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

sashi · Mar 8, 2011

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

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 · Mar 8, 2011

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

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 · Apr 25, 2011

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

Bev D said:
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 · Apr 28, 2011

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

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.

Amit Nisar · Nov 17, 2011

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

It is arrived from std table. There are std values for A2, A3 (X bar chart) D3, D4 (R chart) and B2, B3 (s chart). This value can be choosed and it is based on the Value of N that is sample size or number of Data. In your case it is 30. Please find attached chart.

Shelly Tigler · Jun 22, 2012

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

I really need someone to show me how to work this out.
Can someone help witih this problem please?
The following data was compiled for measurements on a machine that fills 6 OZ tubes of yogurt.
Tube Number
Sample
1
2
3
4
5
6
1
6.00
6.01
6.02
6.05
6.06
6.07
2
5.95
5.97
5.99
6.05
6.01
5.99
3
6.11
6.30
6.22
6.33
6.21
6.20
4
6.04
6.05
6.07
6.06
6.01
6.00
5
5.96
5.99
6.01
6.05
6.02
5.99
6
5.97
5.99
5.99
6.00
6.03
6.05
7
6.00
6.01
6.00
6.01
5.99
6.00

. . a.Determine the CL, UCL, and LCL for both an X-bar and an R-chart for this process.
b. Generate the X-bar and R-charts for this problem
c. Is the process in or out of control?

Steve Prevette · Jun 22, 2012

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

One question, Shelly, is this a real work problem, or a homework problem for a course you are taking?

Justpit · Oct 24, 2012

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

=3/1.128 But if we consider that data come from a Normal distribution. Formula is for UCL and LCL is 3*R-bar/d2. When we have 2 data d2 = 1.128

ssz102 · Oct 24, 2012

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

sunff114 said:
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.

I don't 2.66 is how to calculate? if that's X-R chart, the UCL and LCL's calculate formula as following：
UCL/LCL=Xbar?A2*Rbar

and you mentioned 2.66=3/d2, what's mean, and 2.66 equal to A2?
but there is no number of subgroup size

Steve Prevette · Oct 25, 2012

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

ssz102 said:
I don't 2.66 is how to calculate? if that's X-R chart, the UCL and LCL's calculate formula as following：
UCL/LCL=Xbar?A2*Rbar

and you mentioned 2.66=3/d2, what's mean, and 2.66 equal to A2?
but there is no number of subgroup size

2.66 is used in the case of the average moving range - taking the absolute value of the difference between sequential points. You are in effect using a subgroup size of 2 when you do that. d2 is 1.128, 3/1.128 is 2.66.

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

sashi

Bev D

Heretical Statistician

QC Rick

sunff114

Amit Nisar

Attachments

Shelly Tigler

Steve Prevette

Deming Disciple

Justpit

ssz102

Steve Prevette

Deming Disciple

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