a. If the specification is such that no washer should be greater than 2.4 millimeters, assuming that the thicknesses are distributed normally, what fraction of the output is expected to be greater than this thickness? (6 marks)

Assignment 2

Answer the following questions and submit your answers in a single file of Word format only to Dr YH Hung by 10 November 2018 via Blackboard. Your file name is: Name (as shown in Student ID) LGT5171 A2. For example:

Chan Tai Man LGT5171 A2

Your name should be appeared on each page of the submitted file.

1. The quality control department of an online order supplier has mapped out the flow of an operating process for order placement shown in the below flowchart. A new staff of the department who will manage customer complaint finds it is very hard to understand the process.

Questions

a. You are requested to refine the operation flow to make it become feasible handling customer complaint. (20 marks)

b. From customer’s viewpoint, identify all value-added activities of the supplier in above flowchart. (4 marks)

c. Give suggestions to the supplier for process improvement.

2. As part of the process for improving the quality of their cars, Toyota engineers have identified a potential improvement to the process that makes a washer that is used in the accelerator assembly. The tolerances on the thickness of the washer are fairly large since the fit can be loose, but if it does happen to get too large, it can cause the accelerator to bind and create a potential problem for the driver. (Note: This part of the case has been fabricated for teaching purposes, and none of these data wereobtained from Toyota.)

Let’s assume that, as a first step to improving the process, a sample of 40 washers coming from the machine that produces the washers was taken and the thickness measured in millimeters. The following table has the measurements from the samples:

Questions

a. If the specification is such that no washer should be greater than 2.4 millimeters, assuming that the thicknesses are distributed normally, what fraction of the output is expected to be greater than this thickness? (6 marks)

b. If there are an upper and lower specification, where the upper thickness limit is 2.4 and the lower thickness limit is 1.4, what fraction of the output is expected to be out of tolerance? (4 marks)

c. What is the Cpk for the process? (4 marks)

d. What would be the Cpk for process if it were centered between the specification limits (assume the process standard deviation is the same?) (4 marks)

e. What percentage of output would be expected to be out of tolerance if the process were centered? (6 marks)

f. Set up Xഥ and range control charts for the current process. Assume the operators will take samples of 10 washers at a time.

3. The American University of Beirut Medical Center (AUBMC) in Lebanon is certified by US medical boards. Like similar hospitals internationally, it must meet standards such as the American College of Surgeons’ criteria for operating rooms. Level I and II trauma centres are required to have an operating room (OR) staffed 24 hours per day. A base level of at least one OR team available 24 hours a day is mandatory. During normal business hours, AUBMC will typically have additional OR teams available, since surgery is scheduled during these times and additional teams can be used in an emergency. An important decision must be made concerning the availability of a backup team during the evening hours. A backup team is needed during the evening hours if the probability of having two or more cases simultaneously is significant. “Significant” is difficult to judge, but for the purposes of this case assume that a backup OR team should be employed if the expected probability of two or more cases occurring simultaneously is greater than 1 percent. In one published year-long study, emergency OR patients that arrived after 11 p.m. and before 7 a.m. were studied in a hospital similar to AUBMC. During this time period, there were 62 patients that required OR treatment. The average service time was 80.79 minutes.

In analyzing the problem, think about this as a single-channel, single-phase system with Poisson arrivals and exponential service times.

Questions a. Calculate the average customer arrival rate and service rate per hour. (6 marks)

b. Calculate the probability of zero patients in the system (P0), the probability of one patient (P1), and the probability of two or more patients simultaneously arriving during the night shift. (10 marks)

c. Using a criterion that if the probability is greater than 1 percent, a backup OR team should be employed, make a recommendation to hospital administration.