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12 Cards in this Set

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SPC
Technique for applying statistical analysis to measure, monitor, and control processes
Variation
Classified as chance (common) cause, assignable cause
Subgroup selection
Makes subroup as homogenous as possible and maximizes opportunity for variation from one subgroup to another
Sources of variability
1) Lot-to-lot
2) Stream-to-stream
3) Time-to-time
4) Piece-to-Piece
5) Error of measurement: equipment and human
Process in statistical control
Characterized by plot points that do not exceed the upper or lower control limits.
X bar - R Chart
UCL(Xbar)= Xbarbar + A2*Rbar
LCL(Xbar)= Xbarbar - A2*Rbar

UCL(R)= D4*Rbar
LCL(R)=D3*Rbar

Used when data is readily available

Limits at 3 sigma (covers 99.73% of population)
Xbar-s
s=√(Σ(X-Xbar)^2/(n-1))

UCL(Xbar)=Xbarbar + A3*sbar
LCL(Xbar)=Xbarbar - A3*sbar

UCL(s)=B4*sbar
LCL(s)=B3*sbar

Used when larger sample sizes are used for increased sensistivity to variation
MXbar-MR
UCL(Xbar)=Xbarbar + A3*sbar
LCL(Xbar)=Xbarbar - A3*sbar

UCL(s)=B4*sbar
LCL(s)=B3*sbar

Individual Xbar's and R's are calculated based upon some number of measurements in a sample. Each sample is comprised of one new measurement and the rest old measurements.

Used where data is less readily available
X-MR
Individual data points and moving range

UCL(X)= Xbar+E2*MRbar
LCL(X)= Xbar-E2*MRbar

UCL(MR)= D4*MRbar

ONLY chart which may have specification limits
NOT as sensitive to process changes
CuSum
More efficient at detecting small shifts (2 sigma or less)

If process remains in control, centered at μ0, the CuSum plot shows variation in a random pattern about zero. If the process drifts, the CuSum points will drift as well.
Exponentially Weighted Moving Average (EWMA)
EWMA(t)=λY(t)+(1-λ)EWMA(t-1)

s^2(EWMA)=(λ/(2-λ))s^2

UCL=EWMA0+ks(EWMA)
LCL=EWMA0-ks(EWMA)

k=3
p Chart
Fraction defective

UCLp=pbar+3*sqrt((pbar(1-pbar))/n)