Can anyone tell me the formula used for Z-bar & W charts? I know Z is the Z-score but how about W? What does W stand for? Please help.

Out of my knowledgebase, but I'll bump this up. Things are a bit slow here and probably will be through the first of January.

Can anyone tell me the formula used for Z-bar & W charts? I know Z is the Z-score but how about W? What does W stand for? Please help.

About Z charts I posted an attachement on 28 sept (L006.pdf)

Criteria in Process Control: No Control Charts (http://elsmar.com/Forums/showthread.php?t=9669)

Can you explain W Charts ?, I don't find any info on the net, can be a typo error ?(maybe another way to skin the thing). :frust:

Even Google search and ASQ info search is not returning any relevant results for “W charts”. Could be Exponentially “Weighted” Moving average charts?
Regards,
Govind.

Even Google search and ASQ info search is not returning any relevant results for “W charts”. Could be Exponentially “Weighted” Moving average charts?
W Chart terminology is used by Wheeler. (Ref: Short Run SPC by Donald Wheeler; SPC Press Inc.)

For individual values:
1. Z-W Charts
Z=(X-Nominal) / Sigma(X), where Sigma(X) is calculated using RBar/d2.
Center line for Z-Chart is at 0 and Control Limits are obviously: +/- 3.0

W is the moving range calculated using the Z values.
For W chart, Center line is at d2=1.128 and UCLw= d2 + (3*d3) = 3.686.

Wheeler has also given a few variants of these:
2. Z*- W* Charts

Z* chart where Z* = (X-Nominal) / (RBar)
For Z* chart, Center Line at 0, and Control Limits at +/- 2.660

W* is a 2 point moving range calculated from Z* values. W* Chart has its center line at 1.0 and UCLw = D4 = 3.268.

For Subgrouped Data:
3. ZBar-W Charts
ZBar = (XBar-Nominal) / Sigma(XBar)
Center at 0, Control Limits at +/-3.0 and
Sigma(XBar)= RBar/(d2 * Sqrt(n))

Subgroup ranges are converted to W values using:
W = R/(Sigma(X))
Center at d2; Control Limits at d2 +/- (3 * d3)

Further:
4. Z*Bar-W* Charts

Z*Bar = (XBar - Nominal) / RBar
Center line at 0, Control Limits at +/-A2
W* = R/RBar
Center at 1.0; Control Limits at D3 and D4.

For subgrouped data, Sigma(XBar) and Sigma(X) are to be calculated separately for each product (Nominal) plotted on the chart.

For more detailed explanation and examples, you may please refer the book above.

:thanx: everyone for the feedback.

Hi Atul Khandekar,
Can you show a Zbar & W chart sample? Thanks very much.

B.T.W. What is the book title? Can you share with me?


Thanks n best regards
Guo Qing

Welcome to the Cove, Guo Qing.

Sorry, I do not have a ready sample of the charts.
The title of the book as mentioned above, is "Short Run SPC".

Go to http://www.knoxshops.com/spcpress/ or to www.spcpress.com and follow the link to SPC Store. You will find the complete list of Don Wheeler's books. If you want you can purchase this book on line for US$ 20 (+ Shipping).

Hi Atul Khandekar,
Can you tell me the d2 & d3 meaning for Zbar & W chart?

Thanks n best regards
Guo Qing

Hi Atul Khandekar,
Can you tell me the d2 & d3 meaning for Zbar & W chart?

Thanks n best regards
Guo Qing

Sorry Guo, I missed your post somehow..I hope its not too late now for a reply. :o

d2, d3 etc. are standard control chart constants. You will find them listed in any good book on SPC.