1. Tech 31: Unit 3 Control Charts for Variables
Statistical Process Control (SPC)

2. Control Charts
Control charts are tools used to determine whether or not a manufacturing process is in a state of statistical control

3. Process Variation is Present in Every Process Due to a Combination of Factors:
Equipment
Materials
Environment
Operator

4. Types of Variation Within-piece variation Piece-to-piece variation
Time-to-time variation
Chance causes
Assignable causes

5. Statistical Process Control
A method of quality control using statistical methods.
Applied in order to monitor and control a process.
Monitoring and controlling the process ensures that it operates at its full potential.
At its full potential, the process can make as much conforming products as possible with a minimum waste, rework or scrap.
SPC can be applied to any process.

6. Standard Normal Curve = 99.74% of Quality

7. Examples of Normal Distribution

8. Normality & Control Charts: Principles

9. Sample Control Chart

10. Elements of the Control Chart. .
UCL = CL+ 3s . . . . X .
CL = X
LCL = CL - 3s
Time/Order

11. Elements of a Control Chart. . .
UCL = CL+ 3s . . R . .
CL = R
LCL = CL - 3s
Time/Order

12. Determining X-Bar and X-Double Bar
X-Bar = Mean or Average of sub-groups, usually made up of 4 items per sub-group
X-Bar of = 15.3/4 = 3.8
Class projects will involve 25 subgroups
X-Double Bar is the mean (grand mean) of all the sub-group means

14. Determining the Control Limits
The control limit is equal to the grand mean
CL = Grand mean or X-double bar
UCL = Upper control limit = CL + 3ϱ
UCL = Upper control limit = CL + A2R-bar
LCL = Lower control limit = CL - 3ϱ
LCL = Upper control limit = CL - A2R-bar

15. Objectives of Control Charts
For quality improvement
To determine process capability
For decisions in regard to product specifications
For decisions in regard to new and existing production processes

16. Process Capability Vs Specifications

17. Process Capability Vs Specifications

18. Process Capability Vs Specifications

20. Control Chart Techniques
Select the quality characteristic
Choose the rational subgroup
Collect Data
Determine the trial central line (CL) and control limits (UCL & LCL)
Establish the revised CL, UCL, & LCL
Achieve Objectives

21. Control Charts Types of Control Charts Control Chart for Variables
X-bar charts
R charts
The sample standard deviation control chart
The median and range chart
The individual and range chart

22. Control Charts continued
Control Charts for Attributes
p & np charts
c charts
u charts

23. State of Control
Process in control
Process out of control

24. Process in Control

25. . . . . . . . Process Out of Control X CL = X 1 2 3 4 5 6 7 Time/Order
UCL = CL+ 3s . .
CL + A2R-bar . . X .
CL = X
LCL = CL - 3s
CL - A2R-bar
Time/Order

26. Analysis of Out-of-Control Condition
Change or jump in level
Trend or steady change in level
Recurring cycles
Two populations (mixture)
Mistakes

27. Specifications Individual values compared to averages
Central limit theorem
Control limits and specifications
Process capability and tolerance

28. Process capability = Six X Sigma
UCL A B C CL C B A
LCL

29. Cpk = Min{(USL-X-bar) or (LSL-X-bar)}/3s
Process Capability
Control Limits & Specification Limits
Process Capability = 6s
Process Capability Index:
CP = (USL-LSL)/ 6s
Cpk = Min{(USL-X-bar) or (LSL-X-bar)}/3s

30. Six sigma
If sigma can be reduced to the point that the specifications are at + or – 6 sigma, then % of the product or service will be within specifications

31. Different Control Charts
Charts for better operator understanding
Charts for variable subgroup size
Charts for trends
Charts for moving average and moving range
Charts for median and range
Charts for individual values
Charts with non-acceptance limits