Refer to Exercise 9-33 on the order completion time of a logistics firm. Upon conducting a methods study of the various operations, the firm was able to reduce the mean times of operation 1 to 5.8 hours and that of operation 3 to 7.5 hours. Assume that the tolerances did not change. The customer requires an order completion time of 23.2 hours. Assuming normality, what proportion of orders will not meet the customer requirements?

Exercise 9-33

A logistics firm has identified four operations, which are to be conducted in succession, for an order to be processed. The tolerances (in hours) are shown in Table 9-9. Assume that the tolerances are independent of each other and that the time in each phase is normally distributed. Further assume that for each operation the processes are barely capable.

• (a) Find the natural tolerance limits for order completion time.

(b) If the company sets a goal of 23.5 hours, what proportion of the orders will fail to satisfy this goal?

(c) Find an appropriate capability index and comment.

(d) Using a methods study, the company has improved operation 3 to a mean time of 7.0 hours. What proportion of the orders will now meet the goal?

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TABLE 9-9 Operation 1 2 3 4 Mean Time (hours) 600 L 4 8 5 Tolerance (hours) 6+0.6 4+0.6 8+0.8 5+0.3