1. Process Capability Process capability For Variables
The 6 versus specification limits
For attributes
Pareto chart
Cause and effect diagram

2. Process Capability
There is a difference between a process conforming to the specifications and a process performing within statistical limits
A process in statistical control will not necessarily meet specifications as established by the customer
The control limits on the charts represent what the process is capable of producing

3. Process Capability
Specifications are set by the customer. These are the “wishes.”
Control limits are obtained by applying statistical rules on the data generated by the process. These are the “reality.”
Process capability refers to the ability of a process to meet the specifications set by the customer or designer

4. The 6 Versus Specification Limits
It is important to compare the natural tolerances, 6, with the specification range (USL-LSL).
Recall that  may be estimated as follows:

5. The 6 Versus Specification Limits
Suppose that process mean = (USL+LSL)/2
Case I: 6 < USL - LSL
The specifications will be met even after a slight shift in process mean
Case II: 6 = USL - LSL
As long as the process remains in control with no change in process variation, the specification will be met
Case III: 6 > USL - LSL
Although the process may be in statistical control, it is incapable of meeting specifications

6. The 6 Versus Specification Limits
Capability potential
The relationship between process mean,  and its target value, is obtained from an index
Exercise: If the target mean value = (USL+LSL)/2, is the process capable if

7. Process Capability Some indices:
If the above indices are more than 1, the 3-sigma control limits are within the specification limits, and the process is capable - all but at most 0.27% items meet the specification
If CpL < 1, too many items are outside LSL
If CpU < 1, too many items are outside USL

8. The 6 Versus Specification Limits
Sometimes, only one of CpL and CpU may be relevant e.g., testing for steel hardness
If the process is not capable, actions may be taken to adjust the
process mean
variation
specifications

9. Problem 9.6: A certain manufacturing process has been operating in control at a mean  of mm with upper and lower control limits on the chart of and respectively. The process standard deviation is known to be 0.15 mm, and specifications on the dimensions are 65.00±0.50 mm.
(a) What is the probability of not detecting a shift in the mean to mm on the first subgroup sampled after the shift occurs. The subgroup size is four.
(b) What proportion of nonconforming product results from the shift described in part (a)? Assume a normal distribution of this dimension.
(c) Calculate the process capability indices Cp and Cpk for this process, and comment on their meaning relative to parts (a) and (b).

10. Pareto Chart 50 100 80 30 60 40 10 20 Cumulative percentage
Number of defects
100 80 60 40 20 50 30 10
Cumulative percentage
The next sequence translates the data from the checklist to a Pareto chart. 10

11. Pareto Chart 50 100 80 30 60 C 40 10 20 Cumulative percentage
Defect type C D A B
Number of defects
100 80 60 40 20 50 30 10
Cumulative percentage
The four defect types are charted with the chart height being the relative frequency of occurrence and the defects ordered in descending order of magnitude. This is a discrete chart, one of the two ways Pareto charts are commonly constructed. 11

12. Pareto Chart 50 100 80 30 60 C 40 10 20 Cumulative percentage
Number of defects
100 80 60 40 20 50 30 10
Cumulative percentage
Defect type C D A B
This chart adds the cumulative line to the chart showing the alternate charting technique. 12

13. Cause and Effect Diagram
Measurement
Men/Women
Machines
Faulty testing equipment
Poor supervision
Out of adjustment
Incorrect specifications
Lack of concentration
Tooling problems
Improper methods
Inadequate training
Old / worn
Quality
Problem
Inaccurate
temperature
control
Poor process design
Defective from vendor
Ineffective quality
management
Not to specifications
A cause-and-effect diagram, or fishbone diagram, is a chart showing the different categories of problem causes.
Dust and Dirt
Material-
handling problems
Deficiencies
in product design
Environment
Materials
Methods

14. Cause and Effect Diagram
Common categories of problems in manufacturing
5 M’s and an E
Machines, methods, materials, men/women, measurement and environment
Common categories of problems in service
3 P’s and an E
Procedures, policies, people and equipment

15. Reading and Exercises
Chapter 9:
pp (Section 9.2)
9.1, 9.5