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:

2d

R

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

6

LSLUSLC p

),min( 00

0

XUSLLSLX

Xk

0X

?. if ?. and . 2040331 kkC p

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

),min(

,

pUpLpk

pUpL

CCC

USLC

LSLC

33

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 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).

X

10

Pareto Chart

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11Defect type

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12

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Defect type

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Pareto Chart

13

Cause and Effect Diagram

QualityProblem

MachinesMeasurement Men/Women

MethodsEnvironment Materials

Faulty testing equipment

Incorrect specifications

Improper methods

Poor supervision

Lack of concentration

Inadequate training

Out of adjustment

Tooling problems

Old / worn

Defective from vendor

Not to specifications

Material-handling problems

Deficienciesin product design

Ineffective qualitymanagement

Poor process design

Inaccuratetemperature control

Dust and Dirt

14

• 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

Cause and Effect Diagram

15

Reading and Exercises

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