2.29
With no shift; P(Z) = 0.989
Defective = 1.1 %
11,000 DPMO
0.29
0.16
0.07
0.07
0.07
LSL = 3.5
xave
= 3.8
USL = 3.95

34. Measure Z = min. (ZU, ZL) = 2.29 Zshift = 2.29 – 1.5 = 0.79
sigma score
Zu = (3.95 – 3.79) / = 2.29
Zl = (3.79 – 3.5) / = 3.85
Z = min. (ZU, ZL) = 2.29
Zshift = – 1.5 = 0.79
With shift; P(Zshift) =
21.48% defective
214,800 DPMO
0.29
0.16
0.07
0.07
0.07
LSL = 3.5
xave
= 3.8
USL = 3.95

35. Measure
2.29

36. Measure A Sigma scores changes if: The mean shifts
The standard deviation changes
The specs change

37. Measure sigma score = (260 – 240) / 6.5 = 260 LSL = 240 = 255
= Cpk > 1
No shift
P(Z) =
Defective = 0.1%
DPMO = 1,000
With shift
Zshift = 1.57
P(Z) =
Defective = 5.75%
DPMO = 57,500
Improvement as previous values were
no shift: 6,200 DPMO
w shift 158,650 DPMO
After some changes to the equipment, the average psi is increased to 260. However, the standard deviation increased a bit to 6.5 psi. 20
6.5
6.5
6.5
xave
= 260
LSL = 240
xave
= 255

38. Measure New equipment to pack the dip is purchased and installed.
Data from 400 containers resulted in an average of 3.7 ounces with a standard deviation of 0.02 ounces
sigma score
Zu = (3.95 – 3.7) / = 12.5
Zl = (3.7 – 3.5) / = 10
Z = min. (ZU, ZL) = 10
With no shift; P(Z) ∼ 1
Assuming sigma shift,
P(Zshift) ∼ 1.
This is a 10 sigma process.
Basically, DPMO = 0.
0.2
0.25
LSL = 3.5
xave
= 3.7
USL = 3.95
xave
= 3.8

39. Measure Measurement System must be precise Measurement System Audits
Repeated measurements of the same thing should result in the same value, regardless of other conditions.
Measurement System Audits
Used to determine how the MS is working
Select several items, run them through the process several times. Measurement should be the same.
Audits are very important in human measurement systems