Introduction to Statistical Process Control: Objectives

1
Introduction to Statistical Process Control
Objectives

• React to process variation appropriately and
  beneficially
• Recognize the four possible process states
• Take the steps necessary to move any process to
  the ideal state

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A Manufacturing Process
3
Process Parameter Targets

• There is some ideal value for any process
  parameter - this is called the parameter target
• A perfect process would always produce
  measurements exactly on target

4
Specification Limits

• In addition to a target, process parameters often
  have specification limits
• Material with measurements outside of
  specification limits has no value to the customer
• Specification limits depend only on customer
  requirements, and have nothing to do with actual
  process performance
• Determining realistic specification limits can be
  a challenging task

5
Variation from Target

• Any variation from target is bad, and bigger
  variations are worse than smaller variations
• The purpose of a process control system is to
  keep the process running on target
• Prevent variation from target
• Minimize variation from target
• Do all of this economically

6
The Two Kinds of Variation

• Variation in industrial processes falls into one
  of two categories
• Common cause variation
• Random in nature
• Happens all the time
• Relatively small in magnitude
• Special Cause variation
• Has an assignable cause
• Usually rare
• Relatively large in magnitude

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Common Cause Variation

• This type of variation occurs in all processes -
  it cannot be eliminated without making
  fundamental changes in the process
• Attempting to adjust the process to reduce common
  cause variation is tampering - this actually
  increases variation from target

8
Tampering

• Drive from Phoenix to Tucson and keep your speed
  between 74.5 and 75.5 mph
• Step on the brake if your speed exceeds 75.5
• Step on the gas if your speed falls below 74.5

9
Stable Processes

• Only common cause variation is seen
• Outputs show the same pattern and range over time
• Most stable processes are normally distributed

10
Control Limits

• Control limits are computed from observation of a
  stable process
• A stable process will almost always (99.7 of the
  time) run inside the control limits

11
Special Cause Variation

• Special cause variation is the result of some
  assignable cause
• Special cause variation might indicate a serious
  qualitative change in the process
• Special cause variation is often persistent, so
  failing to react quickly will allow more material
  to be produced far from target
• Reaction Find the assignable cause, eliminate
  it, and restore the process to stability

12
Unstable Processes

• Special causes regularly influence unstable
  processes

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Stable Processes Are More Profitable

• They produce better products, and less scrap
• They take less work to maintain
• Output schedules are more predictable
• They transfer less variation to following
  processes

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Components of a Process Control System (PCS)

• Take some measurements
• Summarize measurements
• Plot summarized measurements on a control chart
  appropriate to the process
• Use decision rules to decide if the process is
  unstable
• React uniformly and beneficially if special
  causes are observed

15
An Example Process Control System

• A gate oxide process is targeted to grow 225
  Angstroms of silicon dioxide on each of 150
  wafers in
  a load

16
Measurements

• Three wafers
  from each load are measured on the Nanospec
• Wafers are chosen from the same locations in the
  load every time this facilitates
  troubleshooting
• Many wafers in the load are not measured

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Calculations

• The average thickness is computed - this is
  called X-bar
• The range of the thicknesses is also computed

18
Control Chart

• Two control charts are actually used - one for
  X-bar, and one for the range
• Control limits for the X-bar chart are set at 207
  and 243

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Trend Rules

• Five rules are used for the X-bar chart
• One point outside of 207 or 243
• Two of three successive points outside 237
• Two of three successive points outside 213
• Four of five successive points outside 231
• Four of five successive points outside 219
• Someone can beneficially react to a violation of
  any of these rules

20
Response Flow

• The response flow is a programmed set of actions
  for the operator to take when the process appears
  to be unstable
• The order of the actions is chosen to lead to the
  source of the problem quickly
• The response flow should usually allow the
  operator to fix the process without engineering
  intervention
• Everybody uses the same response flow, every time

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Four Types of Process

• All processes can be categorized as one of four
  types
• Ideal
• Promising
• Treacherous
• Turbulent
• Different types require different actions
• Engineers should strive to move all processes to
  the ideal state

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Ideal Process

• A stable process
• Almost always produces material within
  specification limits

