Need help with Control Charts, Control Limits (UPL, LPL, UCL)

[MechEng]

Like last time I posted, I was given an assignment for college, this time its on limits (UPL, LPL, UCL etc etc) Basically we were left fend for ourselves. We are to research this topic and answer questions.

TO be honest, I haven't got a clue.

Here's an example of a question

1. Control charts for x(with a line over it) and R are maintained for an important quality characteristic. The sample size is n=7. X(with a line over it) and R are computed for each sample. After 35 samples we have found that

Sum of( E)(35above and i=1 below the E) X(line over it)i = 7805 and Sum of( E)(35above and i=1 below the E) Ri = 1200

(i) Calculate suitable limits for X(line) and R control charts using this Data.

(ii) Assuming that both charts exhibit control, estimate the process mean and standard deviation and the natural process limits.

(iii) If the quality characteristic is normally distributed and if the specifications are 220 +/- 35, calculate the Cp and the Cpk indices. Make a comment on the process capability.

(iv) using a suitable sketch, illustrate roughly the proportion of product which is conforming from the process. Assuming the variance to remain constant, state where the process mean should be located to minimise the fraction non-conforming.

Can someone please(x10000) provide me with a link or something that will help me through this assignment. I'm starting to panic now..lol

[Tim Folkerts]

Originally Posted by MechEng

Like last time I posted, I was given an assignment for college, this time its on limits (UPL, LPL, UCL etc etc) Basically we were left fend for ourselves. We are to research this topic and answer questions.

TO be honest, I haven't got a clue.

When faced with a situation where I feel confused or lost, I find it helpful to go back and make sure I understand the basics - like the terminology and symbols.

1. Control charts for x(with a line over it)

x(with a line over it) - often called "x bar" just means the average for a set.

and R

R is the range = max-min for each set.

After 35 samples we have found that

Sum of( E)(35above and i=1 below the E) X(line over it)i = 7805

The "E" is a Greek "Sigma", meaning summation. X(line over it)i is the average for the set parts in set "i". You are adding all the averages - starting from i=1 (writen below the Sigma) and ending with i=35 (writen above the Sigma).

So you are just adding
[ xbar(1) + xbar(2) + ... + xbar(35) ] = 7805

Furthermore, since the average of any set of numbers is the total divided by how many numbers you have, the average of x-bar (writen as x with TWO lines over it) would be
[ xbar(1) + xbar(2) + ... + xbar(35) ] / 35

and Sum of( E)(35above and i=1 below the E) Ri = 1200

similar to the last section.

Hopefully, at least some of that was already familiar!

(i) Calculate suitable limits for X(line) and R control charts using this Data.

Now you will have to find the appropriate equations for the control limits. These will involve x-bar, R, and various constants with names like "A4" and "D2". Your book should have those; some posts here should have those; there is a great online resource at www.nist.gov/stat.handbook that should have those.


See if you can get a little farther and then come back if you have specific questions.


Tim F

[Steve Prevette]

You may want to take a look at some of the control chart materials I have on the internet at http://www.hanford.gov/rl/?page=1144&parent=169

"The Life Cycle of a Trend" is posted here at the Cove as a word document, and also there is a power point of it at http://www.hanford.gov/rl/uploadfile...Life_Cycle.ppt which may help with the "big picture" as to what is trying to be accomplished with SPC.

[Jim Shelor]

Originally Posted by MechEng

Like last time I posted, I was given an assignment for college, this time its on limits (UPL, LPL, UCL etc etc) Basically we were left fend for ourselves. We are to research this topic and answer questions.

TO be honest, I haven't got a clue.

Here's an example of a question

1. Control charts for x(with a line over it) and R are maintained for an important quality characteristic. The sample size is n=7. X(with a line over it) and R are computed for each sample. After 35 samples we have found that

Sum of( E)(35above and i=1 below the E) X(line over it)i = 7805 and Sum of( E)(35above and i=1 below the E) Ri = 1200

(i) Calculate suitable limits for X(line) and R control charts using this Data.

(ii) Assuming that both charts exhibit control, estimate the process mean and standard deviation and the natural process limits.

(iii) If the quality characteristic is normally distributed and if the specifications are 220 +/- 35, calculate the Cp and the Cpk indices. Make a comment on the process capability.

(iv) using a suitable sketch, illustrate roughly the proportion of product which is conforming from the process. Assuming the variance to remain constant, state where the process mean should be located to minimise the fraction non-conforming.

Can someone please(x10000) provide me with a link or something that will help me through this assignment. I'm starting to panic now..lol

Dear MechEng,

The process your assignment is about is called Statistical Process Control. The following three links contain a lot of easy to understand statistics instruction and Six Sigma knowledge. The first two links are electronic books. The third link gives you a variety of tools for use in understanding the topics.

http://www.statsoft.com/textbook/stathome.html

http://www.itl.nist.gov/div898/handbook/index.html

http://www.isixsigma.com/tt/

The sections you want to look at for the specific topic you are faced with are topics dealing with Control Charts.

There are links within the chapters that will take you back to information regarding parts of the subjects that the books assume you know before you get to this subject.

If you have any trouble using the books or have specific questions you need to ask, post your questions here or send me an email at the e-mail in my profile.

I will be happy to provide you with any help I can.

Good studying and best of luck.

Jim Shelor
PMP, SSBB