Page 435 - Design for Six Sigma for Service (Six SIGMA Operational Methods)

Chapter
11

Statistical Basics and
Six Sigma Metrics

11.1 Introduction

Six Sigma is a data-driven management system with near-perfect performance
objectives (Pande et al. 2000). By data-driven we mean that in Six Sigma,
the real data collected in the process under study is the only source to measure
the current performance, analyze the root causes for the problem, and derive
improvement strategies. Near-perfect performance objectives means that in
Six Sigma, we will improve the process until it achieves a very low level of
defects and a very high level of performance. Clearly, it also needs the real data
from the process to verify if the desired performance requirements are met.

Data analysis is a very important part of Six Sigma. In the real business and
engineering process, many data collected are random variables; that is, their
value will vary with some degree of uncertainty. Let us look at Example 11.1.

Example 11.1
In a semiconductor manufacturing process, we have a step where an oxide film
is grown on a silicon wafer by using a furnace. In this step, a cassette of wafers
is placed in a quartz “boat” and the boats are placed in the furnace. A gas flow is
created in the furnace, and it is brought up to temperature and held there for a
specified period of time. In this process, it is required that the most desirable
oxide film thickness be 560 angstroms (Å); the specification of the oxide
thickness is 560 ± 100 Å. That is, an oxidized wafer is out of specification if its
thickness is either lower than 460 Å or higher than 660 Å. We collected the
following film thickness data in the process:
547 563 578 571 572 575 584 549 546 584 593 567
548 606 607 539 554 533 535 522 521 547 550 610
592 587 587 572 612 566 563 569 609 558 555 577
579 552 558 595 583 599 602 598 616 580 575
Does this process satisfy our quality requirement?

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