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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

A Manufacturing Process

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

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

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

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

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

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

Stable Processes

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

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

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

Unstable Processes

- Special causes regularly influence unstable

processes

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

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

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

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

Calculations

- The average thickness is computed - this is

called X-bar - The range of the thicknesses is also computed

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

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

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

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

Ideal Process

- A stable process
- Almost always produces material within

specification limits

Reaction to an Ideal Process

- Use a process control system to maintain this

process - Do not tamper with the process

Promising Process

- A stable process
- Produces a significant amount of material outside

specification limits

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

Treacherous Process

- An unstable process
- By luck, it usually produces material within

specification limits

USL

UCL

Target

LCL

LSL

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

Turbulent Process

- An unstable process
- Often produces material outside of specification

limits

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

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

Costs of Process Control Systems

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

SPC for Variables Data

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

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

X-Bar Chart Appearance

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

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

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

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

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

The Central Limit Theorem

- Means taken from almost any distribution tend to

be normally distributed

n1

n5

n10

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

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

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.

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

Additional Lines on the X-Bar Chart

2s

1s

-1s

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

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

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)

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.

Control Limits for the p Chart

p-bar is 0.0717, so the UCL for the first sample

is

Does the first sample indicate an OOC process?

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

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

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

Process Control Evolution

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?

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

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

SPC Implementation in the Factory

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

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

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

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

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

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

SPC Maintenance and Improvement

- A process control system is itself a process, and

some process monitors have been developed

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

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

Step Function Loss

- The use of specification limits for product

screening assumes a step function loss

Quadratic Loss

- Taguchi (and others) recognized that step

function loss was unrealistic, and proposed

quadratic loss

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

Expected Loss

- If the process is normally distributed with mean

m and standard deviation s, then the average loss

from that process will be

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

Specification limits are at /- 3

EL0.693, Cpk0.50

EL0.773, Cpk1.00

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

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

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

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

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

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

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

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

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

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

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

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

Advanced Statistical Process Control

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

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

Jump up 2.3s

Shift up .9s

Reset EWMA

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

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

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

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

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