I need help with this problem. Please work in excel and provide as detailed a so
ID: 3266742 • Letter: I
Question
I need help with this problem. Please work in excel and provide as detailed a solution as possible with the excel formulas please and thank you.
1. You are doing accelerated life-cycle testing on 100 Knutson valves. The data given in worksheet “Problem 1” in the “Data” file gives test results (number of days each valve lasted).
a. Determine the Weibull distribution parameters for the reliability of the valves.
b. What is the average lifetime of each design (in days)?
Days N remaining 0 100 100 99 202 98 304 97 408 96 512 95 618 94 725 93 833 92 943 91 1053 90Explanation / Answer
Solution:
a) We Use R programing to solve thi this problem
> X=c(100,99,98,97,96,95,94,93,92,91,90)
> library(MASS)
> FIT=fitdistr(X, densfun="weibull", lower = 0)
> FIT
shape scale
=33.5804224 96.5280039
=( 7.8861494) ( 0.9174118)
This are shape and scale parameter of Weibull distribution.
b) mean is E(X) = b (1 + 1/a)
> a = 33.5804224 # (shape parameter )
> b =96.5280039 #(scale parameter)
> mean = b*gamma(1+(1/a))
> mean95
[1] 94.9512
average lifetime of each design is approximetly 95 Days