Case Study 1:Designing the Multi-Vari-------Printed Circuit Board Drilling.

The Green Y was excessive debris from the printed circuit boards during dilling. A Likert scale ( see Chapter 7) was used to measure the printed circuit board debris, with the quantity of debris graded from one ( no debris) to 10 (maximun debris).

The various families of variation were the identified.

It was decided to run the esperiment for just one day in the expectatition thah one day would be sufficient to capture at least 80 percent of the historic variation.

Each day had three shifts. There were 13 identical drilling machines. Eight operators per shift manned the machines. Each machine had three panels, stacked up, of printed circuit boards. Each machine had 10 drill sizes.

These three major families of variation and the seven subfamilies are shown linked together in the family tree of Figure 8-3. As the multi-vari investigation procedes, the subfamily not contibuting to debris variation can be ruled out and crossed off.

Determining Sampling Frequency and Number of Units Required.

How long sgould a multi-vari study continue? As mentioned earlier, an empiricial rule states that periodic samples should continue to be taken from the process until al least 80 percent of historic variation or the specification tolerance—whichever is less—is captured. If a lower figure, such as 50 or 60 percent, is used, the chance of finding the Red X quirckly is reduced. Multi vari studies can range from one hour or less, in total, up to four weeks or more in order to capture 80 percent or more of the historic variation. Tipically, however, multi-vari studies need not las more tan one to three days. How many samples are need? Inthe unit-to-unit family, the simple size is three to five consecutive units.

In the within-unit family, the sampling can either be 100 percent in each subfamily or a reasonable simple taken from each subfamily. The object is to keep the total number of units requires to a pracatical upper limit, while allowing enough opportunities for the Red X to be captured.

For instance, in the printed circuit board example, if we selected three as the simple size unit-to-unit variation an tokk such samples from each og 10 machines, four machine heads, eight operators, and 10 drill sizes, the total number of units requires each hour would be 3 x 10 x 4 x 8 x 10, or 9,600 units each hour. Multiply that by three hours and three shifts, and the total would be an unwieldy 86,400 units. So a decisión can be made to simple just three of the 10 machines-historically the worst, the best, and one in –between. Similarly, only three operators, three drill sizes, and two machine heads could be selected. This would reduce the total number of units per hour to 3 x 3 x 3 x 3 x 2, or 162 units. Multiply

that by three shifts and three samples per shift, and the total number of units required would be only 1,458 units. These smaller quantities in each subfamily are shown in Figure 8-3.

An alternative would be to start with just one shift. If 80 percent or more of the historic variation is captured, the second and third shifts could be deleted, reducing the total number of units to just 162.

We have deliberately chosen a case study with many families of variation and many units within each family. The absolute mínimum for a multi-vari would be three units and three time periods, or a total of nine for the whole experiment. Very rarely would the total number of units exceed 100. Table 8-A and B depicts tables for gathering data, by families of variation, with Table 8-1B being a subset of Table 8-1ª. Such a table can easily be given to an operator or inspector to log.

TABLE 8-1 . Multi-Vari Preparation Table: Printed Circuit DrillingTable 8-1 A

DAY 1

Shift # Shift 1 Shift 2 Shift 3Hour # Hour 1 Hour 2 Hour 3 Hour 1 Hour 2 Hour 3 Hour 1 Hour 2 Hour 3

Unit# 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

Variation Family

Workshop Exercise 1: Semiconductor Wafer Multi-Vari Plan.

On semiconductor wafer (containing several hundred chips or dies), thickness measuresments were made to determine which families of variation contributed the most to thickness differences in a multi-vari study.

Th Green Y es variation in thickness. Asume that the accuracy of the measuring instrument is more tan six tines the specified thickness tolerance. Desing a multi-vari plan to address the following questions from aspects of the plan listec below.

1. Identifity the major families of variation (i.e; time-to-time, unit-to-unit, within-unit) for each of the following eight aspects of the plan.

1. On each wafer, five dice were measured (north, south, east, west, and center).

2. Three wafers were sampled from eachbatch exiting the deposition process.

3. Wafers were selected from three locationsIn the batch process: left, center, and rightLocations in the chamber.

4. Two deposition chambers were used. 5. Each batch took two hours, with four

batches per shift. 6. Samples were taken from two consecutive

batches on shift 1 and shift 2. 7. Sampling was done on Monday, Tuesday,

and Wednesday. 8. Wafers were sampled over the three

Consecutive weeks.

(The answres to each workshop exercise are given immediately folowing the exercise throughout the text).

2. Draw a family tree. 3. How many wafers should the total multi-vari run include?4. What reductions could de made inthe total samples of waters required if

previous history indicates few significant variations occurred from week to week, day to day, or shift to shift.

Answers

Questions 1 1. Five dice on each wafer N, S, E, W, ans Center Whithin-unit2. Three wafers from each bath Unit-to-unit3. Three locations in each batch Whithin-unit4. Two deposition chambers Whithin-unit5. Four batches per shift Unit-to-unit6. Batches from shift 1 and 2 Time-to-time7. Sampling on Monday, Tuesday, and Time –to-time

Wednesday.8. Samples from three consecutive weeks Time-to-time

Questions 2See figure 8-4.

Question 3

Weeks Day/s per week

Shifts per day

Batches Wafers per batch

Deposition chamber

Locations per batch.

3 x 3 x 2 x 4 x 3 x 2 x 3= 1,296; numbers of readings= 1,296 x (5 dice per wafer) = 6.480

Figure 8-4. Multi-Vari Family Tree

Questions 4

If the time variations (week, day, shift) were minima,, the total number of wafers would be: 1,296/(3 x 3 x 2)= 1,296/18 =72 and the number of readings would be: 72 x 5 (i.e: 5 dice) =360.

Green Y: Wafer thickness variation

Time-to-time: personal

Unit-to-unit: cyclical Within-unit: positional

Depositions chambers (2)

Locations per batch (3)

Position in each wafers (5)

Batchers per shift (4)

Wafers per batch (3)

Weeks (3)

Shifts per day (2)

Days per week (3)