Need guidance on Weibull Analysis + modeling

[JohnnyTan]

I need to construct a spreadsheet model to simulate these situations for 100 trials assuming, the bulbs’ lifespan follows the Weibull distribution.

1) to change the light bulbs after a certain use time systematically from room to room before they even have the chance to fail.

2) put two or three smaller bulbs in each lamp so that it still functions when at least one of the bulbs is working

Bulb A cost USD$3, with Weibull scale parameter a of 420 days and shape parameter b of 1.3.

Smaller bulb B cost USD$2, with Weibull scale parameter of 350 days and shape parameter of 1.2.

I am kinda confused as to how to start doing this model. Could anyone kindly point me in the right direction with regards to the perimeters I should be focusing on in my modeling? I will really appreciate it if anyone can give me pointers on how I should approach this problem. Cheers.

 

[oldbrewer]

1) is a given - you pay $3 every 420 days MINUS your safety factor "guessed" from shape parameter

2) calculate how many bulbs are predicted to fail in 100 days or less and then calculate the probability of 3 specific bulbs failing in 100 days or less
repeat for 120 days 130 days etc

read up on normal distribution and how the probabilities of occurrences are calculated it will get you pointed in the right direction

 

[shg]

Aren't you missing a lot of data to develop a cost model?

What does it cost to replace a bulb PRN (i.e., when it fails), versus replacing them systematically in some rotation?

Do you use two bulb B's to replace one bulb A, or three? Or do you need to model both cases?

If you have multiple bulb B's, do you replace failed bulbs as failures occur? Or if there are three bulb B's, when you're down to one operating?

Is there a cost associated with a fixture being non-operational (or degraded), and a time to replace a bulb on notification that a failure has occurred?


I have a user-defined function that generates Weibull-distributed deviates for a given scale and shape, but it seems like you're a long way from needing it.

[Table="width:, class:grid"][tr][td] [/td][td]

A​

[/td][td]

B​

[/td][td]

C​

[/td][/tr]
[tr][td]

1​

[/td][td]

Bulb​

[/td][td]

A​

[/td][td]

B​

[/td][/tr]

[tr][td]

3​

[/td][td]Scale[/td][td]

420​

[/td][td]

350​

[/td][/tr]

[tr][td]

4​

[/td][td]Shape[/td][td]

1.3​

[/td][td]

1.2​

[/td][/tr]

[tr][td]

5​

[/td][td]

Sample​

[/td][td]

Weibull​

[/td][td]

Weibull​

[/td][/tr]

[tr][td]

6​

[/td][td]

1​

[/td][td]

460.9​

[/td][td]

43.2​

[/td][/tr]

[tr][td]

7​

[/td][td]

2​

[/td][td]

636.8​

[/td][td]

226.2​

[/td][/tr]

[tr][td]

8​

[/td][td]

3​

[/td][td]

134.4​

[/td][td]

481.8​

[/td][/tr]

[tr][td]

9​

[/td][td]

4​

[/td][td]

1014.7​

[/td][td]

198.5​

[/td][/tr]

[tr][td]

10​

[/td][td]

5​

[/td][td]

1059.6​

[/td][td]

220.9​

[/td][/tr]

[tr][td]

11​

[/td][td]

6​

[/td][td]

310.5​

[/td][td]

108.7​

[/td][/tr]

[tr][td]

12​

[/td][td]

7​

[/td][td]

995.7​

[/td][td]

385.6​

[/td][/tr]

[tr][td]

13​

[/td][td]

8​

[/td][td]

292.1​

[/td][td]

188.5​

[/td][/tr]

[tr][td]

14​

[/td][td]

9​

[/td][td]

146.2​

[/td][td]

450.5​

[/td][/tr]

[tr][td]

15​

[/td][td]

10​

[/td][td]

458.6​

[/td][td]

483.4​

[/td][/tr]

[tr][td]

16​

[/td][td]

11​

[/td][td]

244.1​

[/td][td]

253.0​

[/td][/tr]

[tr][td]

17​

[/td][td]

12​

[/td][td]

1064.4​

[/td][td]

121.9​

[/td][/tr]
[/table]

 

[JohnnyTan]

hi SHG, i am sorry that I did not post the entire perimeters that I was given to work with. Perhaps this could explain the question better:

The entire perimeters are as follows:


The maintenance section has been busy last year responding to urgent requests to change light bulbs when they failed.Currently, all bulbs are only changed one at a time when they fail.


I need to construct a spreadsheet model to simulate alternatives for 100 trials assuming, the bulbs’ lifespan follows the Weibull distribution.


1) to change the light bulbs after a certain use time systematically from room to room before they even have the chance to fail.
2) put two or three smaller bulbs in each lamp so that it still functions when at least one of the bulbs is working


Also to. Compare the average or mean time to failure (MTTF) of the lamps for the scenarios:
1) bulb A,
2) bulb A with scheduled bulb change at 200 days,
3) bulb A with scheduled bulb change at 250 days,
4) 1 bulb B in each lamp,
5) 2 bulbs of B in each lamp, and
6) 3 bulbs of B in each lamp.


And, For each of the scenario, evaluate how often the maintenance department has to respond to ad-hoc failed bulb-servicing request.




Bulb A cost USD$3, with Weibull scale parameter a of 1.3 and shape parameter b of 420 days.
Smaller bulb B cost USD$2, with Weibull scale parameter of 1.2 and shape parameter of 350 days.


I am also told that a random Weibull value can be simulated using
formula= b *(-LN(1-RAND()))^(1/a) and I am not sure how does this help me.


I am kinda confused as to how to start doing this model. Should I be doing a monte carlo simulation(i.e simulate 100 life bulbs and their independent rate of failure) or just do a weibull distribution like


t(days) cumulative distribution(survival probability)
10 0.1%
20 0.2 %
and so on


I hope this explains the perimeters I am working against better.

 

[shg]

The least expensive approach is to change each bulb as it needs changing, unless ...

1. It costs more to replace bulbs on demand than it does to replace the systematically in rotation

2. There is a cost associated with fixture downtime, and some average delay to replace a failed bulb on notification that multiplies that cost

3. There is some other metric that relates to partial failures of a several-bulb fixture.

Am I missing somthing obvious that simplifies the problem to only the parameters you have described? If so, I don't have a clue.

 

[shg]

The worksheet function Weibull will return the percentage of expected falures as a function of time:

=WEIBULL(days, Shape, Scale, TRUE)

e.g.,

=WEIBULL(400, 1.3, 420, TRUE) returns ~ 61%

 

[oldbrewer]

I am not sure why the variation in failure times is not "normal".

 

[shg]

I believe because the Weibull distribution with a shape parameter > 1 describes the probability of failures that occur as a result of a wear-out mechanism.

 

[oldbrewer]

ok shg, but mains voltage is normally distributed about the aim voltage, and during production of the bulbs worker concentration, worker skill and variation in raw materials are both varying normally