Sampling Sampling provides a discrete-time representation of a continuous waveform Sample points are real-valued numbers In order to transmit over a digital system we must first convert into discrete valued numbers

Information content of a random variable Random variable x Outcome of a random experiment Discrete R V takes on values from a finite set of possible outcomes PMF: P(X=y)=Py) How much information is contained in the event X=y? Will the sun rise today Revealing the outcome of this experiment provides no information Will the Celtics win the NBa championship? Since this is unlikely, revealing yes provides more information than revealing Events that are less likely contain more information than likely events

Final exam Very good performance overall Essays were particularly good ·Mean-88.5%0 Standard deviation -5.7%

Objectives Review the format and expectations for the final exam Review material needed to succeed on the final exam Set the material from the course in the context of the product realization process Answer questions

Term Project Final presentation Isual aids available on-campus Computer projection Document camera

Plan for the session Q Questions Complete some random topics Lecture on design of dynamic systems (Signal/Response Systems Recitation on hw#5? 16.881

Standard Orthogonal Arrays Maximum Maximum Number of Colum Orthogonal Number of Number of

Failure modes Noises lead to failure modes(Fm) One set of noise values leads to fm Opposite set of noise values leads to FM Simple problem solving chases the problem from Fm, to Fm, and back again but does not avoid both fms with the same set of design values-endless cycles of build/test/fIx(B/T/F) C Don Clausing 1998 6.881

Ideal response Want Ideal Response to Signal -usuall straight-line function Actual response is determined by values of control factors and noise factors If noise factors are suppressed early, the en difficult problems only appear late Introduce noises early C Don Clausing 1998

Case study An automatic document handler(adh)was developed at the ss level. When integrated into the total system there were many new problems. The TQM Problem Solving Process was used, and many problems were solved. However. at the field readiness Test (frt) before entering production the reliability was 15X worse than acceptable O Don Clausing 1998