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Introduction to Statistical Process Control The assignable cause - - PowerPoint PPT Presentation

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Spanos EE290H F05 Introduction to Statistical Process Control The assignable cause The Control Chart Statistical basis of the control chart Control limits, false and true alarms and the operating characteristic function 1 Lecture 10:

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Lecture 10: Introduction to Statistical Process Control

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Introduction to Statistical Process Control

The assignable cause The Control Chart Statistical basis of the control chart Control limits, false and true alarms and the

  • perating characteristic function
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Lecture 10: Introduction to Statistical Process Control

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Managing Variation over Time

  • Statistical Process Control often takes the form
  • f a continuous Hypothesis testing.
  • The idea is to detect, as quickly as possible, a

significant departure from the norm.

  • A significant change is often attributed to what is

known as an assignable cause.

  • An assignable cause is something that can be

discovered and corrected at the machine level.

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Lecture 10: Introduction to Statistical Process Control

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What is the Assignable Cause?

  • An "Assignable Cause" relates to relatively strong

changes, outside the random pattern of the process.

  • It is "Assignable", i.e. it can be discovered and corrected

at the machine level.

  • Although the detection of an assignable cause can be

automated, its identification and correction often requires intimate understanding of the manufacturing process.

  • For example...

– Symptom: significant yield drop. – Assignable Cause: leaky etcher load lock door seal. – Symptom: increased e-test rejections – Assignable Cause: probe card worn out.

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Lecture 10: Introduction to Statistical Process Control

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Example:

The pattern is obvious. How can we automate the alarm? Investigate furnace temp and set up a real-time alarm.

20000 15000 10000 5000

  • 3
  • 2
  • 1

1 2 3 time

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Lecture 10: Introduction to Statistical Process Control

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The purpose of SPC

  • A. Detect the presence of an assignable cause fast.
  • 2. Minimize needles adjustment.
  • Like Hypothesis testing

– (A) means having low probability of type II error and – (B) means having low probability of type I error.

  • SPC needs a probabilistic model in order to describe the

process in question.

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Example: Furnace temp differential (cont.)

Group points and use the average in order to plot a known (normal) statistic. Assume that the first 10 groups of 4 are in Statistical

  • Control. Limits are set for type I error at 0.05.

30 20 10

  • 2
  • 1

1 2 LCL -1.2 UCL 1.2

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Lecture 10: Introduction to Statistical Process Control

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Example (cont.)

  • The idea is that the average is normally distributed.
  • Its standard deviation is estimated at .6333 from the first

10 groups.

  • The true mean (μ) is assumed to be 0.00 (furnace

temperature in control).

  • There is only 5% chance that the average will plot
  • utside the μ+/- 1.96 σ limits if the process is in control.

In general: UCL = μ + k σ LCL = μ - k σ where μ and σ relate to the statistic we plot.

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Lecture 10: Introduction to Statistical Process Control

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Another Example

Plot small shift 0.850 0.900 0.950 1.000 1.050 1.100 1.150 100 200 300 400 500 small shift

Variable Control Charts Mean of small shift 0.930 0.950 0.970 0.990 1.010 1.030 1.050 1.070 25 50 75 100 µ0=1.0006 LCL=0.9387 UCL=1.0626 Mean of small shift

Original data Averaged Data (n=5)

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How the Grouping Helps

Small Group Size, large β. Large Group Size, smaller β for same α. Bad Good

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Average Run Length

  • If the type I error (α) depends on the original (proper)

parameter distribution and the control limits, ...

  • ... the type II error (β) depends on the position of the

shifted (faulty) distribution with respect to the control limits.

  • The average run length (ARL) of the chart is defined as

the average number of samples between alarms.

  • ARL, in general, is 1/α when the process is good and

1/(1-β) when the process is bad.

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The Operating Characteristic Curve

  • Fig. 4-5 from Montgomery, pp. 110

These curves are drawn for α = 0.05 β deviation in #σ The Operating Characteristic of the chart shows the probability of missing an alarm vs. the actual process shift. Its shape depends on the statistic, the subgroup size and the control limits.

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Pattern Analysis

Other rules exist: Western Electric, curve fitting, Fourier analysis, pattern recognition...

100 80 60 40 20

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1 2 3

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Example: Photoresist Coating

  • During each shift, five wafers are coated with photoresist

and soft-baked. Resist thickness is measured at the center of each wafer. Is the process in control?

  • Questions that can be asked:

a) Is group variance "in control"? b) Is group average "in control"? c) Is there any difference between shifts A and B?

  • In general, we can group data in many different ways.
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Range and x chart for all wafer groups.

100 200 300 400 500 600

LCL 0.0 UCL 507.09

40 30 20 10 7600 7700 7800 7900 8000

Wafer Groups

LCL 7694.52 UCL 7971.32

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Comparing runs A and B

20 10 100 200 300 400 500 600

Range, Shift B 260 550

20 10 100 200 300 400 500 600

Range, Shift A 220 465

20 10 7600 7700 7800 7900 8000

Mean, Shift A 7704 7831 7958

20 10 7600 7700 7800 7900 8000

Mean, Shift B 7685 7835 7985

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Why Use a Control Chart?

  • Reduce scrap and re-work by the systematic

elimination of assignable causes.

  • Prevent unnecessary adjustments.
  • Provide diagnostic information from the shape of

the non random patterns.

  • Find out what the process can do.
  • Provide immediate visual feedback.
  • Decide whether a process is production worthy.
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The Control Chart for Controlling Dice Production

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The Reference Distribution

2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7

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The Actual Histogram

2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7

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In Summary

  • To apply SPC we need:
  • Something to measure, that relates to

product/process quality.

  • Samples from a baseline operation.
  • A statistical “model” of the variation of the

process/product.

  • Some physical understanding of what the

process/product is doing.