Laplace Trend test

[Levent]

Hello

I am using the Laplace Trend Test for detecting reliability trends in electrical (power systems) engineering. Specifically, I am using it to find improving or deteriorating trends for some feeders (based on feeder age at each failure). Feeders are circuits that distribute electricity to customers (homes, businesses etc.) in an electrical distribution system.

I would like to get some help with regard to two points:

1
I understand that Laplace Trend test indicates whether a trend (improving or deteriorating) exists or does not exist for historical failure data. That is, it gives an indication of whether the variation in the age at failures for a system (the system is the feeder in this case) is simply due to statistical (seasonal, cyclical, irregular etc.) variation or due to an actual improving or deteriorating trend. A deteriorating trend might indicate wear-out, which is the primary concern.

Does Laplace Trend test also give an indication also of the future trend? That is, if we have a Laplace test value of +4 for a feeder (or +2 or + 1.8 for example), can we say that this deteriorating trend is likely (more or less likely depending on the value) to continue for the next, say, year? In other words, can it be used for predicting the future trend?

2
Laplace Trend Test is a function of failure times, but it is not a function of failure impact.

So, an improving trend indicates failures are occurring less and less frequently with time.
A deteriorating trend indicates failures are occurring more and more frequently with time. It does not say whether failures are occurring with less or more severity each time.

Severity in the case of feeder failures could be defined as duration of the failure, for example, or number of distribution customers interrupted as we tend to use for feeders.

Is there any way to quantify this increasing or decreasing trend in severity? The only way I can think of is maybe to use a trend line (best fit line), but I don’t know whether to have time (in hours) or the failure number (index) (1, 2, 3, 4, 5, …) on the horizontal axis.

Sample data for illustration:

column1: Failure Number (index) 1493 95 548 1132770194 Levent Hello

I am using the Laplace Trend Test for detecting reliability trends in electrical (power systems) engineering. Specifically, I am using it to find improving or deteriorating trends for some feeders (based on feeder age at each failure). Feeders are circuits that distribute electricity to customers (homes, businesses etc.) in an electrical distribution system.

I would like to get some help with regard to two points:

1
I understand that Laplace Trend test indicates whether a trend (improving or deteriorating) exists or does not exist for historical failure data. That is, it gives an indication of whether the variation in the age at failures for a system (the system is the feeder in this case) is simply due to statistical (seasonal, cyclical, irregular etc.) variation or due to an actual improving or deteriorating trend. A deteriorating trend might indicate wear-out, which is the primary concern.

Does Laplace Trend test also give an indication also of the future trend? That is, if we have a Laplace test value of +4 for a feeder (or +2 or + 1.8 for example), can we say that this deteriorating trend is likely (more or less likely depending on the value) to continue for the next, say, year? In other words, can it be used for predicting the future trend?

2
Laplace Trend Test is a function of failure times, but it is not a function of failure impact.

So, an improving trend indicates failures are occurring less and less frequently with time.
A deteriorating trend indicates failures are occurring more and more frequently with time. It does not say whether failures are occurring with less or more severity each time.

Severity in the case of feeder failures could be defined as duration of the failure, for example, or number of distribution customers interrupted as we tend to use for feeders.

Is there any way to quantify this increasing or decreasing trend in severity? The only way I can think of is maybe to use a trend line (best fit line), but I don’t know whether to have time (in hours) or the failure number (index) (1, 2, 3, 4, 5, …) on the horizontal axis.

Sample data for illustration:

column1: Failure Number (index)
column2: Failure Time (days)(Ti)
column3: Customers interrupted (severity measure 1)
column4: Duration (hours) (severity measure 2)

0 0 1500 2
1 100 1200 1
2 150 200 1.5
3 175 500 0.15
4 180 600 2.6

(m=4)

( Note: Laplace Trend test is a function of m and summation of Ti's. )

[Harry]

Hi:
1. Laplace Trend test can only tell you if there is a time trend (of number of failures) for the data you analysized. If a model can fit your current data very well (Through Goodness-of-fit test), you can think the same trend will continue for your future observations. Of course, any model only can make good short-term prediction. For long-term prediction, no model will be trustable because the system may change over time. The best way to make better predictions is to dynamically adjust your model using the new observations.

2. For the second question, since you only have few data, it is difficult to test any trend. You can simply plot (failure number or failure time) vs. (Custormers interrupted or Duration) and look at the plots to see whether there is any trend. If you have more data, say more than 20 data points, you can use the tools in Weibull ++ called "Degradation Analysis" to build models to further analysis the relationship between time(failure number) with the severity.