**OMIS 627 Process Analysis, Quality, and Queuing Assignment**

** ****Problem 1**

The Kishwaukee Hospital emergency room (ER) is currently organized so that all patients register through an initial check-in process. At his or her turn, each patient is seen by a doctor and then exits the process, either with a prescription or with admission to the hospital. Currently, 55 people per hour arrive at the ER, 10% of who are admitted to the hospital and the other 90% get a prescription. On average, 7 people are waiting to be registered (Buffer 1) and 34 are registered and waiting to see a doctor (Buffer 2). The registration process takes, on average, 2 minutes per patient. Among patients who receive prescriptions, average time spent with a doctor is 5 minutes. Among those admitted to hospital, average time spent is 30 minutes. Assume the process to be stable; that is, average inflow rate equals average outflow rate.

- On average, how long does a patient spend in the E R?
- On average, how many patients are being examined by doctors?
- On average, how many patients are there in the ER?

**Problem 2**

Andy’s Android-a-Rama provides remanufactured Android phones for people who like to save money and don’t have to have the latest and greatest phones.

Andy receives about 500 phones per week and makes accept/reject decisions based on an extensive evaluation of their worthiness. These phones go through an extensive 15-point inspection where 20% of the phones are rejected. The other 80% move forward to the disassembly area where 10% are rejected after uncovering previously hidden problems. Most the phones (60%) then move to the reassembly area but 30% of the phones require additional cleaning before they can move to the reassembly area. After reassembly the phones are put through final inspection where another 10% are rejected.

Andy asked his two interns, Donna and Tom to gather information about each of the process tasks. Donna found that the initial inspection took 0.2 weeks to complete and that disassembly took another 0.1 weeks. Tom found that the work-in-process for cleaning was 36 phones, for reassembly it was 108 phones, and that there were 18 phones going through final testing.

- What is the total inventory of Androids at Andy’s?
- How long on average does an Android spend at Andy’s?

**Problem 3**

A machine at the Pacific Fruit Company fills boxes with raisins. The labeled weight of the boxes is 10 ounces. The company wants to construct an R-chart to monitor the filling process and make sure the box weights are in control. The quality control department for the company sampled five boxes every two hours for three consecutive working days. The sample observations are as follows.

Sample |
Box Weights (oz.) |
Sample |
Box Weights (oz.) |
||||||||

1 | 9.06 | 9.13 | 8.97 | 8.85 | 8.46 | 7 | 9.00 | 9.21 | 9.05 | 9.23 | 8.78 |

2 | 8.52 | 8.61 | 9.09 | 9.21 | 8.95 | 8 | 9.15 | 9.20 | 9.23 | 9.15 | 9.06 |

3 | 9.35 | 8.95 | 9.20 | 9.03 | 8.42 | 9 | 8.98 | 8.90 | 8.81 | 9.05 | 9.13 |

4 | 9.17 | 9.21 | 9.05 | 9.01 | 9.53 | 10 | 9.03 | 9.10 | 9.26 | 9.46 | 8.47 |

5 | 9.21 | 8.87 | 8.71 | 9.05 | 9.35 | 11 | 9.53 | 9.02 | 9.11 | 8.88 | 8.92 |

6 | 8.74 | 8.35 | 8.50 | 9.06 | 8.89 | 12 | 8.95 | 9.10 | 9.00 | 9.06 | 8.95 |

Construct an R-chart from these data with 3σ control limits.

**Problem 4**

The Commonwealth Banking Corporation issues a national credit card through its various bank branches in five southeastern states. The bank credit card business is highly competitive and interest rates do not vary substantially, so the company decided to attempt to retain its customers by improving customer service through a reduction in billing errors. The credit card division monitored its billing department process by taking daily samples of 200 customer bills for 30 days and checking their accuracy. The sample results are as follows:

Sample |
Number of Defectives |
Sample |
Number of Defectives |
Sample |
Number of Defectives |

1 | 7 | 11 | 9 | 21 | 13 |

2 | 12 | 12 | 6 | 22 | 9 |

3 | 9 | 13 | 3 | 23 | 10 |

4 | 6 | 14 | 2 | 24 | 12 |

5 | 5 | 15 | 8 | 25 | 15 |

6 | 8 | 16 | 10 | 26 | 14 |

7 | 10 | 17 | 12 | 27 | 16 |

8 | 11 | 18 | 14 | 28 | 12 |

9 | 14 | 19 | 16 | 29 | 15 |

10 | 10 | 20 | 15 | 30 | 14 |

Develop a ρ-chart for the billing process using 3control limits and indicate if the process is out of control.

**Problem 5**

The new-accounts officer at the Huskie Savings Bank enrolls all new customers in checking accounts. During a three-week period in August encompassing the new school year at NIU, the bank opens a lot of new accounts for students. The bank estimates that the arrival rate during this period will be Poisson distributed with an average of four customers per hour. The service time is exponentially distributed with an average of 12 minutes per customer to set up the new accounts. The bank wants to determine the average number of customers waiting to be served and the average waiting time.

**Problem 6**

** **A vending machine in Barsema Hall dispenses ice cream treats with a constant service time of 20 seconds. Students arrive at the vending machine at a mean rate of 60 per hour, Poisson distributed.

- What is the average number waiting in line?
- What is the average number in the system?
- What is the average waiting time?
- What is the average time in the system?