Reliability HotWire: eMagazine for the Reliability Professional
Reliability HotWire

Issue 46, December 2004

Hot Topics

Using Weibull++ and BlockSim to Calculate t0

A question that was posted on ReliaSoft's Discussion Forum asks whether ReliaSoft's Weibull++ software can calculate t0 for a data set provided in an article by another author and use the analysis to calculate a variety of results, including the optimum replacement time. This article presents ReliaSoft's response. Note: The referenced article was formerly distributed via the Web but is no longer available. The relevant data set is reproduced here.

In the referenced article, 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 can repeat this in Weibull++ 6 using Free Form data as shown below:

Estimated 3-parameter Weibull distribution parameters of free form data

The computed parameters (using the data as presented by the author) are shown next:

Beta = 3.5988
Eta = 596.1637
Gamma = 898.2500 (same as t0)

The location parameter calculated by Weibull++ (also called gamma or t0) is 898.2500, which is very close to the authors calculation of 900. 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. For example, to determine the optimum interval, you can use the Function Wizard to generate a table of optimum replacement times. The Function Wizard is shown next.

Function Wizard

Based on the inputs, a table of optimum replacement times will be generated for times from 1000 hours up to 1200 hours with an interval of 10 hours. The cost for a planned replacement is 250 and the cost of an unplanned replacement is 600. The results are displayed in the General Spreadsheet, as shown next.

Table of optimum block replacement times

As you can see from these results, the optimum replacement time is equal to 1150 hours based on the lowest Cost/Unit Time. A more precise optimum replacement time can be calculated by decreasing the increment time or by using ReliaSoft's BlockSim software. A diagram consisting of a single block with a failure distribution defined by the estimated Weibull++ parameters can be used to calculate the optimum replacement time, as shown next.

Optimum replacement time in BlockSim

The optimum replacement time is equal to 1152.7964 hours.

ReliaSoft Corporation

Copyright 2004 ReliaSoft Corporation, ALL RIGHTS RESERVED