# Cp and Cpk Chart Fundamentals

J

#### jpal20002001

Hello All,

I am in the final stages of developing an application that gathers inspection data, plots them in a chart, monitors my data for me, and is also capable of printing out a summary form as needed.

To Simplify matters, I will tell you what I know, where I'm at and how you can help me.

What I know:
MAX, MIN, MEAN, Range, Standard Deviations & Critical Limits

... are used to help me calculate my Cp, Cpu, Cpl, & Cpk

Where I'm at:
[DATA]
I have data, and I'm able to calculate the easy stuff, Max, Min, Mean, Range, Standard Deviations.
My Nominal & Critical limits (UCL, LCL) are given.

[CHART]
I can automatically produce a chart that plots the actual dimensions, with my Critical Limits and nominal shown. a sample is shown as an attachment named, "myBasicChart.png"

How you can help me:
I need help understanding how to take my data, and calculate my CPK, Cpu, Cpl, Cp. Once calculated, I need to fundamentally understand how to create a chart of my CPK. I have uploaded an excel form to help me to comprehend how this is all handled. In that spreadsheet, they have a Cpk sheet. and they also have data for the "Chart Setup." If you can first help me to understand the "Chart Setup" that would be a great leap in the right direction for me. The reason being, is that if i can graph something either in excel or manually, then i can create it programatically. And that's what I'm after! Understanding the fundamentals.

From B37 to B237 they have a list that incrementally increases by 0.1.
For what reason?

From C37 to C237
It looks like there calculating the green box(range) for the Cpk. Does it really work out that way for every Cpk, by using the formula method they used. Very interesting...

Can you explain to me what's happening between D37 to D237? What calculation is that? Where are all of these formulas coming from???

Between E37 & E237, these define what the green box is doing along the y-axis. How am i supposed to know when the box jumps up as theres did?
Between E37 & E86 there y-didn't change, and then all of a sudden on E87, the chart box starts being created by rising on its y-value. How did they know to start at that point???

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J

#### jpal20002001

Re: CP, CPK Charts - Fundamentals

I forgot to attach some sample data, so here you go.

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#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: CP, CPK Charts - Fundamentals

before we get too detailed in our many responses, may I ask why you are trying to 'program' this basic statistical and charting function?

The reason I ask is that there is a lot of very good software out there that does this work for us. It does it well, it does it quickly and it does it cheaply.

J

#### jpal20002001

Re: CP, CPK Charts - Fundamentals

I know this won't make sense to you, because it didn't to me, but here I go.

1st. We will have some software in place that will perform spc functions, but it will not be directly available in my inspection department.

2nd. By custom building this software to the company, I will be able to better provide the specific needs that this company will be requiring as we go into manufacturing high volumes of parts. Yes, there are software's out there that can do all the spc i want them to do, but when it comes down to specific tasks and the continued changes that the company undergoes as it grows, I cannot hope on another software company to make any changes I would inquire, nor is this company willing to pay all the fees associated with the demands it's asking for.

In reality, what i am doing, is providing a secondary channel of catching any potential problems that can be avoided. I will be tailoring this software to the company, as I have already done to it's sister company, which turned out extremely successful.

For the record, I did try selling the company on purchasing software, and just going that route, but there not willing to do that... at least not now. They just don't want to spend \$\$\$ on software. Why??? I don't know. I know it doesn't make sense, because there spending money on me?

Anyhow, this will make my job a lot easier. Since I am programmer, I can develop this application to do exactly what i need it to do and also monitor and send alert notifications upon any problems that it found.

In addition to, once i get this Cpk in tact, i will be merging it with other related Cpk results to monitor parts, without user interaction.

#### Darius

##### Quite Involved in Discussions
I recommend:
Site's Excel posts

There is a lot of code there

From B37 to B237 they have a list that incrementally increases by 0.1. For what reason?
If you want to chart a function, you need to add values to it, the closser the values are, the better continuity of the data points will appear.

From C37 to C237
It looks like there calculating the green box(range) for the Cpk. Does it really work out that way for every Cpk, by using the formula method they used. Very interesting...
Because it just obtain the minimum and maximum, max-min = range
min+ range* ( from 0.5 ranges bellow to specs to 0.5 ranges above), that is strange, and sometimes will not work (if the data is far away from specs, looks a waky condition but it could happen), it could be better to use the minimum (from the data points or specs) minus a delta and add a differential until maximum (from the data points or specs) plus a delta

Can you explain to me what's happening between D37 to D237? What calculation is that? Where are all of these formulas coming from???
its the normal distribution function, you will find some approximations checking on this site, googling I found (not the best but the "standard" wikipedia)

Normal Distribution on Wikipedia

Between E37 & E237, these define what the green box is doing along the y-axis. How am i supposed to know when the box jumps up as theres did?
Between E37 & E86 there y-didn't change, and then all of a sudden on E87, the chart box starts being created by rising on its y-value. How did they know to start at that point???
Easy, all the table is about moving arround the specs (+/- 0.5), when it is a the lower spec position (aka lower spec minus 0 {column B}), jump up, and when it reached the upper (aka lower spec plus (upper - lower)*1 {column B}), jump down.

note: I don't know how you obtained the variation estimate, if the calculation is to obtain Cp/Cpk you need not to use stdev but the calculation according to the sample size (the size does matter!)

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J

#### jpal20002001

Makes sense!

Now, I have a question about the formula for Sigma Estimator. I have attached an image for clarification. You will probably need to look at it, for my question to make sense.

In regards for a subgroup size between 1 to 4, what are the referring to as the sample size???

So let's say I inspected 20 parts, then another 20 then another 20.
So now i have 3 groups, and each group contains 20 parts. Is that my d2? 20???

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#### Darius

##### Quite Involved in Discussions
In regards for a subgroup size between 1 to 4, what are the referring to as the sample size???
So let's say I inspected 20 parts, then another 20 then another 20.
So now i have 3 groups, and each group contains 20 parts. Is that my d2? 20???
The sample size is how many groups are made, the Subgroup size is being redundant = "Subgroup size", the SPC constants are assigned acoording to the subgroup size, so if the subgroup size is 20, then the constant is the constant for 20, is strange a subgroup size so huge:mg:, the most common subgroup size is 1 (moving range), 3 or 5, but the subgroup size MUST be assigned rationally (there must be a reason, not just because many uses 5), so you must seek about "rational subgroups" on SPC.

Remember that you chart the subgroups, so..., what do you think when you see a chart with just 3 points?, many experts recommend to calculate control limits (and of course the indicators) with at least 20 subgroups (magically, 5*20=100 data points) in order to achive some stability with the statistics (the tables to determine normality are until 70 as I remember), :truce:there is no harm calculating it with less, but aiming to deal with more data points..., call it "early estimates".

by the way.. d2(20) = 3.735, but if you are using a subgroup size that big must use c4

if you want to calculate c4

c4 Excel calculation

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J

#### jpal20002001

Thanks for clearing up my terminology. I didn't know that sample size and Subgroup Size were used interchangeably.

You also mentioned the having enough data to determine normality. By 70, I a supposing you were referring to 70 groups.
ie;
group1: 20 parts
group2: 20 parts
group3: 20 parts
...
group70: 20 parts <<< At this point, normality can be determined.

Also, thank you for the code submission that you shared on the other link. I will study the code and will definitely be using it.

Do you have code or explanation for d2

#### Darius

##### Quite Involved in Discussions
You also mentioned the having enough data to determine normality. By 70, I a supposing you were referring to 70 groups.
ie;
group1: 20 parts
group2: 20 parts
group3: 20 parts
...
group70: 20 parts <<< At this point, normality can be determined
Nop , the 70 is for individuals (for other kind of tests but I try to show that 70 measurements is a "nice" sample, IMHO if you subgroup the measurements or leave them as individuals, the statistical are robust as the number of measures taken), as it is stated in other posts, the SPC control limits (and their variation estimate) don't depend on "normality", but the chebyshev theorem (and work even if the distribution show "non-normality" <not talking about control rules>), but if you are using the mean (even in the indicators), you are asuming "normality".

Are you sure 20 is a rational sample??, to be able to do it, doesn't mean you need to do it.

J

#### jpal20002001

I saw your other posting for the actual formulas

"Formulas for Factors d2 and d3 for range charts"

I really wanted you to know that, so that you know I am reading as much of the other threads as i can find.

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