###### Fundamentals of Modern Manufacturing: Materials, Processes, and Systems

74 SOLVED PROBLEMS

Question: 40.2

## Determining the Sigma Level of a Process A final assembly plant that makes dishwashers inspects for 23 features that are considered important for overall quality. During the previous month, 9056 dishwashers were produced. During inspection, 479 defects among the 23 features were found, and ...

Summarizing the data, $N_u$ = 9056 , ...
Question: 40.1

## x and R Charts Eight samples ( m = 8) of size 4 ( n = 4) have been collected from a manufacturing process that is in statistical control, and the dimension of interest has been measured for each part. It is desired to determine the values of the center, LCL , and UCL for x and R charts. ...

The calculation of $\bar{x}$ and R va...
Question: 39.1

## Make or Buy Cost Comparison Suppose that the quoted price for a certain component from a vendor is $8.00 per unit for 1,000 units. The same part made in the home factory would cost$9.00. The cost breakdown on the make alternative is as follows: Unit material cost per unit = \$2.25 per unit ...

The vendor ’ s quote seems to favor a buy decision...
Question: 38.2

## Automated Transfer Line An automated transfer line has 20 stations and an ideal cycle time of 1.0 min. Probability of a station failure is p = 0.01 , and the average downtime when a breakdown occurs is 10 min. Determine the (a) average production rate Rp and (b) line efficiency E . ...

The frequency of breakdowns on the line is given b...
Question: 38.1

## Manual Assembly Line A manual assembly line is being planned for a product whose annual demand = 90,000 units . A continuously moving conveyor will be used with work units attached. Work content time = 55 min . The line will run 50 wk/yr , 5 shifts/wk , and 8 hr/day . Each worker will be assigned ...

(a) Hourly production rate required to meet annual...
Question: 37.3

## Control Resolution, Accuracy, and Repeatability Referring back to Example 37.1 , the mechanical inaccuracies in the open-loop positioning system can be described by a normal distribution whose standard deviation = 0.005 mm. The range of the worktable axis is 550 mm, and there are 16 bits in ...

(a) Control resolution is the greater of CR...
Question: 37.2

## NC Closed-Loop Positioning An NC worktable is driven by a closed-loop positioning system consisting of a servomotor, ball screw, and optical encoder. The screw has a pitch = 5.0 mm and is coupled to the motor shaft with a gear ratio of 4:1 (four turns of the motor for each turn of the screw). ...

(a) Rearranging Equation (37.12) to find n_...
Question: 37.1

## Open-Loop Positioning A stepper motor has 48 step angles. Its output shaft is coupled to a ball screw with a 4:1 gear reduction (four turns of the motor shaft for each turn of the screw). The screw pitch = 5.0 mm. The worktable of a positioning system is driven by the screw. The table must move ...

(a) To move a distance x = 75 mm , the ball screw ...
Question: 33.3

## Yield in Wafer Processing A silicon wafer with a diameter of 200 mm is processed over a circular area whose diameter = 190 mm. The chips to be fabricated are square with 10 mm on a side. From previous experience, the density of point defects in the surface area is 0.002 defects/cm² . Determine ...

Using Equation (33.3) , n_c =0.34(\frac{D_w...