1. QUALITY CONTROL
CHAPTER 8

2. 8.10. Tools of Statistical Quality Control
Quality: meeting design specifications
8 tools to understand process & improve quality
Flow chart
Cause-and-effect diagram
Data collection form (check sheet)
Pareto analysis
Histogram
Scatter plots
Designed experimentation
Control charts

3. 8.10.1. Flowchart Picture of activities (steps) of a process
Shows sequence & relationships among steps
Avoid:
Dead ends,
Endless loops
Symbols:
Start/end Operation
Decision Flow (sequence)

4. Flow chart example

5. 8.10.2. Cause-and-Effect Diagram
Also called: Fishbone diagram, Ishikawa diagram
Organizes quality problems into logical categories
Problems statement in box to the right (fish head)
Major bones brainstormed by a team
Standard major bones:
Men
Machines
Methods
Materials
Measurement
Environment

6. Cause-and Effect diagram example

7. Data Collection forms
Used to collect, organize, and analyze new data
Specify which data to collect, and units of measurement
Decide when, where, how, in what order data is collected
2 types:
Traditional
Check sheet

8. 8.10.4. Pareto Analysis Pareto = prioritization or classification
Order data by type, category, or other classification
Help to focus attention on important things
80/20 Rule:
80% of quality problems are caused by 20% of the factors
ABC analysis:
Class A: most important
Class B: fairly important
Class C: less important

9. Pareto chart example

10. Histograms
Useful for seeing shape, centering, and spread of data
Usually used for determining probability distribution of data
Horizontal axis:
broken into 5-20 equal-width cells (usually 10)
Vertical axis:
frequency of % of occurrence
Number of data points should be  30, usually  100

11. Histogram example

12. Scatter Plots
x-y plot: shows relationship between 2 variables (x, y)
One variable increases as the other increases: positive correlation
One variable decreases as the other increases: negative correlation
No relationship: zero correlation

13. Scatter Plot example

14. Designed Experiments
One of the most important & needed scientific areas in industry today
Determines which factor (of many) has max effect on quality
1FAT (1 Factor At a Time):
varies one factor only. Inefficient, misleading
Common designs in industry:
Factorial design
fractional factorial design
Taguchi design
central composite design, …

15. 8.11. Background on Control Charts
Useful for studying process variation, developed by Shewhart
Stable process: consistent variation, in-control process, common-cause process
Unstable process: inconsistent variation, out-of-control process, common –cause plus special-cause process
Common (natural, random) causes: inherent in the process, present all the time, affect everyone & all outputs
Special (assignable) causes: not inherent in the process, not present all the time, arise due to specific (exceptional) reasons

16. 8.11. Background on Control Charts
Main types of control charts
Control charts for variables: apply on numbers, measurements
charts: used together to analyze centering & spread of data
Control charts for attributes: apply on categories, characteristics (Ex: conforming, not conforming)
P chart: measures fraction of non-conforming items
C chart: measures number of non-conforming items

17. 8.11. Background on Control Charts
Three control lines
Central Line (CL): center (mean ) of data
Lower Control Limit (LCL): CL - 3
Upper Control Limit (UCL): CL + 3
For normal distribution, the control-limit range [ - 3,  + 3] contains 99.7% of the data (almost all “usual” data)
Therefore, any observation outside the control limits indicates something “unusual” (out of control).

18. 8.12. Control Charts for Variables , charts
Take m samples (sub-groups), each of size n
m = 20 – 30
n = 4 – 5
Assumption:
Variation within each single sub-group = common cause
Variation between different sub-groups = special cause
For each sub-group i, calculate

19. 8.12. Control Charts for Variables: charts
Calculations for the R chart (done first)
D3, D4 , A2 are given in Tables for each value of n
Calculations for the chart (done only if R chart is in control)

20. 8.12. Example for Charts Given the following measurements Sample
1.02
1.04
1.00 2
0.99
0.98 3
0.97
1.01 4
1.06
0.96 5

21. 8.12. Example for Charts m = 5, n = 4 Sample Measurements R 1 1.02
1.04
1.00
0.04 2
0.99
0.98
1.0075
0.06 3
0.97
1.01
0.9925 4
1.06
0.96
1.005
0.10 5
Ave
1.006

22. 8.12. Example for charts
R-chart limits
-chart limits

23. 8.12. Example for charts
R-chart

24. 8.12. Example for charts
-chart

25. 8.13. Sensitivity Checks for Control Charts
The process is judged out of control if one of the following is observed:
At least 1 point outside the control limits (LCL-UCL)
At least 7 consecutive points all above or all below the center line (CL)
At least 2 consecutive points very close to the center line
At least 5 consecutive points continuously increasing or continuously decreasing

26. 8.13. Sensitivity Checks for Control Charts
When the process is found out of control:
the system is inspected,
the special cause(s) are identified and removed,
out of control points are removed,
control limits are re-calculated.

27. End of Chapter 8
Questions?