The north country clothing company is a mail-order company that process thousand

Question

The north country clothing company is a mail-order company that process thousands of mail and telephone orders each week. they have a customer service number to handle customer order problems and monitor the number of complaints. the total number of complaint calls the customer service department has received for each of the last 30 weeks are shown in chart below . the average number of complaints has been 24 in the past year.

1.) Make a control chart to monitor customer service quality.

2.)Is process in control , why or why not ?

Week # of Complaints Week #of Complaints Week # of Complaints 31 23 18 21 20 27 28 19 23 21 17 29 34 12 13 14 15 16 17 18 19 20 25 30 32 31 34 25 19 12 17 18 2 23 24 25 26 27 28 29 30 4 25 28 30 32 15 14 6 7 10

Explanation / Answer

Let C : number of complaints per week

Given that average number of complaints per week in the past year = 24

C ~ Poisson ( lamda = 24 )

E(C) =24 and S.D(C) =sqrt(24) = 4.8989

We used C- chart to check the process in control or not.

The 3-sigma control limit for C- chart

UCL = E(C) + 3 * S.D(C) = 24 + ( 3* 4.8989) = 38.3967

CL = E(C) = 24

LCL = E(C) - 3 * S.D(C) = 24 - ( 3* 4.8989) = 9.3033

b) Since Minimum number of complaints in the week = 12

Maximum number of complaints in the week = 34

Since all the value of number of complaints calls in the week lies in the (9.3033 , 38.3967), none of the value outside the control limits.

Hence the process is in control.

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