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### Pareto Chart

- Process capability
- For Variables
- The 6 versus specification limits

- For attributes
- Pareto chart
- Cause and effect diagram

- For Variables

- 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

- 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

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:

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

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

- 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

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

Problem 9.6: A certain manufacturing process has been operating in control at a mean of 65.00 mm with upper and lower control limits on the chart of 65.225 and 64.775 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 64.75 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).

40

30

20

10

0

100

80

60

40

20

0

C

Cumulative percentage

Number of defects

D

A

B

Defect type

40

30

20

10

0

100

80

60

40

20

0

C

Cumulative percentage

Number of defects

D

A

B

Defect type

Pareto Chart

Cause and Effect Diagram

Measurement

Men/Women

Machines

Out of adjustment

Poor supervision

Faulty testing equipment

Lack of concentration

Tooling problems

Incorrect specifications

Improper methods

Old / worn

Inadequate training

Quality

Problem

Inaccurate

temperature

control

Poor process design

Defective from vendor

Ineffective quality

management

Not to specifications

Dust and Dirt

Material-

handling problems

Deficiencies

in product design

Environment

Materials

Methods

- Common categories of problems in manufacturing
- 5 M’s and an E
- Machines, methods, materials, men/women, measurement and environment

- 5 M’s and an E
- Common categories of problems in service
- 3 P’s and an E
- Procedures, policies, people and equipment

- 3 P’s and an E

- Chapter 9:
- pp. 324-330 (Section 9.2)
- 9.1, 9.5

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