Calculating Ppk on a single sided (unilateral) tolerance

Ok here is my problem:
I have a list of 30 numbers related to customer wait times for a month, USL of 30 minutes and a LSL of 0.

How do I calculate the Pp,Ppk numbers? I only have Excel 2007 and cannot afford to buy minitab or any other software. I know the formula says that you can only calculate Cp,Cpk when you only have a unilateral tolerance.

My professor won't break it down and walk me through the calculation steps in order for me to figure this out. And he won't allow any of the other students to help either.

I need help ASAP please.

Vince

Lightning546 said:

Ok here is my problem:
I have a list of 30 numbers related to customer wait times for a month, USL of 30 minutes and a LSL of 0.

How do I calculate the Pp,Ppk numbers? I only have Excel 2007 and cannot afford to buy minitab or any other software. I know the formula says that you can only calculate Cp,Cpk when you only have a unilateral tolerance.

My professor won't break it down and walk me through the calculation steps in order for me to figure this out. And he won't allow any of the other students to help either.

I need help ASAP please.

Vince

Click to expand...

Hello Vince!

Welcome to The Cove Forums.

Begin by looking at these threads.

It's weekend; more help is underway...

Stijloor.

You have misunderstood some of the basics.

First, Cp/Cpk are used when you have rational subgroups (such as from Xbar/R charts) and is used to determine short term capability. The standard deviation used in this calculation is estimated using the subgroup range. Pp/Ppk is used to determine long term process performance and is calculated using the overall standard deviation.

Second, Cp and Pp both require upper and lower specification limits. Cpk and Ppk only require an upper or a lower specification limit, but can also be calculated for two-sided specifications.

Ok, here is the question (I changed the wait time numbers to avoid a cheating allegation):

Instructions for you:1. Construct a histogram from the data below. (I have done this)2. Is the processes random, or normally distributed? (Normal) 3. Calculate Pp and Ppk indices. (This is where I am stuck)4. Are the processes acceptable?(Yes)

Data:Wait times: 5,13,12,10,8,14,11,11,10,15,13,9,9,12,16,6,10,12,11,11,17,11,11,8,12,11,9,11,10,7 (Upper spec is 30 minutes)

(These are the answers I came up with, Instructor says they are wrong)

Pp:1.900Ppk::::2.700Random?:::YesAcceptable? :::Yes

By my calculations I get the following:

StDev 2.68
Mean 10.83

Ppu 2.38 (Upper Spec Limit - Mean) / (3 * StDev)
Ppl 1.35 (Mean - Lower Spec Limit) / (3 * StDev)

Ppk 1.35 (Minimum of Ppu & Ppl)

Pp 1.87 (Upper spec limit - Lower Spec Limit) / (6 * StDev)

*EDIT* This was done using Open Office spreadsheet package - I'm not sure how this program in particular calculates Standard Deviation, I am assuming it's the same as Excel.

Lightning546 said:

(These are the answers I came up with, Instructor says they are wrong)

Pp:1.900Ppk::::2.700

Click to expand...

Ppk <= Pp

Pp assumes that the process is centered. Ppk takes the deviation from the center of the spec into account. Therefore, Ppk is always less than or equal to Pp.

achorste said:

By my calculations I get the following:

StDev 2.68
Mean 10.83

Ppu 2.38 (Upper Spec Limit - Mean) / (3 * StDev)
Ppl 1.35 (Mean - Lower Spec Limit) / (3 * StDev)

Ppk 1.35 (Minimum of Ppu & Ppl)

Pp 1.87 (Upper spec limit - Lower Spec Limit) / (6 * StDev)

*EDIT* This was done using Open Office spreadsheet package - I'm not sure how this program in particular calculates Standard Deviation, I am assuming it's the same as Excel.

Click to expand...

These agree pretty close to what minitab gives.



I do wonder about the phrasing of this questions:
I would say that the normal distribution IS a random distribution. It seems to ask this as an either/or question. (By the way, minitab also confirms that the distribution is normal -- or more precisely, that we do not have sufficient evidence to conclude that it is NOT normal.)

Tim F

I've just looked at the question again however and I would question whether you would apply the lower spec limit of 0 - as it is customer wait times being examined, using the lower spec limit seems dubious.

In the instance of a single sided tolerance, you would use either Ppu or Ppl as your Ppk value (dependent on which limit you are using), in this case Ppu, which would give you a value of 2.38 for Ppk. The Pp value would be un-affected.

Tim Folkerts said:

I do wonder about the phrasing of this questions:

Is the processes random, or normally distributed?
​

Click to expand...

This may be an imprecise way of asking whether the process is stable. That is, there are no signs of non-random causes such as trends, runs, etc.

Thanks everyone, I didn't post the histogram or my standard deviation calculation spreadsheets because I didn't know how and I didn't want to completely compromise my answer.

So if I understand correctly my Pp and Ppk should be the exact same number since this is a unilateral tolerance, correct?