# How Do I Get the Z-Bench Value?

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• #54197

Joe Roberts
Guest

Hi, I am trying to compute the Z-Bench value based on my results and I am getting an * for the Z-Bench value in Minitab. The only reason that I need it is that is part of a school project which requires the Z-Bench value.

Basically, I am getting these results:

LSL = 0
USL = 10
Target = 5
Sample Mean = 30.2516
Sample N = 20
Std Dev (within) = 0.089
Z.Bench = *
Lower CL = *
Z.LSL = 339.45
Z.USL = -227.24
Cpk = -75.75
Lower CL = -99.83
Upper CL = -51.66

I would appreciate it very much if someone can explain why I am getting a * for the Z-Bench value in the Minitab.

BTW, I am a programmer and not a statistics guy so all this terms above are new to me. I have no clue what Cpk or CL is but I believe that Z-Bench is basically the sigma level, meaning how many DPMO I should expect.

Anyway, any help that you can all provide will be appreciated very much.

Joe

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#194159

Joe Roberts
Guest

BTW,

Just in case, here is my sample data:

30.135
30.375
30.152
30.278
30.168
30.153
30.375
30.177
30.136
30.315
30.285
30.355
30.339
30.351
30.252
30.232
30.351
30.238
30.175
30.189

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#194160

Joe Roberts
Guest

Also, is this correct?

Z-Bench = Min(((Mean – LSL)/Std.Dev)), ((USL-Mean)/Std.Dev)))

0
#194161

Chris Seider
Participant

Nope. Hint: Take a closer look at your USL and LSL and where your data’s central tendency is.

0
#194167

Joe Roberts
Guest

Hi Chris,

Thanks for your reply. I think what you are saying is that because my range for LSL and USL is 0 – 10, and because my mean is normally 30, then that explains why Z-Bench is *. Is that correct?

If so, then I don’t understand why I also get a * for Z-Bench with these values:

4.768
4.766
4.736
4.836
4.820
4.789
4.758
4.788
4.851
4.789
4.758
4.801
4.773
4.721
4.805
4.789
4.745
4.805
4.774
4.758

Those are very close to the middle of the range 0 – 10, yet I still get an * for the Z-Bench value.

Here are my results from minitab with the 4.x values:

LSL = 0
Target = 5
USL = 10
Sample Mean = 4.7815
Sample N = 20
StdDev(Within)=0.0359276
StdDev(Overall)=0.0326456

For Potential within Capacity, I get the following figures:
Z-Bench=*
Lower CL=*
Z.LSL = 133.09
Z.USL = 145.25
Cpk = 44.36
Lower CL = 30.26
Upper CL = 58.47

For Overall Capacity, I get the following figures:
Z-Bench = *
Lower CL = *
Z.LSL = 146.47
Z.USL = 159.85
Ppk = 48.42
Lower CL = 33.30
Upper CL = 64.35
Cpm = 7.36
Lower CL = 6.96

Joe

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#194168

Joe Roberts
Guest

Or are you saying that because all the points are so close to each other then it is impractical to calculate the Z-Bench value because the chance of getting a single DPMO is very slim?

0
#194170

Joe Roberts
Guest

HI @CSeider,

Not sure if you are getting my replies or not. Not sure how I am supposed to make sure my replies get back to you.

If you have a moment, I posted some additional follow up questions, as I am not sure that I understand your hint completely.

Thanks,

Joe

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#194174

Chris Seider
Participant

Contact Minitab if it’s that important to understand the mechanics of their calculation specifics but the last set of data is so narrowly distributed and well within both specs you have no issues–both Zu and Zl are superb. If this is real data, find a new problem to work on.

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#194212

MBBinWI
Participant

@jrobertsz66 – now that your test is over, perhaps others may learn from this thread. In your first data set, you are essentially asking for the ratio of infinity over a small range (in your case, 10). In the second, you are asking for essentially zero over a range that is proportionately very large (even though the same range of 10). The calculated numbers, therefore, are either extremely large or small, thus Minitab defaults to a null instead of giving a non-sensical number (although Joel might have more technical justification).

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