Question

Rick? Wing, salesperson for Wave Soldering? Systems, Inc.? (WSSI), has provided you with a proposal for improving the temperature control on your present machine. The machine uses a hot-air knife to cleanly remove excess solder from printed circuit? boards; this is a great concept, but the hot-air temperature control lacks reliability. According to Wing, engineers at WSSI have improved the reliability of the critical temperature controls. The new system still has the four sensitive integrated circuits controlling the? temperature, but the new machine has a backup for each. The four integrated circuits have reliabilities of 0.87, 0.89, 0.91, and 0.93. The four backup circuits all have a reliability of 0.87.

A)The overall reliability of the new temperature controller? =

B) if you pay a premium, Wing says he can improve all four of the backup units to 0.91The overall reliability of the new temperature controller with the upgraded backup unit? = (enter your response as a percentage rounded to two decimal? places).

Answer 1

As the Backups are placed parallel to the Original circuits, the Reliability of one integrated circuit with its backup is given by -

R_o + R_b*(1 - R_o). In this way, there are four integrated circuits in series.

(A)

Overall reliability
= (0.87 + 0.87*(1 - 0.87)) x (0.89 + 0.87*(1 - 0.89)) x (0.91 + 0.87*(1 - 0.91)) x (0.93 + 0.87*(1 - 0.93))
= 0.9490 i.e. 94.90%

(B)

Overall reliability
= (0.87 + 0.91*(1 - 0.87)) x (0.89 + 0.91*(1 - 0.89)) x (0.91 + 0.91*(1 - 0.91)) x (0.93 + 0.91*(1 - 0.93))
= 0.9645 i.e 96.45%