Market Sales Forecasting Related to the Semiconductor

Manufacturing Industry

Jingyi Guo

Department of Statistics, Rutgers University, New Brunswick, U.S.A.

Keywords: Multiple Regression Analysis, Semiconductor Manufacturing Industry, Market Sales Forecast.

Abstract: Based on the multiple linear regression model, this paper analyzes and compares the effects of the sales

forecasting models SMT and CIT on the relevant markets of the US semiconductor manufacturing industry.

To be specific, the data is used from the ABCtronics case to conduct a multiple regression analysis on the

status of the semiconductor manufacturing industry. According to the results of multiple regression analysis,

the proposed model of SMT interns has strong explanatory power than the model previously used at

ABCtronics. These results shed light on sales prediction in terms of different relevant variables, which can be

implemented to different industries.

INTRODUCTION

The production of semiconductor manufacturing

industry is closely correlated with the cyclical demand

pattern and the complex nature of chip design. As a

result, it undergoes an economic challenge because of

the excess capacity derived from lower demand, and

the high research and development cost along with the

increasing fixed cost of building the most advanced

facilities for wafer fabrication (G Anderson, Sweeney,

Williams, Camm, Cochran, 2011). ABCtronics, one of

the companies within the industry, recently has been

dealing with issues on improvement of products’

quality control tests, plants’ downtime, and analysis of

customer feedback.

The first problem is associated with chips’ quality

control tests. ABCtronics has been using Lot

Acceptance Testing Method (LATM) for quality

control, taking a sample of 25 IC chips from a lot of

500 without replacement. A lot will pass the check if

the sample has less than 2 defective chips. The method

has shown that on average, every 500 ICs has 2

defective chips, and entails that the probability of

producing a defective chip is 0.004. ABCtronics is

debating on whether to use Individual Chip Testing

System (LCTM) as an alternative, which is a similar

statistical method that takes a sample of 25 IC chips

from a lot of 500 but with replacement. On this basis,

they hope to narrow down the probability of defective

https://orcid.org/ 0000-0002-9782-0501

production to 0.002. With regards to high downtime

and chemical impurities, Mark, the head of QRT,

proposes that the plants’ average downtime should be

reduced to 5 hours. On the contrary, Stuart, the

president of the fabrication plant, states that they have

to replace their ion implanter because the machine and

its subsequent activities follow a uniform distribution

instead of a Gamma distribution. Moreover, he and

Mark point out that the percentage of chemical

impurities per lot follows a beta distribution.

According to the policy, it will not be used in the

fabrication process if the impurities take up more than

30%, and the process has been working fine.

Another urgent issue is their analysis on customer

relationships and prediction of sales figure. For

customer feedback, ABCtronics randomly surveyed

40 customers for their 74XX chip family. 32 out of 40

chosen customers rated their products beyond good or

satisfactory. Jim is skeptical about the results because

the overall spread of the customer feedback rating is

very high even though the mean is 56. He holds that

redesigning the survey, e.g., taking more samples of

customers might help. Furthermore, one highly

suggests that the company should use multiple linear

regression models for predicting the sales figure

(Berenson, Mark, et al, 2012). Therefore,

multicollinearity problems can be avoided when

dealing with sales figures for various demand

scenarios (Maxwell 2000). The rest part of the paper

714

Guo, J.

Market Sales Forecasting Related to the Semiconductor Manufacturing Industry.

DOI: 10.5220/0011235800003440

In Proceedings of the International Conference on Big Data Economy and Digital Management (BDEDM 2022), pages 714-719

ISBN: 978-989-758-593-7

is organized as follows. The Sec. 2 will introduce the

data origination and statistic principles, Subsequently,

the Sec. 3 will display the results of linear regression.

Afterwards, the explanation of the results as well as

the limitation of the method will be demonstrated in

Sec. 4. Eventually, a brief summary is given in Sec. 5.

2 DATA &METHOD

If a sample n is taken without replacement from a

finite (small) population of size N in which M has an

attribute (and hence N – M do not possess that

attribute), the number of sample units (Wang 2021), X

possessing that attribute follows a Hyper-geometric

distribution with parameters N, M, n. Probability mass

function (pmf) is:

𝑝



𝑥



= 𝑃



𝑋 = 𝑥





𝑀





𝑛−𝑚



– 𝑥



𝑁







This probability can also be directly obtained using

Excel Function-Statistical-Hypgeomdist. If X~B(n,

p). i.e., X has Binomial Distribution with parameters

n and p, where n = number of trials and p = probability

of one success, then, probability mass function (pmf)

of X is given by

𝑝



𝑥



= 𝑃



𝑋 = 𝑥



=𝑛



𝑝





1 − 𝑝









This probability can also be directly obtained using

Excel Function: Statistical, BINOMDIST. To work

out the solution, N = 500, n = 25, Number of

defectives in the lot = 2, i.e., proportion of defectives

in the lot, p = 0.004. Let X represents number of

defectives found in a sample of 25. Current system

(LATM), one can easily get the data. Based on Eq. (1),

X ~ Hyper-geometric with N = 500, M = 2, n = 25. P

(lot is accepted) = 0.9976. Proposed system (ICTM),

Here X ~ B (25, 0.004), P (lot is accepted) = 0.9047.

Table 1: Table Type Style.

Year

Sales

Volume

Market

demand

Price per

chip

Condition

2004 2.39 297 0.832 0

2005 3.82 332 0.844 1

2006 3.33 195 0.854 0

2007 2.49 182 1.155 1

2008 1.56 93 1.303 0

2009 0.97 98 1.265 0

2010 1.32 198 1.368 1

2011 1.42 188 1.208 0

2012 1.48 285 1.234 1

2013 1.85 264 1.282 1

The variables for regression are summarized in

Table. I. For the same lot size and defective level,

ICTM would reject the lot more often than LATM.

Thus, it is more stringent. Flaw in the current system.

For a defective level of 0.4%, an acceptance number

of 1, which out of 25 is 4%, is clearly too lenient.

Consequently, lots with higher defectives level are

likely to get accepted and passed on to the customer.

Primarily, one needs to count the expression of the

exponentially distributed, and its probability density

function is f(x)=λe

–λx

(λ＞0), when λ＜0， f(x)=0.

Besides, its distribution function is F(x)=1-e

-λx

. From

the picture “probability density function”, one can

easily know that when x=5, f(x)=4.1% (assuming that

x=time before IC chip failure (in years)). On this basis,

the expression can be derived as 0.041=λe

-5λ

. However,

at this time, one can easily solve this problem, because

the data is not integer. Thus, it should use the

distribution function to help us simplify the count

process, through two expressions, one can easily know

the number of λ instead of using complicated count

(Choi 2021). According to the data, one finds that x=5,

F(x)=0.2255 (assuming that x=time before IC chip

failure), i.e., 0.2255=1-e

-5λ

. Then put two equations

together, one gets that the λ=0.041/0.7745=0.053

(assuming that e=2.7), i.e., the f(x)=0.053e

-0.053x

and

F(x)=1-e

-0.053x

. Besides, Customer PQR systems

request that the chips will last more than 6 years, i.e.,

x≥6. Substituting x=6, the F(x)=0.27, f(x)=3.86%. In

this case, Mark is confident that ABCtronics should be

able to meet the expectation of the client Customer

PQR systems.

They have again started experimenting with their

quality control. Circuit module M (CM) has a path

where three chips from ABCtronics get connected in

a series. Before the new testing process, XYZsoft

reported that in a typical lot comprising 20 CMs they

are finding three defective items. In most of those

cases, they observed that the problem was with our

chips. Now, they have put a stricter policy in place.

They have now started to calculate the number of

nondetective before they encounter a particular

number of defectives.

According to the exponentially distribution, the

probability of chip failure keeps decreasing as the time

period increases (Lee 2017). Based on the cross

comparison with the cumulative distribution function

of failure time, the graph of the cumulative

exponential function also shows a decrease in

its slope,

meaning that the chance to fail shrinks after year 5,

which results in an up to forty-year long-lasting value

of IC chips. This is an evident reason why the mark

was so confident that PQR systems expectations can

be met. The increase in the number of complaints

regarding ABCtronics’ IC chips started when

XYZsoft was required to retrieve the whole lot of

Market Sales Forecasting Related to the Semiconductor Manufacturing Industry

715

chips for rework and recheck once there was a

defective item being detected (Sawyer, Richard,

1982).

In retrospect, the average HIGH signal output was

2.7V, which fell within the tangible range of a good

IC chip. However, when the new testing policy is

adopted, the average HIGH signal output drops to

2.3v, which suggests a problematic output. The reason

could be ABCtronic’s method of sampling random

100 chips across lots for the quality test. There is no

separate chip testing only for those defective ones to

get their values of output, i.e., ABCtronic can have a

better idea on how far these chips are away from the

standards given by XYZsoft. As a result, it is

considered that ABCtronic is over-estimating the

output of the chip. In order to improve their

estimation, they don’t need to return the defective

chips. Given N=40, Sum of the observations=2276,

mean 𝑥̅ =2276/40=56.9, the standard

derivation=18.98 with the 90% confidence interval

(51.965, 61.835), which agrees with Robert’s analysis

of customer score that they are doing either good or

satisficing with his products. Based on statistic

analysis, n=61 is minimum sample size required to

shrink the margin of error to 4, i.e., analyze the mean

customer score with 90% confidence.

3 RESULTS

Let ABCtronics’ sales volume, overall market

demand, price per chip, and economic condition be

denoted by 1, 2, and 3, respectively. ABCtronics was

using a simple linear regression model for predicting

its sales figure. As a result, the estimated linear

regression equation of sales volume on overall market

demand is 𝑌



= 0.7534 + 0.00614𝑋



. From the R

Value, it can be concluded that only 28.49% of the

variation in the sales volume is explained by this

regression model. By using all three available

variables, if one runs a multiple linear regression

model, model Y will depict the effect of X

, X

, and

on Y. The estimated multiple linear regression

equation of sales volume on overall market demand,

price per chip, and economic condition is given

by: 𝑌



= 8.8607 − 0.0052𝑋



− 5.5.54𝑋



−

1.1302𝑋



. At 5% level of significance, the p-value

for the overall market demand (X1) is more than 0.05

which is insignificant. Ignore X

, again the regression

analysis of Y and X

, X

is performed. 𝑌



6.4517 − 4.1356𝑋



+ 0.6062𝑋



, for this multiple

linear regression model, the calculated value of the

adjusted R

is 0.7996. In order to check for

multicollinearity, i.e., to see if there exists any linear

relationship between independent variables, they

have computed the variance inflation factor (VIF)

between X2 and X3 which is given by 𝑉𝐼𝐹





,















= 1.0473 . The computed value of VIF

signifies that the modified multiple linear regression

model is not suffered by the problem of

multicollinearity. The results for different models are

listed in Tables II-XIII.

Table 2: Simple linear regression model.

ANOVA df SS MS F Significance F

Regression 1.000 2.217 2.217 3.188 0.112

Residual 8.000 5.563 0.695

Total 9.000 7.780

Table 3: Simple linear regression model.

Regression Statistics

Multiple R 0.534

R Square 0.285

Adjusted R Square 0.196

Standard Error 0.834

Observations 10.000

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716

Table 4: Simple linear regression model.

Coefficients

Standard

Error

t Stat P-value

Lower

95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept 0.753 0.779 0.967 0.362 -1.044 2.551 -1.044 2.551

Makert

demand

0.006 0.003 1.786 0.112 -0.002 0.014 -0.002 0.10

Table 5: Multiple linear regression model.

Regression Statistics

Multiple R 0.953

R Square 0.908

Adjusted R Square 0.861

Standard Error 0.346

Observations 10.000

Table 6: Multiple linear regression model.

ANOVA df SS MS F

Significance

Regression 3.000 7.061 2.354 19.628 0.002

Residual 6.000 0.719 0.120

Total 9.000 7.780

Table 7: Multiple linear regression model.

Coefficients

Standard

Erro

t Stat

P-

value

Lower

95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept 8.861 1.348 6.572 0.001 5.562 12.160 5.562 12.160

Makert

deman

-0.005 0.003 -2.028 0.089 -0.012 0.001 -0.012 0.001

Price per

chi

-5.505 0.881 -6.246 0.001 -7.662 -3.349 -7.662 -3.349

Condition 1.130 0.342 3.304 0.016 0.293 1.967 0.293 1.967

Table 8: Multiple linear regression model(X2,X3 variables).

Regression Statistics

Multiple R 0.919

R Square 0.844

Adjusted R Square 0.800

Standard Error 0.416

Observations 10.000

Table 9: Multiple linear regression model(X2,X3 variables).

ANOVA df SS MS F

Significance

ression 2.000 6.568 3.284 18.960 0.001

Residual 7.000 1.212 0.173

Total 9.000 7.780

Market Sales Forecasting Related to the Semiconductor Manufacturing Industry

717

Table 10: Multiple linear regression model(X2,X3 variables).

Coefficients

Standard

Erro

t Stat

P-

value

Lower

95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept 6.452 0.766 8.422 0.000 4.640 8.263 4.640 8.263

Price per

chi

-4.136 0.680 -6.079 0.001 -5.744 -2.527 -5.744 -2.527

Condition 0.606 0.269 2.250 0.059 -0.031 1.243 -0.031 1.243

Table 11: Test multicollinearity.

Regression Statistics

Multiple R 0.213

R Square 0.045

Adjusted R Square -0.074

Standard Error 0.216

Observations 10.000

Table 12: Test multicollinearity.

ANOVA df SS MS F Significance F

Regression 1.000 0.018 0.018 0.379 0.555

Residual 8.000 0.374 0.047

Total 9.000 0.392

Table 13: Test multicollinearity.

