Control Limits - are calculated as 3 standard deviations ameans from the expect on either side of the suppose. Also well-known as process borders, these are derived basis the procedure data and represents the location within which natural variation have the right to be supposed (prevalent reason variation). Any observation/information point external the regulate boundaries is a factor for examination and will constantly have actually an assignable cause (one-of-a-kind cause)Upper Control Limit - three standard deviations above meanLower Control Limit - three traditional deviations listed below mean


An application oriented question on the topic together with responses have the right to be viewed below. The best answer was provided by Venugopal R on 10th November 2017. 




Name:Vishwadeep Khatri
Posted November 9, 2017

Q 42.

You are watching: Why can the lower control limit not be a negative number?

This question relates to regulate charts for defects data. While the upper control limit has actually noticeable prestige for a regulate chart drawn for defects, what is the prestige of reduced regulate limit in c chart or u chart? Are tbelow particular situations wbelow the LCL is of relevance and various other cases wbelow it has actually no meaning? 


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Venugopal R

Posted November 10, 2017

Venugopal R

Excellence AmbassadorName:VENUGOPAL R
Posted November 10, 2017

The manage borders for Control charts are derived based upon its very own information, using the statistical ethics applicable for the circulation under which the information falls into. ‘c’ charts and ‘u’ charts are supplied for ‘count’ data, such as variety of defects in as part / sample. The choice of ‘c’ or ‘u’ are made based on addressed or varying sample sizes.


It goes without saying that, as soon as these charts are supplied for security count of defects, anyone will certainly just want the defect count to be as low as feasible. Hence the UCL for defect makes sense, yet the question is “why do we need a lower regulate limit for defect count?”


LCL - bit significance:

Some times as soon as the boundaries are worked out, the lower manage limit can assume an unfavorable value; in such situations, the calculated LCL, being negative has actually no interpretation and the LCL is taken as zero. Obviously, no allude is going to autumn below zero, and hence the LCL is of bit meaning here, other than as soon as the count is zero.


However before, if we are making use of the ‘run’ fads for our study of stcapability as per its rules, then the 1sigma and 2sigma boundaries are also supplied, acomponent from the LCL.


LCL - Could unearth crucial finding:

Where we perform have actually a positive LCL, and if some information points fall exterior, it indicates a situation that may be “also great to be true”. It will certainly be worthwhile to investigate the distinct cause(s) that could have brought about this incident.


1. It might be measurement a error. For eg. a wrong gauge might have been provided and it was failing to detect defects.


2. It can be a adjust of an inspector that included subjectivity in the defect identification, particularly if the defect wregarding be visually established.


3. Or it might be some genuinely favorable problem that carried down the defect count. These can be avenues of unearthing some favorable aspect that we have been lacking or ignoring.

One example from my experience is once we were making use of ‘u’ chart for plotting the count of character errors in caught information, processed from multiple sites. Few consecutive days we observed the count falling listed below the LCL. Upon examination, we realized that one specific handling website was down during those days. More probe revealed that this particular website was perdeveloping through an operating application, whose variation was obsolete. Once the correct variation was installed, we were able to sustain a diminished suppose error count and also the manage boundaries can be narrowed.

See more: What Is The Trend In Ionization Energy When Proceeding Down A Group In The Periodic Table?


LCL - More crucial (than UCL?)

4. It is not vital that c and also u charts have to constantly reexisting defects, which are constantly “lower the better”. For eg. a customer goods agency offering a well-known brand also of shaving actually cream, wants to do a examine to see the number of individuals out of sample that use their product. They pick a sample of people in a city every day and uncover out exactly how many kind of of them are making use of their brand. In this situation, considering that the sample varies eincredibly day and also it is a count information, ‘u’ chart applies. However before, this is a instance wright here "higher the count, the better". Hence the LCL and the count falling listed below LCL is of uta lot of prominence.