## Problem Of The Month May 1998—Key Performance Indicators From Weibull Production Plots

The cusps on each Weibull production plot tell about “mixed failure modes” from a variety of cause and effect problems that take away from consistent output.  WinSMITH Weibull (WSW) probability software produced a Weibull plot of production output for the April ’98 problem of the month.   The plot showed multiple cusps, and each segment of the plot was quantified with different Weibull slopes and characteristic values.

This problem of the month shows how you can build a model (you can download instructions in an Excel file on how to perform a Monte Carlo simulation) to find how well your key performance indicator (KPI) compares against the demonstrated production output value from a Weibull plot.

The Problem
The April ’98 problem of the month produced a Weibull plot with cusps shown in Figure 1. The line segments have the following data:

·         Segment  #1 from ~100% reliability to 99% reliability is defined by:
b = 0.1676 and h = 1.77822E+14
and the line segment terminates at X-value = 214 K-Lbs at 1% CDF or 99% reliability

·         Segment #2 from 99% reliability to 95% reliability is defined by:
b = 4.9047 and h = 549.996
and the line segment terminates at X-value = 300 K-Lbs at 95% reliability

·         Segment #3 from 95% reliability to 65% reliability is defined by:
b = 8.9347 and h = 419.688
and the line segment terminates at X-value = 396 K-Lbs at 65% reliability

·         Segment #4 from 65% reliability to 25.5% reliability is defined by
b = 1.2328 and h = 773.336
and the line segment terminates at X-value = 996 K-Lbs at 25.5% reliability

·         Segment #5 from 25.5% reliability to ~0 reliability is defined by
b = 37.1194 and h = 995.812

This information can be used to generate a Monte Carlo simulation in Excel for production output from the plant.  From the “simulated output” from the model, we can ask what’s the best key performance indicator.  Remember, the demonstrated production value produced from the WinSMITH Weibull plot was 995.812 K-Lbs for a plant with only 25.5% reliability.

Suppose you corrected the deficiencies causing the cusps in Figure 1 so that 365 day’s of production fell along the line defined by  b = 37.1194 and h = 995.812 .  Table 2 shows the key performance indicators from 10 simulations averaged—notice the KPI’s have small errors when the process is well behaved and it doesn’t really matter which you choose as the errors are rather small.

Figure 1 shows many problems that need to be addressed, identified, and corrected to get the process under control for more predictable output.  The Weibull plot easily addresses the demonstrated output of the production facility and helps identify problems needing correction.

Other pages you may want to visit concerning similar issue are:

·         Production Output/Problems

·         Six Sigma

·         Coefficient of Variation

·         Nameplate Capacity

·         Production Reliability Example With Nameplate Ratings

·         Process Reliability Plots With Flat Line Slopes

·         Process Reliability Line Segments

·         Papers On Process Reliability As PDF Files For No-charge Downloads

Refer to the caveats on the Problem Of The Month Page about the limitations of the following solution. Maybe you have a better idea on how to solve the problem. Maybe you find where I've screwed-up the solution and you can point out my errors as you check my calculations. E-mail your comments, criticism, and corrections to: Paul Barringer by clicking here. Return to Barringer & Associates, Inc. homepage