mws_ind_dif_discrete_examples

mws_ind_dif_discrete_examples - Chapter 02.03...

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Chapter 02.03 Differentiation of Discrete Functions-More Examples Industrial Engineering Example 1 The failure rate of a direct methanol fuel cell (DMFC) is given by the formula ) ( t h ) ( ) ( ) ( t R t R t h where is the reliability at a certain time , and the values of the reliability are given in Table 1. ) ( t R t Table 1 Reliability of DMFC system. hrs t 0 1 10 100 1000 2000 3000 4000 5000 ) ( t R 1 0.9999 0.9998 0.9980 0.9802 0.9609 0.9419 0.9233 0.9050 Using the forward divided difference method, find the failure rate of the DMFC system at 50 t hours. Solution    t t R t R t R i i i 1 10 i t 100 1 i t i i t t t 1 10 100 90   90 10 100 50 R R R 90 9998 . 0 9980 . 0 5 10 0000 . 2 The reliability at hours is, ) ( t R 50
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02.03.2 Chapter 02.03 ) 10 ( ) 10 50 ( 10 100 ) 10 ( ) 100 ( ) 50 ( R R R R 9998 . 0 ) 40 )( 10 0000 . 2 ( 5 999 . 0 The failure rate at hours is then, ) ( t h 50 t ) 50 ( ) 50 ( ) 50 ( R R h 999 . 0 ) 10 0000 . 2 ( ) 50 ( 5 h 5 10 0020 . 2 ) 50 ( h Example 2 The failure rate of a direct methanol fuel cell (DMFC) is given by the formula ) ( t h ) ( ) ( ) ( t R t R t h where is the reliability at a certain time , and the values of the reliability are given in Table 2. ) ( t R t Table 2 Reliability of DMFC system. hrs
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mws_ind_dif_discrete_examples - Chapter 02.03...

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