Putnam’s Analysis: Software Equation

Putnam offers two equations for estimating software development effort and analyzing the effects of compressing or expanding the schedule. The first equation, which he calls the Software Equation, can be used to compute the development effort required and therefore the cost.

Effort = (B*Size³) / [(Time⁴)*(Productivity Measure³)]

This equation requires the size of the project in source lines of code (SLOC) and the time for development in years as inputs. The equation also has two other parameters. The first parameter, the special skills factor (B), is directly related to the size in SLOC. Putnam provides a table for looking up this value. The second parameter, the Productivity Measure (PM), is related to the type of system that is being developed. Putnam provides two tables for computing this value. The first table shows the values for the productivity measure divided into 40 levels called the Productivity Index (PI). These levels are then related to project type in the second table. This table lists several types of applications and their associated productivity index (circa 1990). The table also gives a standard deviation for each. The standard deviation can be used to compute a range for effort given values for size and time. The inputs that the user must provide are the application type (or the user must directly choose PI or PM), the size in SLOC (either entered directly or computed from function point analysis/backfiring), and the time scheduled for the project in years. The output would be the effort required in person years and a range using the standard deviation.

Manpower Buildup Index

The second equation uses the effort in person years, the size in SLOC, and the special skills factor to compute a Manpower Buildup Index (MBI)Parameterthat can be expressed in sixMBI Levels.

MBI Parameter = Effort / (B*Size³)

MBI Level = log₂ (MBI Parameter) - 2

The MBI Level is the binary logarithm of the MBI Parameter minus 2. The MBI Level is a smaller number that is coarser grain than the MBI Parameter, and thus more appropriate for reports to management. For convenience, Putnam provides a table relating the two values. The MBI is an expression of how manpower is applied to the development effort. An MBI of one represents a schedule that is stretched out and uses a slow buildup of manpower. An MBI of six represents a schedule that is to be compressed by throwing people at the project. MBI Levels of greater than six generally indicate the proposed schedule is too ambitious to succeed for the size of project and type of application, no matter what staffing level is used.

Rayleigh Model

COSMOS implements a simplified Rayleigh Model for the sole purpose of calculating the Manpower Buildup Index (MBI) Level.

The MBI Level may be qualitatively characterized as follows:

MBI Level	Staff Buildup	Effort Effect	Schedule Effect	Error Effect
< 0	Extremely Slow	Lower	Higher	Lower
0	Very Slow
1	Slow
2	Moderate Slow
3	Moderate
4	Moderate Aggressive
5	Aggressive
6	Most Aggressive
> 6	Unrealistic	Higher	Lower	Higher