1. LESSON 3 Analytical Tools
06January2014

2. Lesson Objectives
Upon completion of this lesson, you should be able to:
Identify two methods of statistical sampling
Identify quality tools used in a manufacturing context
Contrast Process Capability (Cp) and the Process Capability Index (Cpk) as measures of variation
Recognize the concepts from the Design of Experiments applied to process improvement

3. Lesson Topics This lesson will cover the following topics:
Statistical Sampling
Seven Quality Tools
Process Capability Analysis
Design of Experiments

4. What’s In It For Me?
Understanding continuous process improvement tools and analysis methods enables you quantitatively monitor your contractors’ manufacturing and supply chain management performance

5. Introduction
How does the use of continuous process improvement tools and analysis methods help you to evaluate and monitor your contractors?

6. STATISTICAL SAMPLING Lesson Topics: Statistical Sampling
Seven Quality Tools
Process Capability Analysis
Design of Experiments

7. Acceptance Sampling Testing a sample of products for defects
Used to determine whether to accept or reject a production batch
Batch is rejected if negative characteristics exceed limits for the batch

8. Statistical Process Control (SPC)
Method to determine if a process is operating within acceptable limits
Used in conjunction with process capability analyses and Continuous Process Improvement (CPI) plans

9. Question and Answer
A contractor is testing a sample of fasteners to ensure that the batch conforms to acceptable limits. What quality control method is the contractor practicing?
Standard Test Analysis
Statistical Process Control
Acceptance Sampling
Conformance Adaption

10. Question and Answer
Which quality method is used in conjunction with process capability analyses to determine if a process is operating within acceptable limits?
Standard Test Analysis
Statistical Process Control
Acceptance Sampling
Conformance Adaption

11. SEVEN QUALITY TOOLS Lesson Topics: Statistical Sampling
Process Capability Analysis
Design of Experiments

12. DoD Implementing CPI
Continuous Process Improvement (CPI) tools have been used in industry for decades:
Statistical Process Control
Total Quality Management
Six Sigma
Lean
DoD Continuous Process Improvement Transformation Guidebook

13. Seven Quality Tools Flowchart Cause and Effect Diagram Check Sheet
Histogram
Pareto Chart
Run Chart
Control Charts

14. Flowchart Pictorial representation showing all the steps of a process
First identify, then analyze the actual process path
Each step is evaluated to improve the overall process
Other types of process charts:
Spaghetti Diagram
Swim Lane Chart
Supplier-Inputs-Process-Outputs-Customers (SIPOC)
Value Stream Map

15. Flowchart (cont.) Content match order? Goods are received at dock
Goods are inspected
Content match order?
Notify purchasing No
Yes
Incoming quality check
Receiving notifies warehouse
= Entrance/exits
= Process
= Decision
= Unknown process

16. Swim Lane Chart Type of process chart (flowchart)
Distinguishes responsibilities for sub-processes of a process
Grouped into horizontal or vertical lanes

17. Cause and Effect Diagram
Identifies possible causes of an effect or problem
AKA: Ishikawa Diagram or Fishbone Diagram
Can be used for brainstorming sessions

18. Check Sheet Translates “opinions” into “facts”
Gather data based on sample observations
Detect patterns
Defect Types
Mon
Tues
Wed
Thu
Fri
Total
Parts rusted 18
Misaligned weld 5
Improper test procedure 1
Wrong part issued 3
Voids in casting 8
Incorrect dimension 12 10 40

19. Histogram Bar graph that displays frequency distribution
Shows how often each different value in a set of data occurs
Vertical axis
Frequency
(counts for each bin)
Horizontal axis
Response variable

20. Helps prioritize problems – which to solve first
Pareto Chart
Special form of vertical bar graph with bars arranged in descending order
The left-hand vertical axis shows the impact of each item. In this case, 120 units were thrown away due to mis-aligned stacks. The units in this column can be counts, dollars, or whatever is appropriate.
Helps prioritize problems – which to solve first

21. Also known as “Time Plots” for data taken over a period of time
Run Chart
Data points plotted on graph in sequence over time
Displays trends or shifts in average
Also known as “Time Plots” for data taken over a period of time

22. Control Charts
Run chart with statistically determined “upper” and “lower” control limits
The plot will help determine if the process is stable (in control) or unpredictable (out of control)
Plotting variation allows us to determine how much variability exists in the process
Common causes
Special causes

23. Basic Control Chart Structure
Measurement Scale
Upper Control Limit (UCL)
Mean
Upper and lower control limits identify any process changes and the existence of variation present due to special causes
Lower Control Limit (LCL)
Observations from Process

24. Continuous (Variable) Data
Control charts for continuous data:
Weight
Power
Length
Tensile strength
Temperature, time, etc.
Control Charts for continuous data are based on the Normal Distribution
The X-Bar Chart and R-Chart
are tools used to graphically
show these types of data

25. Discrete (Attribute) Data
There are separate control charts for discrete, or “count” type data:
Defects per unit
Defective solder joints per board
Accidents per month
Defective pins per connector, etc.
Discrete data has less resolution
because we are only counting if
something specific occurs, not how
close we are to a desired condition

26. Example: Statistical Process Control (SPC)
Approval Time for Documents (Doc) (Days)
Week
Doc 1
Doc 2
Doc 3
Doc 4
Doc 5
X(bar) R 1 36 33 43 51
39.2 18 2 31 50 54 35
40.6 23 3 41 46 26 37
38.6 20 4 40 56 29
40.4 27 5 34 42 28
32.6 16 6 59 47 65 32 7 52 38 21 8
46.8 9 25 61
47.8 10 48 49
48.2 24
X(dblbar) =
42.56
R(bar) =
24.4

