Patty and Rob went to balance the line. They found that this very complex board had 1350 passives, 24 simple ICs (SICs) and nine complex ICs. Currently the chipshooter (CS) is placing all the passives and nine of the SICs. 

The flexible placer (FP) is placing the nine complex ICs and 15 SICs. The placement rate for the chip shooter is 60,000/hr. for passives and 3,000/hr. for SICs. The CS cannot place CICs. The FP places complex ICs at 4,000/hr. and passives and SICs at 8,000/hr.

To balance a line, Rob and Patty start by seeing how long it will take the CS to place all of the passives and the FP to place all of the SICs and CICs.

For the CS to place all of the passives

time_CS = 1350 passives/60K passives/hr. = 0.01945 hr. = 81 sec.

The time FP takes to place all of the SICs and CICs is 

time_FP = 24 SICs/8K SICs/hr   + 9 CICs/4K CICs/hr = 0.003 hrs + 0.00225 hrs = 18.1 seconds

Since the FP is waiting for the CS, Patty and Rob should move passives to the FP. They will determine the number of passives, x, to move to the FP by equalizing the CS and FP times

t_CS = (1350-x) passives/60K passives/hr  = x passives/8K/hr + 18.1 secs/3600 sec/hour

Solving for x:

(1350-x)/60,000 = x/8,000 +18.1/3600

1350 – x = 7.5 x + 301.667

8.5 x = 1048.333

x = 123.33

In other words, 123 passives go to FP (the reason Patty and Rob round down to 123 is due to the much faster placement speed for the CS).

So Patty and Rob moved to 123 passives to the flexible placer.  Each machine’s time should be about the same now.  They performed the following calculation to check their results

t_CS = (1350-123)/60,000 = 0.02045 hrs = 73.62 sec.

t_FP  = 18.1/3600 + 123/8000 = 0.02043 hrs = 73.45 sec.

Patty and Rob then went to the line to physically move the passive feeders to the FP.  They then measured the placement time of the both the CS and FP and found them to be 73.4 and 73.5 sec., respectively, quite close to their calculations.

A meeting was held to discuss the results and the tremendous productivity improvement (81 vs 73.5 second cycle time, an (81-73.5)/81 = 9.26 % improvement.)  Everyone at AJAX was pleased (maybe not Charlie!) and felt the experience was one of great learning.

At the end of the meeting Patty and Rob had a brief chat.

“Patty, I really appreciate all of your help,” said Rob said.

“Don’t forget The Professor. I don’t think I could have handled Charlie without him,” responded Patty.

“Anyway, to show my gratitude, will you allow me to take you to dinner?” asked Rob.

Ed.: Comment on this here.