23
Reaction to an Ideal Process

• Use a process control system to maintain this
  process
• Do not tamper with the process

24
Promising Process

• A stable process
• Produces a significant amount of material outside
  specification limits

25
Reaction to a Promising Process

• Use dispositioning to keep bad material from
  leaving the factory
• Do not tamper with this stable process
• If the process is off-target
• move it to target - this is often an easy fix
• If the process mean is centered
• Then process variation is too large
• Reduce process variation - a more difficult fix,
  often requiring equipment or process changes

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Treacherous Process

• An unstable process
• By luck, it usually produces material within
  specification limits

USL
UCL
Target
LCL
LSL
27
Reaction to a Treacherous Process

• Install a process control system to stabilize the
  process
• This will reduce variation from target, and
  improve the quality of products received by the
  customer
• Failing to react to this type of process is
  dangerous the process could stray outside of
  specification limits

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Turbulent Process

• An unstable process
• Often produces material outside of specification
  limits

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Reacting to a Turbulent Process

• Use product dispositioning
• Stabilize the process
• Make this a promising process
• Improve to an ideal process from there
• The process must be stabilized before it can be
  improved
• An unstable process is very difficult to keep on
  target, so the route to the ideal process must
  include a stop at the promising process

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Benefits of Process Control Systems

• More money for the manufacturer
• Less scrap, more productive equipment
• Better quality for the customer
• Less stress for the engineer
• Less time spent troubleshooting
• More satisfying job for the operator
• Never asked to tamper with the process
• They can resolve most problems themselves

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Costs of Process Control Systems

• Measurement equipment
• Trained people to make measurements
• Automation resources if desired
• Management review and reinforcement

32
SPC for Variables Data

• Control charts for variables
• X-bar
• S
• Chart for individuals
• Moving range chart

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The X-Bar Chart Usage

• Averages of a set of measurements taken at the
  same time are plotted
• Average of six thickness measurements from a
  diffusion process
• Average of 32 CD measurements
• The same number of measurements is taken each
  time
• Averages are plotted in time order

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X-Bar Chart Appearance
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X-Bar Chart Centerline

• The centerline (CL) is the process average, often
  called X-bar-bar
• This might not be the process target
• The target is where you want the process to run,
  the centerline is where it actually runs
• If these happen to coincide, or if correction to
  target is easy and routine, the centerline may be
  the target

36
X-Bar Chart Control LimitsA Nontraditional Method

• Control limits are fixed at three standard
  deviations of the means from the centerline

The data must be taken from a stable process
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X-Bar Chart Control LimitsThe Traditional Method

• Take samples in a rational subgroup
• Measurements likely to exhibit only common cause
  variation, and unlikely to exhibit special cause
  variation
• Base control limits on the average range of these
  measurements

38
Comparison of Methods

• The non-traditional method seems to be necessary
  in a batch-processing environment
• Rational subgroups are within-batch, and do not
  exhibit typical common cause variation
• Control limits by the traditional method are much
  too tight

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Sampling Distribution of X-Bar

• If random variables are normally distributed with
  the same mean and standard deviation
• Then means of n such random variables are also
  normally distributed, but with smaller s

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The Central Limit Theorem

• Means taken from almost any distribution tend to
  be normally distributed

n1
n5
n10
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X-Bar Chart Effectiveness

• False alarm rate (a risk) is 0.30
• The probability of detecting a process shift of a
  defined size is b risk
• The average time to detection of a process shift
  is the average run length
• ARL and b risk can be decreased with the use of
  trend rules, but at the cost of false alarms

42
X-Bar Chart Beta Risk

• b risk is given in Table 6-2 for sudden shifts
  measured in terms of the standard deviation of
  the process
• A process has a s of 32
• You want a 90 chance of detecting a sudden shift
  of 47 in the first sample after the shift
• This is about 1.5 standard deviations
• The sample size must be at least 8

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Average Run Length for the X-Bar Chart

• The ARL is the average number of samples after a
  sudden shift until a point would be outside the
  control limits.

