Life Testing

Chapter 14 Life Testing

  Scilab code Exa 14.3a Lifetime of a transistor

  1 t o t a l =50;

  5 val1 = cdfchi ( ”X” , 2 failure , a l p h a 2 , 1 -( a l p h a 2) )

  6 val2 = cdfchi ( ”X” , 2 failure , 1 - a l p h a 2 , ( a l p h a 2) )

  8 int1 = 2 t val1 ;

  9 int2 = 2 t val2 ;

  10 disp ( ” The 9 5 c o n f i d e n c e interval is”);

  11 disp ( int2 ) ;

  12 disp ( int1 , ” t o ” ) ;

  14 The c o n f i d e n c e interval is from22.35to62.17

  w h e r e a s my s o l u t i o n in Scilab is 22.35to62.53

  15 b e c a u s e of the d i f f e r e n c e in the v a l u e of chi - square

  (0.975 , 30) . The t e x t b o o k says the v a l u e is 1 6 . 8 9

  16 w h e r e a s s c i l a b c a l c u l a t e s its v a l u e as 1 6 . 7 9

  Scilab code Exa 14.3b Lifetime of Battery

  1 t=1800;

  2 t h e t a = 150;

  3 r =20;

  4 pvalue= cdfchi ( ”PQ” ,2 t theta , 2 r ) ;

  5 disp ( pvalue , ”P−v a l u e is”)

  Scilab code Exa 14.3c One at a time sequential test

  4 val1 = cdfchi ( ”X” , 2 r , 1 - a l p h a 2 , a l p h a 2) ;

  5 val2 = cdfchi ( ”X” , 2 r , a l p h a 2 , 1 - a l p h a 2) ;

  6 int1 = 2 T val1 ;

  7 int2 = 2 T val2 ;

  8 disp ( ” The 9 5 c o n f i d e n c e interval is”);

  9 disp ( int1 ) ;

  10 disp ( int2 , ” t o ” ) ;

  12 The c o n f i d e n c e interval is from29.27to103.52

  w h e r e a s my s o l u t i o n in Scilab is 29.265774to

  13 1 0 4 . 2 6 6 8 3 b e c a u s e of the d i f f e r e n c e in the v a l u e of

  chi - square (0.975 , 30) . The t e x t b o o k says the v a l u e is

  14 9.66 w h e r e a s s c i l a b c a l c u l a t e s its v a l u e as 9.5907774.

  Scilab code Exa 14.3d Lifetime of semiconductors

  4 val1 = cdfchi ( ”PQ” , 2 T theta , 2 r ) ;

  5 val2 = 1 - cdfchi ( ”PQ” , 2 T theta , 2( r +1) ) ;

  6 pvalue= min ( val1 , val2 ) ;

  7 disp ( pvalue , ” The p v a l u e is”);

  8 disp ( ”H0 w o u l d b e

  a c c e p t e d when t h e significance

  level is 0.10”);

  Scilab code Exa 14.3e Bayes estimator

  1 X = [5 7 6.2 8.1 7.9 15 18 3.9 4.6 5 . 8 ] ;

  2 Y = [3 3.2 4.1 1.8 1.6 2.7 1.2 5.4 10.3 1 . 5 ] ;

  3 t= sum (X)+ sum (Y);

  8 disp ( estimate , ” B a y e s estimate o f lambda is”);

  Scilab code Exa 14.4a Lifetime of items produced by two plants

  1 X l i f e = 420;

  2 Y l i f e = 510;

  3 Xnum = 10;

  4 Ynum =15;

  5 ts = X l i f e Ynum ( Y l i f e Xnum ) ;

  6 disp ( ts , ” The v a l u e of the test statistic is”);

  7 val = cdff ( ”PQ” , ts , Xnum , Ynum ) ;

  8 p v a l u e = 2(1 - val ) ;

  9 disp ( pvalue , ” The p−v a l u e is”);

  10 disp ( ”We c a n n o t r e j e c t H0” ) ;