The Brennan Aircraft Division of TLN Enterprises operates a large number of computerized plotting machines. For the most part, the plotting devices are used to create line drawings of complex wing airfoils and fuselage part dimensions. The engineers operating the automated plotters are called loft lines engineers. The computerized plotters consist of a minicomputer system connected to a 4- by 5-foot flat table with a series of ink pens suspended above it. When a sheet of clear plastic or paper is properly placed on the table, the computer directs a series of horizontal and vertical pen movements until the desired figure is drawn. The plotting machines are highly reliable, with the exception of the four sophisticated ink pens that are built in. The pens constantly clog and jam in a raised or lowered position. When this occurs, the plotter is unusable. Currently, Brennan Aircraft replaces each pen as it fails. The service manager has, however, proposed replacing all four pens every time one fails. This should cut down the frequency of plotter failures. At present, it takes one hour to replace one pen. All four pens could be replaced in two hours. The total cost of a plotter being unusable is $50 per hour. Each pen costs $8. If only one pen is replaced each time a clog or jam occurs, the following breakdown data are thought to be valid:
HOURS BETWEEN PLOTTER FAILURES
IF ONE PEN IS REPLACED
DURING A REPAIR PROBABILITY
10 ....................................0.05
20 ....................................0.15
30 ....................................0.15
40 ....................................0.20
50 ....................................0.20
60 ....................................0.15
70 ....................................0.10
Based on the service manager's estimates, if all four pens are replaced each time one pen fails, the probability distribution between failures is as follows:
HOURS BETWEEN PLOTTER FAILURES
IF ALL FOUR PENS ARE REPLACED
DURING A REPAIR PROBABILITY
100 ........................0.15
110 ........................0.25
120 ........................0.35
130 ........................0.20
140 ........................0.00
(a) Simulate Brennan Aircraft's problem and determine the best policy. Should the firm replace one pen or all four pens on a plotter each time a failure occurs?
(b) Develop a second approach to solving this problem, this time without simulation. Compare the results. How does it affect Brennan's policy decision using simulation?