DS 412 TEST 1

Question Answer
X-bar Average, use past if offered bc already in control
R-bar Range, use past if offered bc already in control (less accurate as sample size gets larger)
UCLx (X-bar2) + A2*R-bar (for x-bar chart)
LCLx (X-bar2) – A2*R-bar (for x-bar chart)
UCLR D4*R-bar (for R-bar chart)
LCLR D3*R-bar (for R-bar chart)
A2 on table dependent on sample, used in X-bar & R-bar chart
n sample *do not confuse with sample size larger then 10
D3 & D4 used with R-bar chart, on table
Out of Control/Causal past UCL/LCL, run, extreme jump/drop
? standard deviation
?x ?/vn
Z normal deviate (# of standard dev from average) or tolerance; closer to 6 (six sigma) more accurate. 2 if not really important, 3-life threatening/small difference is important
UCLx using ?x x-bar2 + Z*?x
LCLx using ?x x-bar2 – Z*?x
?p v p-bar (1-Pbar)/n
P-bar # defects/#observations
UCLp P-bar + Z*?p
LCLp P-bar – Z*?p
Process Capability Index (Cpk) use when target & x-bar not close
MIN of
[x-bar-Lower spec/3?,Upper-x-bar/3?
Process Capability Ratio (Cp) Upp-Low Spec/6?
Capable? if not below 1.33
Variable MEASURED/quantitative (weight, length, volume, time)*not used if specifications are complex/costly/difficult/unnecessary
Attribute COUNTED/Qualitative (Yes/No) color,taste,smell,surface texture
Non-destructive sampling 100% sampling,if easy/not expensive ie software test comp speed
Destructive Sampling costly, can't be reused
In Control (random) 1. No sample points outside limits
2. Most pts near process avg
3. Approx equal # pts above&below center
4. Randomly distributed around center
5. No extreme jumps
6. Cannot detect trend
Average ? = Average R (when…) n=2
Type I error Probability of searching for a cause when none exists
Type II error Probability of concluding that nothing has changed
Errors controlled by… Choice of control limits
+/- 1? 68.26% normal distribution
+/- 2? 95.44% normal distribution
+/- 3? 99.97% normal distribution