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

• Predicting how well the process will hold the
  tolerances
• Assisting product developers/designers in
  selecting or modifying a process
• Assisting in establishing an interval between
  sampling process
• Specifying performance requirements for new
  equipment
• Selecting suppliers
• Planning the sequence of production processes
• 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

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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