Process Control Charts for Always Healthy:

The performance of front desk staff at the Always Healthy office was assessed. Six receptionists were selected and the customer service they provided was observed seven times. The activities that the receptionists were performing were identified and the times ($($in seconds)$)$ to service a customer were recorded as noted below.

Table 6$6$

Receptionists $$ Sample data ($($service activity duration in seconds)$)$

Receptionist Sample 1$1$ Sample 2$2$ Sample 3$3$ Sample 4$4$ Sample 5$5$ Sample 6$6$ Sample 7$7$

115214590110158264152$115214590110158264152$

28611919812311219886$28611919812311219886$

3152106191172139231152$3152106191172139231152$

416513923119899119165$416513923119899119165$

5158149117145154170158$5158149117145154170158$

617213918111094174172$617213918111094174172$

a)$)$ What value of n ($($number of observations)$)$ should be used for computing the X−$-$bar and R control charts?

b)$)$ Calculate the 3−$3-$sigma control limits for the X−$-$bar and the R charts. Create charts for the X−$-$bar and the R charts based on the values you calculated and the ones provided above.

c)$)$ After the control limits were established, another sample was taken and the following times were recorded ($($in seconds)$)$: 238,165,145,83,206,$238,165,145,83,206,$ and 323.$323.$ Is the process in control? Explain why or why not. Show calculations where applicable.