Question

Table of the most usual probability distribution functions of maintenance processes Create a table of the most usual probability mass functions (pmf) or probability distribution functions (pdf) (for discrete or continuous random variables) and their features that are mostly applied in Maintenance and Reliability. The columns should contain the following information: pmf or pdf, range of the variable, the cumulative distribution function (CDF), parameters, range of parameters, mean value, standard deviation or variance. Draw the table landscape The table is to be used for the following exercises. 1) X is normally distributed with a mean of 15 and variance of 9, then find (a) P(X< 18), (b) P(X<11), (c) Area between (11<x< 18) (d) What is X to have at least 95% acceptance 2) For X-ray machines produced by a certain manufacturer, the following is known. Life time in years follows a lognormal distribution with u = 0.9 and o = 1.2. The expected lifetime of such machines is 15 years. (a) Calculate the probability that an X-ray machine produced by this manufacturer will last at least 12 years.

Answer 1

Ney wal distribution Cure * M, t=0 general shape of a Normally distributed Curve Where, ut mean og std deviation 2= Normal variate ty M = 15 J=9 & x is normally distribute a Z= null for getting probability from rechte value, We should go to 2-table 2=0.33 2 -% a) P(X218) = 2 = 18-15 - 03/= 0.33 lllll PL 12. 18)= 0.62930 (from-able) bp (11) = 24cll 11-15 - 4/6 - 04 P(X511) = 0.3299 () Area blu 11LX218 0 -0.44 2 2 2 0.33 values ( from a fb) (2618) - Prasil) 0.62930. 0.3299 = 0.299 20:44 2 d) Werl is x to have a5, acceptance

221-65 for at acceptance, the 2 Value should be 1.65 1.65= X- 1-65XIS - x= 24.850 Liletime follows loghonmal aisth botion with u=0.9, J=12 - enx follows Normal distribution with M=0.94 = 12 expected lifetime of machine = 15 yeals - P(x), 12) =D2 0( en 12-lnit) - - 0.186 1.2 Ayx 0.186 1-0428 80.572) Probability that machine lasts at least 12 years = 0.52 Thank you ..

probability values are taken from z tables

thank you..