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

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: Introduction to Statistical Process Control

Spanos EE290H F05 Managing Variation over Time • Statistical Process Control often takes the form of 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. 2 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 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. 3 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 Example: Investigate furnace temp and set up a real-time alarm. 3 2 1 0 -1 -2 -3 0 5000 10000 15000 20000 time The pattern is obvious. How can we automate the alarm? 4 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 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. 5 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 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. 2 UCL 1.2 1 0 -1 LCL -1.2 -2 0 10 20 30 6 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 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 outside 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. 7 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 Another Example Original data Averaged Data (n=5) Variable Control Charts Plot 1.150 1.070 UCL=1.0626 1.050 1.100 1.030 Mean of small shift 1.050 small shift 1.010 1.000 µ0=1.0006 0.990 0.950 0.970 0.900 0.950 LCL=0.9387 0.930 0.850 25 50 75 100 0 100 200 300 400 500 small shift Mean of small shift 8 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 How the Grouping Helps Small Group Size, Large Group Size, large β . smaller β for same α . Bad Good 9 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 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. 10 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 The Operating Characteristic Curve 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. β These curves are drawn for α = 0.05 Fig. 4-5 from Montgomery, pp. 110 deviation in #σ 11 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 Pattern Analysis 3 2 1 0 -1 -2 -3 0 20 40 60 80 100 Other rules exist: Western Electric, curve fitting, Fourier analysis, pattern recognition... 12 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 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. 13 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 Range and x chart for all wafer groups. 600 500 UCL 507.09 400 300 200 100 0 LCL 0.0 8000 UCL 7971.32 7900 7800 7700 LCL 7694.52 7600 0 10 20 30 40 Wafer Groups 14 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 Comparing runs A and B Range, Shift A Range, Shift B 600 600 550 500 500 465 400 400 300 300 260 220 200 200 100 100 0 0 0 10 20 0 10 20 Mean, Shift A Mean, Shift B 8000 8000 7985 7958 7900 7900 7835 7831 7800 7800 7704 7700 7700 7685 7600 7600 0 10 20 0 10 20 15 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 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. 16 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 The Control Chart for Controlling Dice Production 17 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 The Reference Distribution 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 10 11 12 18 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 The Actual Histogram 7 6 5 4 3 2 1 2 3 4 5 6 7 8 9 10 11 12 19 Lecture 10: Introduction to Statistical Process Control

Spanos EE290H F05 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. 20 Lecture 10: Introduction to Statistical Process Control