ReliaSoft's Reliability Knowledge Base: Support Answer 012100

This document provides an answer to a question posted on ReliaSoft's Discussion Forum. The question "How does one calculate t-sub-0?" was posed as follows:

"My boss is fascinated with the 6 page web article, Weibull's Distribution Application (Step by Step) found at the hyperlink: http://www.geocities.com/CapeCanaveral/Lab/1418/info2.htm. This article starts by providing a data table consisting of equal length times to failure intervals of 100 hours each with the corresponding observed frequency. It then proceeds onto page 2 where it provides the basic graphical formula for t₀ as

t₀ = t₂ - ( ((t₃-t₂) * (t₂-t₁)) / ((t₃-t₂) - (t₂-t₁)) ) which always becomes t₀ = 1,200 - (10,000 / 0 ) when t₁=1,100 and t₂=1,200 and t₃=1,300.

Of course, this is not the case!!! Obviously, we never divide by zero! Then in the Computer Program case, the article states that t₀ should be 900 hours. I would really appreciate some expert advice and insight on the correct application on the formulas given in the article and on the computer program so that I too can crank out the numbers provided in this excellent article to arrive at the same answers! Does Weibull++ provide t₀ calculations ability and would it also provide 900 hours as its answer too?"

In this example the author is computing a three parameter Weibull Distribution, where t₀ is the same as the gamma parameter (for more discussion see ReliaSoft's Life Data Analysis Reference). You may repeat this in Weibull++ 5.0 using "Free Form Data" as shown below:

Weibull++ answers are based on a more refined algorithm than the one presented by the author and are in our opinion more accurate. All presented results can be very easily obtained in Weibull++ using the QCP, the Function Wizard, or the plot. To determine the optimum interval as presented by the author, you can then use the Function Wizard in Weibull++, either in a general spreadsheet or in the Report generator as shown next:

The answer in this case is that the optimum interval is at 1152.7943 hrs (based on the Weibull++ computed parameters). It should be noted that this is only for one component. The computations can be expanded to multiple components using ReliaSoft's BlockSim as shown next: