Summary
7.1
Updated April-09
Lecture Notes
Chapter 7 Measure
ENTERPRISE EXCELLENCE
7.2
Updated April-09
Learning Objectives
• Process Measurement
• Statistical Process Control (SPC)
• Process Capability Analysis
• Measurement System Evaluation (MSE)
• Gage Reproducibility & Repeatability (R&R)
7.3
Updated April-09
Measure
• The goal of the measure phase is to gather information on the current state process
7.4
Updated April-09
PROCESS MEASUREMENT
• Attribute Data comes from counting conditions being present or not present, such as defective units, good units, number of defects, pass/fail, conforming/non-conforming, etc.
• Variable Data comes from measuring things, such as temperature, weight, length, distance, volume, ohms, diameter, etc. Variable data is objective and quantitative
• Primary (pro-active) data is collected under known, controlled conditions. Control is a state in which all special causes of variation have been removed from a process
• Secondary (passive) data is not directly collected. It is collected from historical databases or other external sources such as logs or field service reports
7.5
Updated April-09
STATISTICAL PROCESS CONTROL
• Statistical process control (SPC) is an analytical and statistical method to analyze collected data and control processes
• SPC focuses on the variability in a process. This variability is due to common causes (randomly occurring variations) or special causes (assignable events)
• The goals of SPC are: 1. Understand the variability within a process
2. Understand the capability of a process
3. Identify and eliminate special cause variation
4. Develop and implement strategies for improving the process
7.6
Updated April-09
STATISTICAL PROCESS CONTROL
• Statistical process control is used to monitor process stability and detect process changes
• It serves as an early warning system to detect potential problems before they cause downtime, inefficiency, or equipment failure.
• It allows you to be proactive and interactive with the process rather than being reactive:
1. To monitor quality parameters 2. To identify special causes of variation (material, equipment,
environmental changes, loading condtions, etc.) 3. To identify common causes of variation (i.e., those inherent to the
system) 4. To minimize or eliminate variation from special & common causes 5. To determine process capability 6. To indicate when adjustments or process corrections are necessary 7. To indicate when to leave a process alone because it is working well
7.7
Updated April-09
STATISTICAL PROCESS CONTROL
STRATEGIES
7.8
Updated April-09
SPC IMPLEMENTATION STRATEGIES
7.9
Updated April-09
7.10
Updated April-09
Subgroup Data with Unknown µ and σ
7.11
Updated April-09
7.12
Updated April-09
7.13
Updated April-09
7.14
Updated April-09
Constants A2, D3, and D4
Picture of the table A2, D3, and D4
7.15
Updated April-09
7.16
Updated April-09
7.17
Updated April-09
Constant PHI
7.18
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7.19
Updated April-09
• Figure below illustrates three cases of interests relative to the (PCR) CP and process specifications:
A. CP > 1, the process uses up much less than 100% of the tolerance band,
B. CP = 1, the process uses up the entire tolerance band
C. CP <1, the process uses up more than 100% of the tolerance band.
7.20
Updated April-09
Revision of Control Limits and Center Lines
7.21
Updated April-09
• Control limits are derived from natural process variability, or the natural tolerance limits of a process
• Specification limits are determined externally, for example by customers or designers
• There is no mathematical or statistical relationship between the control limits and the specification limits
Control vs. Specification Limits
7.22
Updated April-09
Rational Subgroups
7.23
Updated April-09
Guidelines for Control Chart Design
7.24
Updated April-09
• There are several charts available to use when dealing
with go/no-go, qualitative data:
1. p charts: Fraction of parts nonconforming or
defective in a sample of varying size
2. np charts: Number of parts nonconforming or
defective in a sample of constant size
3. c charts: Number of attributes nonconforming or
defective within a subgroup, lot, or sample of
constant size
4. u charts: Number of attributes per unit
nonconforming or defective within a subgroup, lot or
sample area of varying size
Attribute Control Charts
7.25
Updated April-09
The Control Chart for Fraction
Nonconforming, p
• The sample fraction nonconforming is defined as the ratio of the number of
nonconforming items in the sample D to the total number of items in that
sample, n:
• The Mean and Variance are:
7.26
Updated April-09
Fraction Nonconforming Control Chart, p
7.27
Updated April-09
• The np control chart is used when the actual number of items
failing, is a better indicator of the process than the percent failing.
• One essential requirement for this use of the np chart is that the
sample sizes for the subgroups must all be the same. (p charts can
be of varying sample sizes)
• Measure the number of parts nonconforming or defective in a
sample of constant size. np control charts are the best tool for
measuring discrepancies in lot inspections
The np Control chart – based on the
number nonconforming
7.28
Updated April-09
The np Control chart – based on the
number nonconforming
7.29
Updated April-09
• The C control chart is used to measure the number of defects in an inspected item when the sample size is constant. It is used to measure the number failings in an inspection item when we are concerned with the variance between items.
Control Charts for Nonconformities (c chart, Number of Attributes non-conforming or Defects)
7.30
Updated April-09 Control Charts for Nonconformities
(Defects) - Example
7.31
Updated April-09 Control Charts for Nonconformities
(Defects)- Example
7.32
Updated April-09 Control Charts for Nonconformities
(Defects)- Example
7.33
Updated April-09
Choice Between Attributes and Variables
Control Charts
7.34
Updated April-09
• Variables control charts provide much more useful information
about process performance than do attributes control charts.
