In production flowshop problems performance is often evaluat

In production flow-shop problems, performance is often evaluated by minimum make-span, the total elapsed time from starting the first job on the first machine until the last job is completed on the last machine. For a particular flow-shop the make-span was evaluated with respect to the number of jobs to be done. Let the independent variable X denote the number of jobs and the dependent variable Y denote the make-span (in standardized units):

Solution

Find Correlation .

r( X,Y) =    Co V ( X,Y) / S.D (X) * S.D (y)                  
r( X,Y) =    Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )                    
                      
Co v ( X, Y ) =   1 /12 (1258.78) - [ 1/12 *114 ] [ 1/12 *115.03] =            13.833      
S. D ( X ) =   Sqrt( 1/12*1226-(1/12*114)^2)           3.452      
S .D (Y) =    Sqrt( 1/12*1302.9569-(1/12*115.03)^2)           4.086      
r(x,y) =    13.833 / 3.452*4.086   =   0.9807          

Set Up Hypothesis
Null, H0: =0
Alternate, H1: !=0
Test Statistic
Value of ( r ) =0.9807
Number (n)=12
we use Test Statistic (t) = r / Sqrt(1-r^2/(n-2))
to=0.9807/(Sqrt( ( 1-0.9807^2 )/(12-2) )
to =15.86
|to | =15.86
Critical Value
The Value of |t | at LOS 0.05% is 2.228
We got |to| =15.86 & | t | =2.228
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho

Correlation
( X)	( Y)	X^2	Y^2	X*Y
4	3.75	16	14.0625	15
5	4.9	25	24.01	24.5
6	4.88	36	23.8144	29.28
7	7.2	49	51.84	50.4
8	7.3	64	53.29	58.4
9	9.1	81	82.81	81.9
10	9	100	81	90
11	11.9	121	141.61	130.9
12	11.5	144	132.25	138
13	14.1	169	198.81	183.3
14	13.9	196	193.21	194.6
15	17.5	225	306.25	262.5
114	115.03	1226	1302.9569	1258.78	Totals