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

M

#### maxfusion

##### Guest
Hi all

how do i calculate the UCL,LCL & CL for the below data. it has a total of 30 datas and i need to find out also the formula for UCL,LCL & CL as i need to use excel to do the calculations. PLS HELP ME!!!:truce:

Tensile strength
2.1
2.5
3.1
3.2
2.3
1.9
2.1
2.2
2.5
3.1
1.8
2.2
3.2
1.4
1.6
2.0
3.1
2.5
3.6
3.3
2.3
2.1
1.9
1.4
1.5
2.5
3.1
4.0
3.5
3.2

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

calculate the moving range between each value: MR1 = the absolute absolute value of the second value - first value. MR2 = the absolute absolute value of the third value - second value and so on. you will have 29 of these values.
then calculate the average of these 29 values. this is the average moving range, MR Bar

The CL = is the average of the 30 readings.
LCL = average - 2.66*MRbar
UCL = average + 2.66*MRbar

this will ONLY work if the tensile values are in order of PRODUCTION of hte parts. if you dont' know the order of production and you only know the order of the tensile measurements you cannot do the control chart. teh dat must in production time sequence.

But I have to add that I am concerned (no offense intended) that this is a very basic question that can be readily answered by a simpel google search or any SPC book that is lying around. You provide very little background as to the nature of the problem. You seem to have almost no knowledge of SPC and I wonder why you are tasked - feel tasked - to do this on your own (my assumption since you're here)?

P

#### preetham - 2007

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

I would like put some comment on this,

Just calculating the UCL & LCL will not tell you that the process is capable of producing the parts per customer requirement.

The UCL,LCL & CL only tells you that the readings you have got are in statistically under control or Not,you have to calculate the Process capability & index then only you will find out that the obtained values are good enough to satisfy the customer specification.CP & CPk value tells that the process is capable of producing the parts per the customer specification :truce: .

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

of course the LCL and UCL do not provide an assessment fo capability. But, the OP had a very limited and specific question. I answered that question but only after thinking about it for awhile as the OP had obviously not researched the quesiton on their own and provided so little information on his issue that any answer we could give would be highly likely to be mis-used.

M

#### maxfusion

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

my apologies if mine question is not through enough.

i actually want to draw a x-bar control chart using the data that i have
but i just do not know the formula and what should i use for the variables

i would like to know if it is possible to draw a x bar control chart for individual measurement as all 30 datas are individual

Last edited by a moderator:

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

The formulas I described in my original response ARE the formulas you are looking for.

M

#### maxfusion

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

How does 2.66 comes about beacuse in some books they were using d2 as 1.128 under Chart for RANGES. does your 2.66 A3 comes under chart for AVERAGE. please enlighten me.
Thanks

#### Marc

##### Retired Old Goat
Staff member
Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

How does 2.66 comes about because in some books they were using d2 as 1.128 under Chart for RANGES. does your 2.66 A3 comes under chart for AVERAGE. please enlighten me.
Thanks
Can anyone answer this?

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

How does 2.66 comes about beacuse in some books they were using d2 as 1.128 under Chart for RANGES. does your 2.66 A3 comes under chart for AVERAGE. please enlighten me.
Thanks
First, the values in the tables are made for Xbar-R charts. The intent of the n=2 two row is that you are plotting the range values (the first range value is the difference between points 1 and 2, the second range value is the difference between points 3 and 4, etc), and you are plotting the Average of each sequential pair on the xbar chart.

In a x-individuals with moving range, the control limits are NOT the same as xbar-R n=2. The control limits for a xbar n=2 chart are:

xbarbar +/- (3 Rbar)/(d2 x sqrt )

But we don't want the square root of n, since we are not plotting xbars of pairs.

So, the control limits should be:

xbarbar +/- (3 / d2) times the Average moving range.

3/d2 = 3 / 1.128 = 2.66 which is otherwise known as A3

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Re: How to Calculate UCL (Upper Control Limit) & LCL (Lower Control Limit) & CL?

By the way, this may then beg the question - what is d2?

d2 is a correction factor with the ASSUMPTION of a normal distribution.

We estimate a value for the standard deviation of the individuals by dividing the average range value by d2.

Note that the standard deviation is the square root of the sum of all of the x's minus xbar, quantity squared, divided by n - 1.

According to Acheson Duncan's Quality Control and Industrial Statistics, page 151, PB Patnaik in 1950 showed that the square of the average range has a distribution that is approximately the form of a chi square. Patnaik derived the values of d2 from this approximation. Duncan states "The significance of this work by Patnaik is that in any analysis using s we can replace s by the more readily computed Rbar / d2."

An interesting thing nowadays is that in Excel spreadsheet is is actually easier to calculate s, not the moving range. Yet, we stick to using moving ranges.