Specific information about the process mean and variability is
obtained directly.
• In addition, when points plot out of control on variables control
charts, usually much more information is provided relative to the
potential cause of that out-of-control signal.
• For a process capability study, variables control charts are almost
always preferable to attributes control charts. The exceptions to
this are studies relative to non conformities produced by
machines or operators in which there are a very limited number of
sources of nonconformities, or studies directly concerned with
process yields and fallouts.
Choice Between Attributes and Variables
Control Charts
7.35
Updated April-09
1. Determine which process characteristics to control
2. Determine where the charts should be implemented in the process
3. Choose the proper type of control charts
4. Take actions to improve processes as the result of SPC/control
chart analysis
5. Select data-collection systems and computer software
These guidelines are applicable to both variables and attributes
control charts. Remember, control charts are not only for process
surveillance; they should be used as an active, on-line method for
reduction of process variability.
Guidelines for Implementing Control Charts
7.36
Updated April-09
Process Capability
• Process capability refers to the uniformity of the process. Obviously, the variability of critical-to-quality characteristics in the process is a measure of the uniformity of output. There are two ways to think of this variability:
1. The natural or inherent variability in a critical-to-quality characteristic at a specified time: "instantaneous" variability
2. The variability in a critical-to-quality characteristic over time
• Natural tolerance limits are defined as follows:
7.37
Updated April-09
Process Capability Ratios
7.38
Updated April-09 Recommended Minimum Values of the
Process Capability Ratio, Cp
7.39
Updated April-09
Process Capability Ratio for an Off-Center
Process
• The process capability ratio Cp does not take into account where the process mean is located relative to the specifications
• It is a measure of potential capability, not actual capability
7.40
Updated April-09
A Measure of Actual Capability
7.41
Updated April-09
Confidence Intervals and Tests on Process
Capability Ratios
7.42
Updated April-09
Confidence Intervals and Tests on Process
Capability Ratios- Example
7.43
Updated April-09
Confidence Intervals and Tests on Process
Capability Ratios
7.44
Updated April-09
Confidence Intervals and Tests on Process
Capability Ratios
7.45
Updated April-09
• The purpose of most measurement systems capability studies is
to:
1. Determine how much of the observed variability is due to
the gage or measurement system
2. Isolate the components of variability in the measurement
system
3. Assess whether the gauge is capable (suitable for the
intended application)
• We will introduce the two R’s of measurement system capability;
repeatability (do we get the same observed value if we measure
the same unit several times under identical conditions?) and
reproducibility (How much difference in observed values do we
experience when units are measured under different conditions,
such as different operators, time periods, and so forth?).
Gage and Measurement Systems Capability
Studies
7.46
Updated April-09
• To introduce some of the basic ideas of measurement systems
analysis (MSA), consider a simple but reasonable model for
measurement system capability studies
• where y is the total observed measurement, x is the true value of
the measurement on a unit of product, and ε is the measurement error.
• We will assume that x and ε are normally and independently
distributed random variables with means µ and 0 and variances (σ2p) and (σ
2 Gage), respectively. The variance of the total
observed measurement, y, is then
Gauge and Measurement Systems
Capability Studies
7.47
Updated April-09 Gauge and Measurement Systems
Capability Studies
7.48
Updated April-09 Gauge and Measurement Systems
Capability Studies
7.49
Updated April-09
The P/T ratio
7.50
Updated April-09
• There are other measures of gauge capability that have been proposed. One of these is the ratio of process (part) variability to total variability:
• Another is the ratio of measurement system variability to total variability
• Another measure of measurement system adequacy is defined by the AIAG (1995) [note that there is also on updated edition of this manual, AIAG (2002)] as the signal-to-noise ratio (SNR):
• AIAG defined the SNR as the number of distinct levels or categories that can be reliably obtained from the measurements. A value of 5 or greater is recommended. A value of less than 2 indicates inadequate gauge capability.
Estimating the Variance Components
7.51
Updated April-09
Discrimination Ratio
7.52
Updated April-09
• It is also possible to design measurement systems capability
studies to investigate two components of measurement error,
commonly called the repeatability and the reproducibility of the
gauge.
• We define reproducibility as the variability due to different
operators using the gauge (or different time periods, or different
environments, or in general, different conditions) and repeatability
as reflecting the basic inherent precision of the gauge itself.
• The experiment used to measure the components of σ2Gage is
usually called a gauge R&R study, for the two components of σ2Gage.
Gauge R&R Studies
7.53
Updated April-09
Comparing Customer and Supplier
Measurement Systems
• An essential component of the business relationship is the
conformance of the two measurement systems. If the customer and
supplier measurement systems are not in agreement, then
differences in opinion about product quality can occur and the
decision to accept or reject a shipment may become a basis for
dispute between the two parties. This endangers the business
relationship.
• R2 statistic is interpreted as the percentage of variation in the
supplier's measurements, that is explained by the variation in the
customer's measurement. It is used as a measure of the degree of
conformance between the two measurement systems.
• The value of R2 depends directly on the standard deviation of the
distribution of the true product characteristics, the standard
deviation of the supplier's measurement error distribution, and the
standard deviation of the customer's measurement error
distribution.
7.54
Updated April-09
• In this chapter, we have learned the following:
Process Measurement
Statistical Process Control
Process Capability Analysis
Measurement System Evaluation (MSE)
Gage Reproducibility & Repeatability (R&R)
Wrap-up