May '98 Problem Of The Month--Key Performance Indicators From Weibull Production Plots

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

The Weibull plot of production output is similar to looking at a plant as if it’s a black box. Each plot shows “genetic” problems with the plant as the production rarely falls completely on a straight line. You want the production output to be very consistent (steep b’s) with no cusps, and large output (high h’s). What you get is often far different than what you want.

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.

You can download an Excel spreadsheet ( MAY98PRB.XLS )—217Kb file size, which contains the Monte Carlo model. You can run a production output simulation by pressing the F9 key. The F9 key will recalculate the spreadsheet and produce new simulated output from the plant. The plant output will be used to produce some common key performance indicators such as the plant output ratings (of course, every time you run the Monte Carlo simulation, you will get a different answer). Thus the results of the KPI’s must be averaged to get the results shown in Table 1 for 10 simulations—notice the large variations in the KPI’s when the cusps are far from the demonstrated line. This large variation could lead you to believe the problem lies within how the KPI’s are constructed and thus people spend too much time arguing over the non-validity of the KPI rather than fixing the problem which causes the deviation.

Table 1 Results From Key Performance Simulation For Data In Figure 1 With 5 Line Segments
Value	Error	Method
995.8 996.7 961.7 892.0 1037.8 1032.5 1029.0 757.1 708.8 684.5 655.3 633.3	Datum 0.1% -3.4% -10.4% 4.2% 3.7% 3.3% -24.0% -28.8% -31.3% -34.2% -36.4%	Weibull demonstrated output Best 5 day average in a year Best 7 day average in a year Best 10 day average in a year Average of best 10 days in a year Average of best 20 days in a year Average of best 30 days in a year Best 30 day average in a year Best 60 day average in a year Best 90 day average in a year Best 180 day average in a year Average for the year

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.

Table 2 Results From Key Performance Simulation For Data In Figure 1 With Line Segment #5
Value	Error	Method
995.8 1015.6 1010.2 1004.8 1035.5 1030.9 1027.9 993.3 989.4 986.3 983.4 981.4	Datum 2.0% 1.4% 0.9% 4.0% 3.5% 3.2% -0.3% -0.6% -1.0% -1.2% -1.4%	Weibull demonstrated output Best 5 day average in a year Best 7 day average in a year Best 10 day average in a year Average of best 10 days in a year Average of best 20 days in a year Average of best 30 days in a year Best 30 day average in a year Best 60 day average in a year Best 90 day average in a year Best 180 day average in a year Average for the year