Problem 3 Inspection results of video of the month shipmen

Problem 3: Inspection results of video -of - the - month shipments to customers for 25 consecutive days are given in the following table. Using the EXCEL program file, what central line and control limits should be established and posted if it is assumed that any out - of - control points have assignable causes? The number of inspections each dav is constant and equal 1750. Draw the np charts for this question. mber cmins july- 39 Date Number Nonconforming Nonconforming July 647 7 42 8 48 9 58 12 32 13 38 14 53 15 68 16 45 19 37 20 57 21 38 22 53 July 23 37 26 39 27 51 28 44 29 61 30 48 Aug. 2 56 48 40 47 25 35 4

Solution

Total number of non conformities = Sum of non conforming units = 1147

Total number of inspected items = 1750 /day x 25 days = 43750

Hence, proportion of non conformities = pbar = 1147 / 43750 = 0.0262

Sample size = n = 1750

Thus , Central line = n.pbar = 1750 x 0.0262 = 45.85

Upper Control Limit ( UCL )

= n.pbar + 3 x Square root ( n x pbar x ( 1 – pbar))

= 45.85 + 3 x Square root( 1750 x 0.0262 x ( 1 – 0.0262))

= 45.85 + 3 x Square root ( 1750 x 0.0262 x 0.9738)

= 45.85 + 3 x Square root ( 44.6487)

= 45.85 + 3 x 6.68

= 45.85 + 20.04

= 65.89

Lower Control Limit

= n.pbar - 3 x Square root ( n x pbar x ( 1 – pbar))

= 45.85 - 3 x Square root( 1750 x 0.0262 x ( 1 – 0.0262))

= 45.85 - 3 x Square root ( 1750 x 0.0262 x 0.9738)

= 45.85 - 3 x Square root ( 44.6487)

= 45.85 - 3 x 6.68

= 45.85 - 20.04

= 25.81

Control Limits for np chart thus as follows :

Center line = 45.85

Upper Control Limit = 65.89

Lower Control Limit = 25.81

Center line = 45.85

Upper Control Limit = 65.89

Lower Control Limit = 25.81