Homework 3

Problem: Statistical Process Control

THE DATA IN THE FOLLOWING TABLES ARE AVAILABLE IN AN EXCEL SPREADSHEET (HW3-Quality Data.xlsx)

The Los Angeles Metro Rail Authority commissioned a study of travel time variation between two heavily used but adjacent subway stations (A and B) in the city. The following table shows observations in seconds of the time for travel between the two stations over a two-week period (each day 5 observations were collected).

1. Based on the above table, calculate the upper and lower control limits and the center-lines for the mean ( \[\bar{X}\] ) and range ( \[R\] ) charts. Use the "factors" given in your slides (from Session 5).
2. A few weeks after the limits and average case performance were established and agreed upon by the study team, the Authority commissions another round of observations (see below) to determine the process capability and control. Is the process governing travel times (between those two stations) in control? Why or why not?

   	Travel Time between Stations A and B (seconds)
   Day	Trip 1	Trip 2	Trip 3	Trip 4	Trip 5
   1	57.51	60.38	59.99	59.48	58.88
   2	54.42	54.28	58.93	59.45	55.01
   3	60.69	53.30	53.37	58.96	59.04
   4	60.37	58.59	56.39	53.81	60.55
   5	60.49	58.05	59.88	53.53	56.44
   6	60.84	59.26	57.48	60.93	54.46
   7	57.62	58.95	58.54	53.06	59.60
   8	57.67	58.29	57.24	59.36	53.53
   9	60.73	59.17	57.62	54.68	54.05
   10	53.16	53.58	53.69	59.73	56.90
   11	53.20	58.42	54.59	55.68	58.09
   12	58.81	58.16	56.13	56.16	60.38
   13	59.33	59.33	53.20	57.72	53.11
   14	60.78	59.24	57.14	57.02	54.74

3. Suppose the scheduling team within LA Metro specifies that the minimum and maximum travel times between the stations be 53 and 58 seconds respectively, determine whether the process is capable based on the observations in part (b). Also, was the process performance capable to begin with in part (a)?
4. If LA Metro wants to achieve a capable process for this segment (in terms of travel times between Stations A and B), what is their maximum allowable \[\overline{R}\] based on the data in part (b)?

Problem: Semiconductor Manufacturing

A semiconductor manufacturing company has a very involved process to fabricate its chips. However, the process involves repeated visits of a batch of wafers, to five major pieces of equipment in its factory.

The five process blocks visited in each pass are:

1. Electrochemical Deposition, where coats of conductive materials are applied to the wafer substrate
2. Lithography, where circuit patterns are imaged onto the coated wafers
3. Etching, where the circuitry is embossed by dissolving the coat selectively
4. Doping, or Ion implantation, where different parts of the circuit are given special characteristics
5. Furnaces, where the doped regions of the circuits are activated for circuit function

A wafer (with slots for 500 chips or die each) repeats these five major steps 12 times, with some variations each pass, to make the final product, which is sent off to a die-packaging facility.

After each of the 12 passes, an average 2% of the die (or 10 die) are rejected or marked as unusable, so note that at the end of the process a wafer yields less than the 500 chips.

The average waiting and processing times at each pass, through each of the five resources are given below (hence you can assume less than 100% utilization at each resource group):

Suppose demand for the company’s chips is at the rate of 7500 good quality die/day.

1. What is the total WIP (in wafers) in the factory? Also report the average number of wafers in queue at each of the major steps?
2. Each wafer is valued at $25000, and the holding cost is 15% of the value of the wafer per year. What is the total annual inventory holding cost for the factory?
3. Suppose with better information systems and scheduling systems, the wait times are reduced by 20% at each of the major steps. What is the savings in annual inventory holding cost for the factory?

Price: $15.74

Solution: The downloadable solution consists of 7 pages, 874 words.
Deliverable: Word Document