The postmaster of a small western town receives a certain number of complaints e

Question

The postmaster of a small western town receives a certain number of complaints each day about mail delivery. DAY 1 2 3 456 78 910 11 12 13 14 4 11 15 8965 14 14 7642 9 Number of complaints a.Determine two-sigma control limits using the above data. (Round your intermediate calculations to 4 decimal places and final answers to 3 decimal places. Leave no cells blank be certain to enter "O" wherever required. Round up any negative control limit value to zero.) UCL LCL b. Is the process in control? No O Yes

Explanation / Answer

The average number of defects in 14 days , Cbar

= ( 4 + 11 + 15 + 8 + 9 + 6 +5 + 14 + 14 + 7 +6 + 4 +2 + 9 ) / 14 = 114/14 = 8.142

We will use a C Chart to determine Control limits for number of complaints

Using 2 sigma control limit :

Upper Control Limit

= Cbar + 2 x square root ( Cbar)

= 8.142 + 2 x Square root ( 8.142 )

= 8.142 + 2 x 2.853

= 8.142 + 5.706

= 13.848

Lower Control Limit

= = Cbar - 2 x square root ( Cbar)

= 8.142 - 2 x Square root ( 8.142 )

= 8.142 - 2 x 2.853

= 8.142 - 5.706

= 2.436

UCL = 13.848

LCL = 2.436

There are data e.g. 2, 14 and 15 which are outside control limits set by UCL – LCL range. Hence , the process is not in control

PROCESS IS NOT IN CONTROL

UCL = 13.848

LCL = 2.436

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