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 4 9 10 11 12 13 14 Number of complaints 4 10 16 89 6 5 12 137 6 4 210 a.Determine three-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? Yes ? No

Explanation / Answer

To be calculated:

(a) Three-sigma control limits

(b) Determine if the process is in control or not

Given values:

Number of complaints on each day of a 14-days period

z = 3 (three-sigma)

Solution:

(a) Average number of complaints (c-bar) during the 14-days period is calculated as;

c-bar = Sum of number of complaints / Total number of observations

c-bar = (4 + 10 + 16 + 8 + 9 + 6 + 5 +12 + 13 + 7 + 6 + 4 + 2 + 10) / 14

c-bar = 112 / 14

c-bar = 8

Upper Control Limit (UCL) is calculated as;

UCL = c-bar + (z x ?c-bar)

UCL = 8 + (3 x ?8)

UCL = 16.485

Lower Control Limit (LCL) is calculated as;

LCL = c-bar - (z x ?c-bar)

LCL = 8 - (3 x ?8)

LCL = -0.485 or 0 (c-control charts cannot have a negative control limit i.e. number of complaints received each day cannot be in negative values)

LCL = 0

(b) Since, the number of complaints on each day lies within the upper control limit (16.485) and lower control limit (0), YES, the process is in control.

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