Hi,

I am working in a IT company as a SQA. I just wanted to know the steps of how they calculate UCL and LCL and baseline the metrics.

Please share with me any links or useful books related to this topic.

Thanks

Vijay

 LCL and  UCL are actually pretty easy to calculate. They are 3 standard deviations from the mean. So you need the mean, first.

Here are the formulas

Mean

Sum(I=1 to n, Metric[I]) / Sum(I=1 to n, size of Item[I])

Upper Control Limit (UCL)

Mean + 3*Sqrt( Mean / Average item size)

Lower Control Limit (LCL)

Mean - 3*Sqrt( Mean / Maximum item size)

LCL is never allowed to be less than zero

“Maximum item size” makes LCL more sensitive

v

However, LCL, UCL and mean are only meaningful for something that is repeatable. They come from manufacturing, where you're making more of the same thing day after day. The subject area is called 'statistical process control'. So, in software, for example, one use is looking at inspections. Organizations that do software inspections tend to do a lot of them, and the process is (at least in theory) repeatable. So you can plot a series of inspections and calculate the mean - say the average defects per thousand lines of code, or defects per standard page. Or anything else related to the inspection that you think is important enough to plot. And then you can calculate UCL and LCL.

Here are a couple of references to using UCL and LCL to plot inspection data:

Robert Ebenau,

“Predictive Quality Control with Software Inspections”, CrossTalk, Vol 7, Issue 6, June, 1994. Also in David Wheeler, Bill Brykczynski, Reginald Meeson, Software Inspection - An Industry Best Practice, IEEE Computer Society Press, 1996.

Susan Strauss, Robert Ebenau, Software Inspection Process, McGraw-Hill, 1994.

Darn! The system cut off my first reply 

The book is

Florac, William A., and Anita D. Carleton, Measuring the Software Process: Statistical Process Control for Software Process Improvement, Addison Wesley, 1999.

and here are some more links to books on statistical process control

http://www.construx.com/Page.aspx?hid=2482 - statistical process control and its application to software measurement

http://www.construx.com/Page.aspx?hid=2520 - statistical process control and its application to peer reviews

it's important to read a book. There are subtleties to statistical process control that I haven't covered. For example, there are several types of plot. In one you plot the actual observations, as in the Ebenau article. In another, you plot the differences between successive observations. They are used in different situations. So you need to be sure you're using the right type of plot.

Statistical Tests: The Chebyshev UCL Proposal

The theory of confidence intervals

The problem concerns estimating an interval required to cover a distribution-dependent quantity with a minimum probability, such as 95%.  That probability is the confidence level of the interval.  The quantity typically is a mean, standard deviation, or percentile.

This interval is a pair of procedures that assign interval endpoints to any possible experimental outcome (set of observations).  The upper endpoint is the UCL and the lower is the LCL.  We write UCL(x) and LCL(x) to show the dependence on the data.

To determine UCL(x) and LCL(x), first find for each possible distribution a region where the quantity of interest has a 95% probability of occurring.  In the figure, this region--which is a set of outcomes and therefore describes a vertical extent--is shown with a dashed line.

We can find these regions because when we are given the distribution we can do any necessary probability computation.

The endpoints of these 95% intervals trace the wiggly curves in the figure.  The area between the wiggly curves encompasses all pairs (theta, x) where x falls within the 95% probability interval for theta.

web development services

Statistical Process Control (SPC) can be applied to software development processes.  A process has one or more outputs, as depicted in the first figure below.  These outputs, in turn, have measurable attributes.  SPC is based on the idea that these attributes have two sources of variation: natural (also known as common) and assignable (also known as special) causes.  If the observed variability of the attributes of a process is within the range of variability from natural causes, the process is said to be under statistical control.  The practitioner of SPC tracks the variability of the process to be controlled.  When that variability exceeds the range to be expected from natural causes, one then identifies and corrects assignable causes.

IT Jobs Chennai