Calculation of the Mean - Student Question about Cpk calculation

J

jal8712

#1
Ok so i was given this question. I just am getting lost cause it doesnt say a mean. Does this mean i have to calculate the mean

Elle Tire Company recently bought a new compressor which automatically fills automotive tires to specified pressure. It was specified by the compressor manufacturer that standard deviation for the fillings was 2 PSI. For getting best fuel economy, it is suggested the tire pressures should be set in the range 30 to 35 PSI. Since under inflation is lot more undesirable than over inflation, the manager set the compressor to fill the tires at 33.5 PSI. Answer the following questions-
What is the process capability of the system for filling tires?
so what i did is take


33.5-30/3*2 or 35-33.5/3*2
.5833 or .25
to get these values. Am i doing this right?
Or do i have to find the mean and use the 30 and 35 number than divide by 2?
i am assuming the lsl=30 and usl=35?
most problems we are given had like 10+-3 so we could identity the lsl and usl by that. and the mean was always given to us
 
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Miner

Forum Moderator
Staff member
Admin
#2
Re: question about cpk

Do you just want to see whether this compressor is capable or not? Under the best case, that you are centered within the specification at 32.5, you can calculate the Cp index as (USL - LSL)/6s, that would be (35 - 30)/6*2, 0r 5/12 = 0.417. Since the compressor is set higher, at 33.5 you should calculate Cpk upper, which is (35 - 33.5)/3*2, or 1.5/6 = 0.25.

So, the compressor is far from capable. Even centered within the spec, it will still produce many tires that are both over and under inflated. Currently, it will produce more over-inflated tires.
 
Last edited:
J

JasonAREdwards

#3
Re: question about cpk

I agree with your math assuming that 33.5 is the mean.

However, just because the manager sets the machine to 33.5 pounds does not necessarily result in 33.5 as the process mean. It appears that you do not have enough information to answer the question.
 
J

jal8712

#4
Re: question about cpk

ok im so lost. Do we not need to get mean for this? So we can just assume 33.5 is the mean? we are using lower to? so would the lower be 33.5-30/3*2? since we dont need lower you just left it out right?
 
J

jal8712

#5
Re: question about cpk

my teacher gave us this question and its just confusing. Every other time he has supplied the mean and all that.there is this formula as well. xi/n
where xi=observed value and n=total number of observed values. But i didnt think we would use this formula
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#7
Miner's answer is correct and complete.
to address your explicit and unstated questions: you cannot calculate the mean in this exercise as you don't have the individual values, but for this exercise you don't need it. you simply assume that the mean will be where the compressor is set (33.5). in real life of course this probably won't be the actual mean - but this is just an exercise. you also have to assume that the vendors claim of the SD is correct, which won't be correct in real life either. but these assumptions are OK for the exercise if only because you don't have any other data.

as for Cpk_lower, you could of course calculate it in the same manner as Miner did, but traditionally, Cpk is only calculated and reported for the value that comes form the closest spec limit. IF you were taught to also use or report the other Cpk then do so...the math is straightforward.

remember that sometimes questions are 'tricky'. the instructor or author intends them to be that way to get you to THINK.
 
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