44
ARL Application

• With process s of 32, the average run length of
  detecting a sudden shift of 20 with samples of
  size 8 is 10

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Additional Lines on the X-Bar Chart
2s
1s
-1s
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Trend Rules

• Trend rules reduce b risk, but they must be
  chosen carefully
• Every additional trend rule adds a risk
• The operator must be able to react beneficially
  to a trend rule violation
• Some trend rule violations are difficult to see,
  so automation or intensive training may be needed

47
WECO Rules

• One point outside of 3s
• Two of three points outside the same 2s line
• Four of five points outside the same 1s line
• Eight points in a row on one side of the
  centerline

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Range Chart

• The range (R) chart is often used in conjunction
  with an X-bar chart to monitor within-group
  variation

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S-Chart

• The S-chart will detect abnormal variation within
  a subgroup
• Sample standard deviations are plotted
• It should be used anywhere an X-bar chart is used
• The R-chart (range chart) is a more traditional
  choice, but is less effective

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Control Limits for the S Chart

• Table 6-5 gives limits and trend rule lines which
  will give about 1 false alarms.
• Limits are based on an estimate of within-group
  standard deviation
• Traditional limits will differ from these

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SPC for Attributes Data

• Charts for number of defective units
• np (fixed number of units sampled)
• p (varying number of units sampled)
• Charts for number of defects
• c (fixed area inspected)
• u (varying area inspected)

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p Chart for Proportion of Defective Units

• Exactly like an np chart, but the number of units
  sampled varies
• The number of units sampled should not depend on
  the number of defective units observed
• Control limits depend on the number of units
  sampled - people really hate this

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• A sample of die are inspected every day after
  wafer sort to check for probe damage - each die
  is classified as damaged or not damaged. The
  number of die inspected varies from day to day.

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Control Limits for the p Chart
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p-bar is 0.0717, so the UCL for the first sample
is
Does the first sample indicate an OOC process?
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SPC Implementation

• Process control evolution
• Deciding what to measure
• Choose an effective sampling scheme
• Choose the right control charts
• Collect initial data
• Compute control limits and assess stability

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Key Product Characteristics

• Key product characteristics are those few
  measurable things vitally important to your
  customers
• Voltage threshold, package dimensions
• These are often called output parameters
• Process control on only key product
  characteristics is inefficient, but
  dispositioning may be necessary

63
Key Process Parameters

• Key process parameters are those few important
  influences on key product characteristics
• These are the focus of process control
• Finding KPP for each KPC is an important part of
  process characterization

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Process Control Evolution
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Decide What to Measure Select Key Process
Parameters

• How much does it influence a KPC?
• Does it routinely vary?
• Is there a propensity for excursions?
• Can you control it?
• Can you measure it, and before bad material is
  made?
• Does it transmit variance to other KPP?

66
Sample Design

• Sample often enough and intensely enough to
  detect important events
• An analysis of process history can help you
  anticipate which types of events to expect
• Sampling at fixed locations or times may enhance
  troubleshooting
• Simulation is often used to evaluate sampling
  plans

67
Control Chart Selection

• Control charts appropriate for most situations
  are given in Table 6-3
• Several control charts can be produced from the
  same set of measurements
• X-bar chart
• S-chart for within-lot standard deviation
• S-chart for within-wafer uniformity

68
SPC Implementation in the Factory

• SPC Elements
• Measurements
• Calculations
• Control Charts
• Trend Rules
• Troubleshooting
• SPC maintenance and improvement

69
Measurements

• Failure to take measurements is the most common
  reason for SPC failure
• People need to know how and when to take the
  measurement
• Measurement must be part of the written
  specification for their job
• There should be rewards for taking the
  measurements, and punishment for failing to take
  the measurements

70
Calculations

• Automate all calculations if possible
• Make calculations easy and intuitive
• Dont ever expect anyone to calculate a standard
  deviation - even with a calculator
• Have the operators design data entry spreadsheets

71
Control Charts

• Automate if possible, but even automated charts
  must be readable and accessible
• Make the rules clear
• Is on the line in or out?
• Do they have to circle the last point in a trend
  rule violation?
• Audit and reward good performance