27. Control Charts for Continuous Data

28. Question and Answer
What quality tool uses pictorial symbols to show all the steps in a process?
Flowchart
Cause and Effect Diagram
Check Sheet
Histogram

29. This graph displays frequency distribution in a bar graph format.
Question and Answer
This graph displays frequency distribution in a bar graph format.
Control Chart
Cause and Effect Diagram
Check Sheet
Histogram

30. Question and Answer
This quality tool is also called a Fishbone Diagram and is used for brainstorming sessions to sort ideas into useful categories.
Control Chart
Cause and Effect Diagram
Pareto Chart
Swim Lane

31. PROCESS CAPABILITY ANALYSIS
Lesson Topics:
Statistical Sampling
Seven Quality Tools
Process Capability Analysis
Design of Experiments

32. Variation: Common & Special Causes
If only common causes of variation are present, the output of a process forms a distribution that is stable over time and is predictable
Prediction
Prediction?
Time
Time
If special causes of variation are present, the process output is
not stable over time and is
not predictable

33. Process Control
A process must first be brought into statistical control. The process mean (X-Bar) and range must be known
CONTROLLED STABLE PROCESS
(No Special Causes, Only Common causes)
Time
OUT-OF-CONTROL PROCESS
(Special Causes of Variation Present)

34. Process Stability IN CONTROL AND CAPABLE
(Acceptable Variation from Common Causes)
IN CONTROL BUT NOT CAPABLE
(Excessive Variation from Common Causes)
Time
UPPER SPECIFICATION LIMIT
LOWER SPECIFICATION LIMIT

35. Process Capability (Cp) Decision Table
Cp Value
Decision
Cp < 1.00
Not Capable
Cp = 1.00 – 1.33
Marginally Capable
Cp > 1.33
Capable
Cp ≥ 2.00
6σ Quality
Cp Computation:
T = Tolerance = Upper Specification Limit (USL) – Lower Specification Limit (LSL)
Cp = T
6 s

36. Capable Process? T
A process may appear to be capable with one set of sample data… = X
But how does the process perform over time?
LSL
Mean Time Down (MTD)
USL
PQM-201B CPI Tools OCT 2012

37. Process Performance Index (Cpk) Decision Table
Cpk Value (Lower of the 2 values)
Decision
Cpk < 1.00
Not Meeting Specification
Cpk = 1.00 – 1.33
Marginally Meeting Specification
Cpk > 1.33
Meeting Specification
Cpk ≥ 1.50
6σ Quality
Cpk Computation: OR

38. Process Performance Index (Cpk) Comparison
LSL = USL = LSL = USL = 24
Cp= 1.33
Cpk= -0.5
Cp= 1.33
Cpk= 1.00
MTD
MTD
LSL = USL = LSL = USL = 24
Cp= 1.33
Cpk= 1.33
Cp= Cpk= 0
MTD
MTD

39. Cp and Cpk Results Review
Cp - simple indicator of process capability potential
Cpk - measures how close a process is running to its specification
Both analytical tools are useful for understanding if a process is capable of fitting into the specifications or not

40. Question and Answer
For a process to be brought into statistical control, what first must be known?
Weight, power, and length
Sample size and production batch
Root cause and manufacturing process steps
Process mean (X-Bar) and range

41. What analytical tool measures process capability?
Question and Answer
What analytical tool measures process capability? T Cp
Cpk 6σ

42. Question and Answer
What indicator measures how close a process is running to its specification? T Cp
Cpk 6σ

43. DESIGN OF EXPERIMENTS Lesson Topics: Statistical Sampling
Seven Quality Tools
Process Capability Analysis
Design of Experiments

44. Design of Experiments (DOE)
A formal method of analyzing how factors, parts or ingredients in a manufactured product affect its quality, performance or other attributes
Components:
Factors (inputs to the process)
Levels (settings for each factor)
Responses (output of the experiment)

45. Example: DOE Analysis

46. Benefits of Experimentation
Compare alternatives
Identify significant inputs affecting an output
Separating “the vital few from the trivial many”
Achieve an optimal process output
Reduce variability
Minimize, maximize or target an output
Improve process or product robustness
Balance tradeoffs

47. DOE: Seven Steps Define the problem
Gather all of the background information
Design the test program
Plan and carry out the experiment
Analyze the data
Interpret the results
Report conclusions

48. What is the purpose of the Design of Experiments (DOE) tool?
Question and Answer
What is the purpose of the Design of Experiments (DOE) tool?
Analyzes how factors in a product affect its quality, performance or other attributes
Investigates each output factor and how they influence a product’s ingredients

49. Which of the following is not a step in the DOE process?
Question and Answer
Which of the following is not a step in the DOE process?
Define the problem
Gather all of the background information
Plan and carry out the experiment
Implement the solution

50. Summary Having completed this lesson, you should now be able to:
Identify two methods of statistical sampling
Identify quality tools used in a manufacturing context
Contrast Process Capability (Cp) and the Process Capability Index (Cpk) as measures of variation
Recognize the concepts from the Design of Experiments applied to process improvement

51. Summary (cont.)
Understanding continuous process improvement tools and analysis methods enables you quantitatively monitor your contractors’ manufacturing and supply chain management performance.