IES 331 Quality Control

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IES 331 Quality Control
Chapter 7 Process and Measurement System
Capability Analysis Week 10 August 911, 2005
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Process Capability

• Uniformity of the process
• A uniformity of output
• Process Capability Analysis Quantifying
  variability relative to product requirements or
  specifications

Natural tolerance limits are defined as follows
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Process Capability Analysis

• Process Capability Analysis
• In the form of probability distribution having
• a specified shape,
• center (mean), and
• spread (standard deviation)
• A percentage outside of specifications
• However, specifications are not necessary to
  process capability analysis

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Major Uses of Process Capability Analysis

1. Predicting how well the process will hold the
   tolerances
2. Assisting product developers/designers in
   selecting or modifying a process
3. Assisting in establishing an interval between
   sampling process
4. Specifying performance requirements for new
   equipment
5. Selecting suppliers
6. Planning the sequence of production processes
7. Reducing the variability in a manufacturing
   process

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Reasons for Poor Process Capability
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Process Capability Analysis using a Histogram or
a Probability Plot

• If use Histogram, there should be at least 100 or
  more observations
• Data collection Steps
• Choose machines or machines. Try to isolate the
  head-to-head variability in multiple machines
• Select the process operating conditions
• Select representative operator
• Monitor data collection process

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Exercise 7-11 page 377

• The weights of nominal 1-kg containers of a
  concentrated chemical ingredient are shown here.
  Prepare a normal probability plot of the data and
  estimate process capability

0.9475
0.9705
0.9770
0.9775
0.9860
0.9960
0.9965
0.9975
1.0050
1.0075
1.0100
1.0175
1.0180
1.0200
1.0250
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Exercise 7-11 page 377 (cont)
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Process Capability Ratios

• Process capability ratio (PCR Cp) introduced in
  Chapter 5
• Percentage of the specification band used up by
  the process
• Exercise 7-7 A Process is in statistical control
  with CL(x-bar) 39.7 and R-bar 2.5. The
  control chart uses sample size of 2.
  Specification are at 40/-5. The quality
  characteristic is normally distributed. Find Cp
  and P

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One-Sided PCR
Exercise 7-7 A Process is in statistical control
with CL(x-bar) 39.7 and R-bar 2.5. The
control chart uses sample size of 2.
Specification are at 40/-5. The quality
characteristic is normally distributed. Find C
pu and Cpl
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Interpretation of the PCR
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Assumptions for Interpretation of Numbers in
Table 7-2

• The quality characteristic has a normal
  distribution
• The process is in statistical control
• In the case of two-sided specifications, the
  process mean is centered between the lower and
  upper specification
• Violation of these assumptions can lead to big
  trouble in using the data in Table 7-2.

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• Cp does not take process centering into account
  
• It is a measure of potential capability, not
  actual capability

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A Measure of Actual Capability

• Cpk minimum (Cpu, Cpl)
• Measure the one-sided PCR for the specification
  limit nearest to the process average.
• If Cp Cpk, the process is centered at the
  midpoint of the specifications,
• If Cpk lt Cp , the process is off-center
• Cp measures potential capability,
• Cpk measures actual capability

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Normality and Process Capability Ratios

• The assumption of normality is critical to the
  usual interpretation of these ratios (such as
  Table 7-2)
• For non-normal data, options are
• Transform non-normal data to normal
• Extend the usual definitions of PCRs to handle
  non-normal data
• Modify the definitions of PCRs for general
  families of distributions

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Confidence Interval and Tests of Process
Capability Ratios

• Confidence intervals are an important way to
  express the information in a PCR

• Exercise 7-20 Suppose that a quality
  characteristic has a normal distribution with
  specification limits at USL 100 and LSL 90. A
  random sample of 30 parts results in average of
  97 and standard deviation of 1.6
• Calculate a point estimate of Cpk
• Find a 95 confidence interval on Cpk
• How can we decrease the width of confidence
  interval on Cpk?

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Process Capability Analysis Using a Control Chart

• Process must be in an in-control state to produce
  a reliable estimates of process capability
• When process is out of control, we must find and
  eliminate the assignable causes to bring the
  process into an in-control state

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Gauge and Measurement System Capability Studies

• Determining the capability of the measurement
  system
• Variability are from (1) the items being
  measured, and (2) the measurement system
• We need to
• Determine how much of the total observed
  variability is due to the gauge or instrument
• Isolate the components of variability in the
  instrument system
• Assess whether the instrument of gauge is capable

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Example 7-7
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Setting Specification Limits on Discrete
Components

• For components that interact with other
  components to form the final product
• To prevent tolerance stack-up where there are
  many interacting dimensions and to ensure that
  final product meets specifications
• In many cases, the dimension of an item is a
  linear combination of the dimensions of the
  component parts

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Exercise 7-30

• Three parts are assembled in series so that their
  critical dimensions x1, x2, and x3 add. The
  dimensions of each part are normally distributed
  with the following parameters
• µ1 100 std dev1 4
• µ2 75 std dev2 4
• µ3 75 std dev3 2
• What is the probability that an assembly chosen
  at random will have a combined dimension in
  excess of 262