72
Trend Rules

• Do more good than harm Use trend rules only
  when you can react beneficially to them
• Troubleshooting is determined for each rule
  violation
• Reaction and adjustment does not upset the
  process
• It is better to start with a few rules than with
  many

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Response Flows (OCAP)

• A response flow should allow the operator to fix
  the process 75 of the time
• Call Engineering is a last resort (at the end
  of the response flow)
• Involve the operators in writing the response
  flow, and respond quickly to their requests for
  improvements

74
SPC Maintenance and Improvement

• A process control system is itself a process, and
  some process monitors have been developed

75
Specification Limits

• Hard limits determined by customer
• Material inside the limits is good
• Material outside the limits is bad
• Cpk is an index used to relate process
  performance to ability to specification limits
• Originally formulated for normally-distributed
  processes with two-sided specification limits

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Cpk and Percent OOS

• If the data is normally distributed and there are
  two-sided specification limits, then there is a
  simple correspondence between Cpk and the percent
  of material out of specification

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Cpk Is Often Misused

• Cpk is applied to non-normally distributed data -
  probability interpretations no longer apply here
• Cpk is applied to processes with one-sided
  specification limits
• A process can run far off target, but with small
  variance, and still have good Cpk

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Step Function Loss

• The use of specification limits for product
  screening assumes a step function loss

80
Quadratic Loss

• Taguchi (and others) recognized that step
  function loss was unrealistic, and proposed
  quadratic loss

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Upside-Down Normal Loss

• Bounds the loss between zero and one
• Recognizes that fact that all material too far
  from target is equally bad, and is adjustable
• Has very useful mathematical properties
• Bounded and infinitely differentiable
• Easy closed-form solution for expected value with
  normally distributed processes
• Extends to multivariate case with ease

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• UDN is exactly the upside-down probability
  density function for the normal distribution
• t is process target, l is a scale parameter
• Larger l gives a less sensitive loss function
• Use actual loss data to choose l, or scale l to
  give 50 loss at a specification limit

85
Expected Loss

• If the process is normally distributed with mean
  m and standard deviation s, then the average loss
  from that process will be

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Comparison of Cpk and ELUDN

• The expected loss punishes deviation from
  target, even if the process standard deviation is
  small
• Expected loss can also be computed for other
  underlying distributions, so is not dependent on
  the assumption of process normality

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Specification limits are at /- 3
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EL0.693, Cpk0.50
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EL0.773, Cpk1.00
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Extensions to Simple UDNLF

• Asymmetric UDNLFs have similar properties, and
  formulae for expected values exist
• Any form of distribution can be used for the
  process, but numerical integration may be
  required for expected value
• All UDNLF properties extend easily to MUDNLF,
  where correlations between process variables can
  have interesting consequences
• For more information, see David Drain and Andrew
  M. Gough, Applications of the Upside-Down Normal
  Loss Function, IEEE Transactions on
  Semiconductor Manufacturing,Vol. 9, No. 1,
  February 1996

91
Common Errors in the Application of SPC

• Tampering
• In control, but off-target
• Single set of limits
• Control limits never reset
• Confusing specifications with control limits
• Attributes used instead of variables
• Charting output parameters
• Ineffective response plans
• Misuse of capability indices
• Charts on special causes

92
Tampering

• Also called over-adjustment, or
  over-controlling
• A common error with ambitious young engineers
• Tight control limits or too many trend rules are
  evidence of systematic tampering
• Effects are well-documented
• Operator frustration and distrust in SPC
• Increased variation from target

93
In Control, but Off-Target

• Often seen in stable processes which are not
  receiving sufficient attention - usually only the
  3-sigma rule is being applied
• Easily detected by loss function computation or
  trend rule usage
• Effects
• Short-term inferior products
• Long-term drift from target - an unintentional
  process change. Readjusting to target later can
  be risky

94
Single Set of Limits for a Fleet of Equipment

• Engineers often try to apply the same control
  limits to a set of similar equipment
• The equipment should all be the same
• More convenient to use a single set of limits
• This allows all pieces of equipment to perform at
  the lowest performance level for the fleet
• Some equipment runs off-target forever
• Large variation is tolerated where it is not
  necessary

