2 Table 1110 shows the processing times in hours for samples

2. Table 11.10 shows the processing times (in hours) for samples of five home mortgage applications submitted at a financial services company each day for the last 15 days. The company guarantees to its customers that it will process all applications within a 24-hour time period. Based on these standards, calculate process capability indices. Also plot x– and R charts and find out if the process is in control. Briefly explain the results.

Day	App 1	App 2	App 3	App 4	App 5
1	14.5	11.5	15.5	13.5	9.5
2	12.75	12.75	8.75	10.75	13.75
3	15.5	17.5	21.5	18.5	14.5
4	6.25	10.25	10.25	6.25	9.25
5	10.25	10.25	6.25	9.25	12.25
6	22	18	16	15	16
7	17.25	16.25	14.25	18.25	17.25
8	15.75	12.75	12.75	15.75	12.75
9	9.5	7.5	3.5	2.5	0.5
10	12	9	11	8	12
11	18	21	23	22	19
12	11.5	11.5	10.5	9.5	13.5
13	22	23	19	18	15
14	21.75	21.75	24.75	26.75	29.75
15	12	9	10	11	10

Solution

Average    for   Application five days samples and Range = Highest number - smallest number

Day1            Average                           

14.5 + 11.5 +15.5 + 13.5 + 9.5 = 64.5/5=12.9

Range = 15.5 - 9.5= 6

DAy 2=

12.75 + 12.75 + 8.75 + 10.75 + 13.75

=58.75 / 5

=11.75

Range =13.75 - 8.75= 5

Day 3

15.5+ 17.5 + 21.5 + 18.5 + 14.5

=87.5/5

=17.5   

Range = 21.5 - 14.5 = 7

Day 4

6.25 + 10.25 + 10.25 + 6.25 +9.25

=42.25/5

=8.45

Range = 10.25 - 6.25 =4

Day 5

=10.25 + 10.25 + 6.25 + 9.25 + 12.25

=48.25 / 5 = 9.65

Range = 12.25 - 6.25 =6

Day 6

= 22 + 18 + 16 + 15 + 16

=87/5

=17.4

Range = 22 - 15 =7

Day 7

= 17.25 + 16.25 + 14.25 + 18.25 + 17.25

=83.25/5=16.65

Range = 18.25 - 14.25 = 4

Day 8

15.75 + 12.75 + 12.75 + 15.75 + 12.75

=69.75 / 5

=13.95

Range = 15.75 - 12.75 =3

Day 9

9.5 + 7.5 + 3.5 + 2.5 + 0.5

=23.5 / 5

4.7

Range = 9.5 - 0.5 =9

Day 10

12 + 9 + 11 + 8 + 12

=52/ 5 =10.4

Range = 12 - 8 = 4

Day 11

18 + 21 + 23 + 22 + 19

=103/5

=20.6

Range = 23- 18 = 5

Day 12

11.5 + 11.5 + 10.5 + 9.5 + 13.5

=56.5/ 5

=11.3

Range = 13.5 - 9.5 = 4

Day 13

22 + 23 + 19 + 18 + 15

= 97 / 5

=19.4

Range = 23 -15 =8

Day 14

21.75 + 21.75+ 24.75 + 26.75 + 29.75

=124.75 / 5

=24.95

Range = 29.75   - 21.75 = 8

Day 15

12 + 9 + 10 + 11 + 10

=52 / 5

=10.4

Range = 12-9 =3

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step 2

Adding all average to find out X

12.9 + 11.75 + 17.5 + 8.45 + 9.65 + 17.4+ 16.65 + 13.95 + 4.7 + 10.4 + 20.6 +11.3 + 19.4 + 24.95 + 10.4

=210 / 15 = 14

Adding All Range =R Or S.D

6 +5+ 7 + 4 +6 + 7+ 4 + 3 + 9 +4 + 5 + 4 + 8 + 8 + 3 =83/15=5.5

So, x= 14, R = 5.5

Step 3 :

Calculate the control limits of X

UCL =X + A2R

LCL= X - A2R

A2 is derived from the three sigma control limits is 0.56

UCL= X +A2R

=    14 + (0.56 * 5.5)

=14+3.08

=17.08

LCL=X – A2R

=14 - (0.56 * 5.5)

= 14 - 3.08

=10.92        

Control limits of R

UCL =D4 R

LCL=D3 R    

D3 and DR are derived from control limit 0 and 2.08     

UCL = 2.08 * 5.5

=11.44

LCL= D3 R

0 * 5.5    = 0

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Calculate cpk

CPK=X – LSL / 3 S.D ;   USL – X /3 S.D     

   =       14 – 0 / 3* 5.5; 11.44 – 14 / 3 * 5.5

=14 / 16.5      ;2.56 / 16.5

=0.85     : - 0.16

Minimum value should be taken = -0.16    for theis process.

NOTE:

X=mean

S.D= Standard deviation              

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