Hi everyone,


I attach this Excel file below, Its from a book I purchase. The question ask in the book, How can I estimate the probability that a machine will work without failing for at least 20 hours?

All the calculations are there in the workbook except for the Alpha and the Beta. The book says it used solver to get the alpha and the beta but it does not show you how.

My question is how do you get the Alpha and the Beta in excel by using formulas or solver? Look in cell E2 and E3 in the workbook how did they get those results?

I also posted this question to the link below.


http://groups.google.com/group/microsoft.public.excel.worksheet.functions/browse_thread/thread/89f8d4d455801b58/4900c5d425098a36?hl=en#4900c5d425098a36

I think they used quantile matching to estimate the parameters

Estimate two quantiles from the sample (say 25%,75%)

Then solve the system

.25=F(x(25%))
.75=F(x(75%))

You can use solver to solve this but it's easy to do it by hand.

Hi mp83,


I'm sorry to say but I know very little of stats. Can you give me the instructions how to use solver?


But I found these 2 formulas.

ALPHA: =B13*SQRT(EXP(GAMMALN(1+2/B14))-EXP(GAMMALN(1+1/B14))^2)

BETA: =B2*EXP(GAMMALN(2+3/B3))

Do you know if these formulas are correct to use in my stitution?

Anyone could verfiy those formulas I posted or show me how to use solver?

You don't need to use Solver.All you need is to solve the equations system. I'll do this for you in the following

X~Wei(a,b)->F(x)=1-exp{-(x^a)/b}

I assume you can find the quantiles of the sample

.25=1-exp{-(x25^a)/b}
.75=1-exp{-(x75^a)/b}

Dividing this equations you can estimate a. The estimate is log(3)/log(x25/x75). Then substituting this into one equation you will find an estimate of b, that is -(x25^a)/log(.25)

You don't need to use Solver.All you need is to solve the equations system. I'll do this for you in the following

X~Wei(a,b)->F(x)=1-exp{-(x^a)/b}

I assume you can find the quantiles of the sample

.25=1-exp{-(x25^a)/b}
.75=1-exp{-(x75^a)/b}

Dividing this equations you can estimate a. The estimate is log(3)/log(x25/x75). Then substituting this into one equation you will find an estimate of b, that is -(x25^a)/log(.25)


Thank You so much for the help I really do appreciate for the equations you have given me mp83. Can we apply those equations in solver? Because I'll really need to know how to use solver. Its work related.

A Solver you'd be useful in the case you should maximize (or minimize) an equation that is defined by parameters that are cells (with some costrains possibly). For example, a linear programming problem can be efficiently solved.

You can find many resources [> http://www.solver.com/stepbystep2.htm]

> http://www.google.com/search?q=solver%2Bexcel%2Btutorial

A Solver you'd be useful in the case you should maximize (or minimize) an equation that is defined by parameters that are cells (with some costrains possibly). For example, a linear programming problem can be efficiently solved.

You can find many resources [> http://www.solver.com/stepbystep2.htm]

> http://www.google.com/search?q=solver%2Bexcel%2Btutorial

Thank you for the links I'll try to learn from those. Once again thank you so much for the help.