95
Control Limits Never Reset

• Simple lack of attention causes this
• Control limits should be periodically examined
  and reset when
• There is a process change
• The limits conflict with actual process
  performance
• If limits are too tight, excessive false alarms
  undermine confidence in the system
• If limits are too loose, an opportunity for
  process improvement is lost

96
Confusing Specification and Control Limits

• Specification limits reflect customer desires,
  but do not necessarily have any relation to where
  the process actually runs
• Using specification limits for control limits
  defeats every purpose of SPC
• Tampering occurs if the limits are too tight
• Ignoring occurs if the limits are too loose

97
Charting an Attribute when Variables Data is
Available

• Variables data is inherently superior to
  attribute data
• Smaller samples required for the same quality of
  decision
• Usually better measurement capability
• More likely to be associated with causes of
  observed variation
• Attribute data is often based on imprecise visual
  assessments
• High inter-evaluator variability
• Fatigue and pressure influence measurement quality

98
Control Charts for Output Parameters

• One of the first signs of an immature process
  control system
• Often a futile practice - once the material is
  ruined, no reaction is effective to prevent the
  event
• To improve this situation
• Find the key process parameters which influence
  important output paramters
• Install true SPC on these parameters

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Ineffective Response Plans

• A response plan (to out-of-control) should be
  effective at least 75 of the time it is used
• A response plan should lead to the most probable
  cause as quickly as possible
• Improve the response plan
• Include new special cause sources
• Reorder activities to lead to a quicker
  resolution
• Eliminate extraneous measurements and work
• Involve the operators in response plan definition

100
Control Charts Applied when Every Event is a
Special Cause

• A control chart for the number of construction
  fatalities at your site is futile
• Every event is treated as a special cause -
  nobody would refuse to react if the number of
  fatalities was in control
• The response to a fatality will not depend on the
  number of fatalities that month
• This is another case of reacting to an output
  parameter
• Find the key process parameters that control
  fatalities, and control them instead

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Misuse of Capability Indices

• The interpretation of Cpk for non-normal
  parameters is not obvious
• Cpk must be adapted for parameters with one-sided
  specification limits
• Cpk does not adequately punish off-target
  performance

102
Advanced Statistical Process Control

• Exponentially weighted moving average charts
• Cusum charts
• Multivariate SPC
• Run-to-Run control
• Process oriented basis representations
• Profile analysis

103
EWMA Charts

• Plots a smoothed estimate of current performance
  (zt)
• Degree of smoothing is determined by l (usually
  0.2 to 0.3)
• Tables can be used to balance alpha risk and ARL
• EWMA charts are usually not very good at
  detecting one-time jumps from target

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Jump up 2.3s
Shift up .9s
Reset EWMA
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Cumulative Sum Charts

• Best suited to a process where small shifts from
  the target must be detected
• The positive and negative cumulative sums of
  differences from target (or mean) are plotted on
  the same chart
• Parameters (h,k) can be chosen from tables to
  meet ARL goals

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Multivariate SPC

• Process parameters
  are often
  correlated, and control charts on individual
  parameters will not detect departures from the
  typical process

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Hotellings T Control Chart

• Plots a distance measure from the center for
  the data that comprehends correlation between
  variables.
• Once an out of control is signaled, considerable
  examination of the data may be necessary to
  determine why that point was unusual

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Principal component charts

• Linear combinations of the original variables are
  chosen in a way that makes them uncorrelated
• A few of these new variables can summarize most
  of the variation in all the variables
• BUT the original variables are still not
  readily apparent when a component goes out of
  control

112
Run to Run Control

• Use information from recent runs (batches, often)
  to adjust the process for the next run
• Some people call this tampering, but if done
  correctly, the process can be kept closer to
  target

113
Process Oriented Basis Representations

• Some linear combinations of multivariate
  measurements are excellent indicators of
  particular process problems
• Find an (independent) set of such linear
  combinations
• Control chart these excursions indicate
  specific problems rather than overall process
  misbehavior

114
Profile Analysis

• The process outcome can be monitored by observing
  the relationship between some set of measured
  variables (Xs) and a response (Y).
• Control charts on the slope and intercept are
  simple examples of profile analysis