Calculating Cp and Cpk

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Sue0113

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Meena Corporation produces DRAM computer chipswith an average life of 1,800 hours and a standard deviation = 100 hours. The tolerance upper and lower specificationslimits are 2,400 hours and 1,600 hours, respectively. Is this process capable of producing DRAMchips to specifications? In other words,calculate the Cp and Cpk and draw a conclusion with explanation.
upper specifications is 2,400 and lower specification is 1,600
standard deviation is 100

Cp
=2400-1600/6(100)
=800/600
=1.333333333

Cpk
=1800-1600/3(100) , 2400-1600/3(100)
=200/300 , 800/300
=.666666666666667 , 2.66666666666667
Are my calculations correct? I'm not really understanding this so from the calculations is the process capable of processing chips to specification? Can someone explain the conclusions and if i'm calculating this correctly or if I'm not where I made mistakes! Thanks
 
1) Very bad notation. Remember the Order of Operations and add parentheses where necessary:

2400 - 1600/100 = 2400 - 16 = 2384
(2400 - 1600)/100 = 800/100 = 8

2) How did you get a six (6) in the denominator? Maybe I don't know what Cp or Cpk mean?
 
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tkhunny said:
1) Very bad notation. Remember the Order of Operations and add parentheses where necessay:

2400 - 1600/100 = 2400 - 16 = 2384
(2400 - 1600)/100 = 800/100 = 8

2) How did you get a six (6) in the denominator? Maybe I don't know what Cp or Cpk mean?
Click to expand...

The Cp index is calculated using specification limits and the standard deviation only. This index indicates, in general, whether the process is capable of producing products tospecifications. No information on the ability of the process to adhere to the target value is included in this index.
[h=3]This Cpk index is calculated using specification limits, the standard deviation, and the mean. The index indicates whether the process is capable of producing within specification and is also an indicator of the ability of the process to adhere to the target specification.[/h]Don't believe order of operations applies!
 
The Order of Operations ALWAYS applies. It is the difference between communicating and not communicating. The version without the parentheses is WRONG, not just another way to write it.

It appears you mostly have it. Oddly, I found quite a bit of information concerning such 6-sigma processes that was also published incorrectly and you have presented your problem statement consistently with these incorrectly published methods.

Cp is a capability measure and you have (2400-1600)/(6*100) = 800/600 = 1.33333. Perfect.

Cpk is a precision measure, not just can we do it, but how close to specifications, and comes in two pieces, indicating whether a process needs adjustment. One of them is incorrect as you have it. Each should be a limit compared to the mean. We're not comparing the limits to each other.

(2400-1800)/(3*100) = 600/300 = 2.00000
(1800-1600)/(3*100) = 200/300 = 0.66667

Closer?
 
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Closer

Yes I believe your closer. I see my mistake now after viewing what you did and comparing to mine. Thanks for your help and for taking time to look it up.
 
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