How does PSP help solve the problem?

 To see how PSP can improve the quality of your application development and reduce its cost, read this example from the SEI, Carnegie Mellon University.
"In this study we examined five personal process improvement dimensions of the PSP: size and effort estimation accuracy, product quality, process quality, and personal productivity. We found that the PSP improved performance in the first four of these dimensions without any loss in the fifth area, productivity." Statistics from "The Personal Software Process (PSP): An Empirical Study of the Impact of PSP on Individual Engineers, Will Hayes and James  W. Over, December 1997, Software Engineering Institute, Carnegie Mellon University"

Proof that PSP works

And now read about software quality improvement statistics, again from SEI.
"Before learning the PSP, a group of three engineers took an average of five times longer than they had estimated to develop three components of a software system. After PSP training, the same engineers completed the next six components of the same product in 10.4% less time than they had planned. When measured in customer-found defects, the quality of the components they finished after PSP training was five  times better than the qualifty of the earlier program components."

Defect Injection and Removal Examples

500 Lines of Code
Without PSP With PSP
Total defects 50 25
Found in code review 0 15
Defects remaining 50 10
Found in compile 25 5
Found in unit-test 20 4
Defects remaining 5 1
Code review time 0 2.5
Compile time 2 0.5
Unit test time 10 2
Total Defect-Removal Time 12 5

From "Introduction to the Personal Software Process, Watts S. Humphrey, Software Engineering Institute, Addison-Wesley, 1997.

Further reading on software quality improvement:
Personal Software Process and Team Software Process (TSP)
An Empirical Study of the Impact of PSP on Individual Engineers
Applying Statistical Process Control for Software

Plan for Success

From the KPMG Peat Marwick study,  project managers of these same projects identified several critical  success factors that they would employ to avoid a runaway software project  next time. From a project management perspective they found: "Runaway Projects - Causes and Effects", Software World, vol. 26, no. 3.