How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

[kotamballi]

Bev
Thanks for the reply.. Yes I meant Control limits... Will try to use this. Thanks a lot..
Thanks
KP

[sashi]

Hi, please help to clarify on whether the way i am calculating the control limits are correct.
I have 128 data (with 4 subgroups-each subgroup represents 32data) and the following will be the step that I took to calculation the control limits for X-Bar: -
1. Determine an average, mean (x-bar)
2. UCL = Average+(Average/6)x3
3. LCL = Average-(Average/6)x3

Can I use the same set of data (128 data with 4 subgroups) to calculate the range control limits?
Can I use the same method to calculate the control limits?
Thanks.

[Bev D]

those are not the formulas for the control limits on the average. I'm curious as to where you got those formulas?

do you have categorical (pass/fail or count) data or do you have continuous (measurement) data? the type of data will dictate the formula.

[Steve Prevette]

The PERT Chart (which is NOT a control chart) uses 1/6 of the range of times in the schedule as an estimate of the standard deviation. This would NOT be appropriate for SPC.

[sashi]

Hi Bev,
Yes, I do have continuous data. Does it mean my control limits will be change on daily basis?
I am taking 5 data in a day for each parameter with an interval of 2~3 hours since our parts are using high precision care with high turnover cost.
The following data was collected (around 20days) for parameter P. Height
6.9140
6.9040
6.9020
6.9030
6.9170
6.9070
6.9140
6.9160
6.9140
6.8980
6.9030
6.9040
6.9200
6.9030
6.9220
6.9170
6.9110
6.8980
6.9170
6.9060
6.9230
6.9150
6.9090
6.9040
6.9040
6.9010
6.9130
6.9110
6.9240
6.9160
6.9050
6.9110
6.9110
6.9180
6.9250
6.8990
6.9070
6.9180
6.9210
6.9170
6.9100
6.9150
6.9200
6.9030
6.9010
6.9130
6.9040
6.9030
6.9270
6.9150
6.9120
6.9010
6.9150
6.9030
6.9030
6.9060
6.9090
6.9020
6.9060
6.9130
6.9110
6.9090
6.9130
6.9170
6.9020
6.9140
6.9050
6.8960
6.8960
6.8900
6.8980
6.8990
6.9070
6.9160
6.9080
6.9180
6.9100
6.9050
6.9160
6.9100
6.9090
6.9050
6.9170
6.9200
6.9140
6.9010
6.9210
6.9140
6.9140
6.9150
6.9190
6.9110
6.9100
6.9120
6.9060
6.9080
6.9040
6.9140
6.9210
6.9160
How should I go with the calculation?

[Bev D]

as long as your subgrop size doesn't change your limits don't change. you also shouldn't calculate new limits everytime you add a subgroup.

the formulas for continuous data, small subgroup size (n<10) are shown below. for the situation you describe you could subgroup by day, so n=5.

Calculate the RANGE for each subgroup. R = max-min value
Calculate the Average Range, Rbar. this is jsut the average of all of your Range values.

Calculate the Average of each subgroup, Xbar.
Calculate the grand average, Xbarbar: this is the average of all of the subgroup averages.

The control limits for the Subgroup Averages are:
Xbarbar + A2*Rbar, A2 is a factor that is dependent on the subgroup size, n. for an n=5, A2 = 0.577

The upper control limit for the Subgroup Ranges is:
D4*Rbar
for an n=5, D4 = 2.115

The lower control limit for the Subgroup Ranges is:
D3*Rbar (for small subgrops there is no lower control limit, it's just zero)
for an n=5, D3 = 0


Since your question is very basic, I am assuming that you have had little or no training in SPC?
I strongly recommend that you buy yourself a basic SPC text and study it. It's fairly easy and straightforward to learn the basics.

The 2 books I recommend are:
Statistical Quality Control by Grant and Leavenworth
Introduction to Statistical Quality Control by Douglas Montgomery

[QC Rick]

In Reply to Parent Post by Bev D

Since you are low volume and you measure each device, it makes sense to use a chart known as and Individuals, Moving Range chart. I have attached the formulas for you.

With a I, MR chart you can include spec limits. (Please note that it makes no sense to include spec limits on charts with ‘subgrouped’ data where you are plotting the average and range or standard deviation of the subgroup or sample.) Remember that your process can be “out of control” but still within specifications. It can also be “in control” and out of specifications.

Things to know:

You do NOT recalculate the limits based on months. You will be setting ‘baseline’ limits from 20-30 units and then plotting your process against those limits. To repeat: do NOT recalculate the limits on an on-going basis.

You need to identify a ‘stable baseline period’. When selecting the first 20-25 subgroups of data to calculate the initial control limits, at least one of the subgroups will fall out of the statistical control limits. This is because real manufacturing processes are never in statistical control for 25 subgroups. Use good common sense to remove the biggest offender and recalculate the limits. Do not remove all out-of-control points, just the worst ones. This is an iterative process.

Each characteristic / part combination will require it’s own chart.


Out of Control Rules
These are some of the rules that define when an “out-of-control” condition exists…The process has changed and needs to be corrected.

• Any plotted point that falls outside a Control Limit
• Any 2 out of 3 points that fall ‘close’ (outer third) to the same Control Limit, even if non of the points exceed the Control Limit.
• Any 7 plotted points in a row that fall above (or below) the Average (or center line).
• Any 7 plotted points in a row that are each greater than (or less than) the plotted point before it
• Any other pattern that does not look “random”

You should recalculate new limits only when a known and sustained improvement has been made.

attached is a spreadsheet with your data in an I, MR chart

you should also invest in a good SPC book.

two authors I highly recommend are:
Donald Wheeler and Fair & Wise.

Finally a simple answer. I sneaked a peek at your setup and formulas and now I understand how to perform the calculation.

Im not a statistician but I did stay at a Holiday Inn once...

[sunff114]

2.66=3/d2

Bev D is building an individual control chart using moving range. The CL, UCL and LCL is

xbar + 3* (MR bar/d2) => x bar + (3/d2) * MR bar

where xbar is the mean, MR bar is the mean of moving range.