Coefficients

Standard

Erro

t Stat

P-

value

Lower

95%

Upper

95%

Lower

95.0%

Upper

95.0%

Intercept 1.092 0.097 11.293 0.000 0.869 1.315 0.869 1.315

Condition 0.084 0.137 0.616 0.555 -0.231 0.400 -0.231 0.400

4 DISCUSSIONS

As a matter of fact, the sales prediction model

proposed by SMT interns has both advantages and

disadvantages. As for disadvantages, the multiple

linear regression is more effective and practical to

predict or estimate the dependent variable by the

optimal combination of several independent variables

(Heinrichs, Nina, et al, 2009). Moreover, it also

considers the price per chip and economic condition,

hence it may be more all-around. Regarding to

advantages, the sales prediction model proposed by

SMT interns is simpler and easier to count. More

importantly, the effect of overall market demand is

larger than other two factors, one can deduct that

actually price per chips and economics condition both

contribute to the overall market demand, when price is

high, the demand is low, on the contrary, the price is

low, demand is high. Besides, the economic condition

is good, the demand is high. Therefore, one can

conclude that the overall market demand directly

affects the sales volume. In addition, Phil’s model

divides overall market demand into 3 level, the same

as sale volumes, which clearly demonstrate the

relationship between them.

Expected sales is about 2.061, thus the expected

sales figure for ABCtronics in this year is 2.061. From

the results in Tables II-XIII, it can easily know that,

when sales volume reach 3 million, total market

demand of PCs is over 200 and between 100 and 200,

i.e., the chance is 0.1+0.1=0.2.

As the semiconductor manufacturing company,

ABCtronic faces an economic challenge for two

reasons: (i) cyclical nature of demand and (ii) the high

cost associated with research and development.

Usually, one uses the way of monitoring some key

parameters for deviations to solve

“major scrap events”

(Prescott, Patricia A 1987, Yang 2019). Moreover, the

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718

other problems are also discussed in memo part.

Additionally, it is considered that ABCtronic should

pay more attention to the XYZsoft, one of the major

clients of ABCtronics, uses IC chips on their personal

computers (PCs). Now that, the ABCtronic is the

biggest customer and also be the main source of

income, ABCtronic should avoid the problems about

chips, which cause much compliant from XYZsoft,

and let it return some chips to recheck and rework it.

From long term, it may do some damage to the stable

partnership between ABCtronic and XYZsoft.

5 CONCLUSION

In summary, the sales prediction based on

multifactorial linear regression models of ABCtronic

is carried out. According to the results, he ABCtronic

should put the quality of products at the first position.

Based on the analysis, one sees that the whole

semiconductor manufacturing industry is facing

fierce competition, and every company should face

the demand of market whenever it be good or bad, at

this time, the innovation or quality will be the most

powerful weapon. After all, it means less rework and

longer lifetime, which will save a lot of money

compared with the large investment in research and

development. Overall, these results offer a guideline

for sales prediction in terms of multi-variables.

REFERENCES

Berenson, Mark, et al. Basic business statistics: Concepts

and applications. Pearson higher education AU, 2012.

Choi, Hyun Il. "Development of Flood Damage Regression

Models by Rainfall Identification Reflecting Landscape

Features in Gangwon Province, the Republic of Korea."

Land 10.2 (2021): 123.

G Anderson, D., Sweeney, D., Williams, T., Camm, J.,

Cochran, J. 2011. Statistics for Business & Economics,

11th ed. Cengage Learning, Mason.

Heinrichs, Nina, et al. "Die Wirksamkeit ambulanter

Psychotherapie der Sozialen Angststörung in einer

universitären Ambulanz: Wird die Forschung in die

Praxis transportiert?." Zeitschrift für Klinische

Psychologie und Psychotherapie 38.3 (2009): 181-193.

Lee, In. "A study of the effect of social shopping deals on

online reviews." Industrial Management & Data

Systems (2017).

Maxwell, Scott E. "Sample size and multiple regression

analysis." Psychological methods 5.4 (2000): 434.

Prescott, Patricia A. "Multiple regression analysis with

small samples: Cautions and suggestions." Nursing

Research (1987), 36, (2): 130.

Sawyer, Richard. "Sample size and the accuracy of

predictions made from multiple regression equations."

Journal of Educational Statistics 7.2 (1982): 91-104.

Wang, Kung-Jeng, Pei-Shan Wang, and Phuc Hong

Nguyen. "A data-driven optimization model for

coagulant dosage decision in industrial wastewater

treatment." Computers & Chemical Engineering

(2021): 107383.

Yang, Qifan, et al. "Revisiting the relationship between

correlation coefficient, confidence level, and sample

size." Journal of chemical information and modeling

59.11 (2019): 4602-4612.

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