Converting Defect Rate To Capability index

optomist1

A Sea of Statistics
Super Moderator
#1
Hi To All,

If only given a defect rate of say .04% (a binary go/no - go process) can you translate this to a capability index??

Your insight is appreciated....

Regards,
optomist1
 
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Steve Prevette

Deming Disciple
Leader
Super Moderator
#4
It can be done, yes. Just look up the inverse normal CDF value for .04 and determine how many standard deviations that is on the normal distribution. Then divide by 3.

Now, the question really is - why do you need to do this? What does it accomplish?
 

optomist1

A Sea of Statistics
Super Moderator
#5
Steve,

Thank you I am in the field on a ^&*(% blackberry, if you could help me out I woul apprciate it. Does your response aplly to go/no-go data a binomial distribution as well? I have a DPM of 104 what would this be in Cp or Cpk? If you could assit me I would appreciate it.
thanks muc optomist1
 

Steve Prevette

Deming Disciple
Leader
Super Moderator
#6
.04% = .0004, NORMSINV(.0004) = -3.4 standard deviations.

So Capability is approximately 1.1. You are better than three standard deviation capability, but not at six sigma (if that matters to you).
 

optomist1

A Sea of Statistics
Super Moderator
#7
Steve, specifical my data is 4 defcts in 38,000 ooporunites or 0.000105 defect rat, I need the Cpk for this.....I owe you thaks!
 

Steve Prevette

Deming Disciple
Leader
Super Moderator
#8
OK, that is -3.7 standard deviations, which is a 1.2 capability.

Note I am not applying the "1.5 sigma shift" that Six sigma folks use.
 

optomist1

A Sea of Statistics
Super Moderator
#9
excellent, so for my informtion, isn't the CDF table for a a binomial different from a one 4 a norm dist? I need to brush up...what is a good source of these tables/charts online

thanks mch for your quick hlp
 
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