statistical forecasting for the semiconductor industry

ARA Consulting

Statistical Forecasting

August’15- © 2015 - 1

ARA Consulting

Semiconductor IndustryDemand Forecasting Using

Custom Models

Russ / Tony 5/28/2015

Russ EliasTony Alvarez

June 2015Russ EliasTony Alvarez


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ARA Consulting

If You Forecast Like Everyone Else

You’ll Get The Same Results ThatEveryone Else Gets


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ARA Consulting

Typical Demand Forecast Process

CustomerForecast

StatisticalForecast

DistributionSell-Through

DesignWins

“External”Variables

DemandCurrent/Historical

MarginOptimization

Strategy“Alignment”

DemandShaping/Promo

Demand TeamForecast

ConsensusDemand Forecast

SalesForecast

MarketingForecast

Typically a Three Stage ProcessWith Multiple Inputs


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ARA Consulting Forecasting Overview

Forecast = Trendt-1 + Seasonalityt-1 + Cyclicalt-1 + Irregularitiest-1 +Causal Factor(s) + Random (Unexplained) Variation

Trend Seasonality

Cyclical Irregular

Time

Time

Time

Causal

X1

Time


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ARA Consulting

A Challenge in Statistical Forecasting is Disaggregating

These Factors to Provide Sufficient Insight Into The Forecast

Forecasting Overview


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ARA Consulting Typical ProgressionNo Seasonality

orTrends?

TrendsBut

No Seasonality?

Trends&

Seasonality?

Trends, Seasonality&

Causal Factors?ARIMAX

Holts-Winters Smoothing(Multiplicative & Additive)

or ARIMA

Holt’s Linear Method(Double Exponential Smoothing)

Simple (Single) Exponential Smoothing(Filters Noise/Irregularities)


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ARA Consulting

Basic Capabilities Required Level 1: Limiting & Damping, Seasonal Smoothing, Demand

Filtering, Reasonability Tests

Level 2: Seasonal-with-Trend, Moving Average and Low-levelPattern Fitting

Level 3A: Trend Models For Products With Sporadic, Low-Volume Demand

Level 3B: Weighting of Historical Demand Seasonality; But“System Doesn’t Know It’s Christmas Until It Sees It Twice.”

Level 3C: Outlier Detection (Irregular Events); DeterminingWhich Elements Are Anomalous and Should Be Filtered


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ARA Consulting

“Boxed” Forecasting Software Typical Sequence

1)Product History Analyzed Using Variety (Dozens!) of Algorithms2)Automatically Selects Best Algorithm For Each Product3)Selection Based on How Well Algorithm Fits Historical Product Data4)Winning Algorithm Used to Project Future Sales

Forecasting Algorithm Will Always Produce Fcst; ButThat Fcst Won’t Always Be a Good One

“Over-Fitting” – Occurs When “Fit Noise in Data RatherThan Discovering Underlying Structure”

Pick Model That is Most Appropriate For Good Fcst;May Not Be Model That “Best” Fits Historical Data


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ARA Consulting

That’s What You Get From “Boxed”

Solutions in Typical Forecasting

Packages

What’s Missing?


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ARA Consulting

Forecast Out of the Box!

Wealth of InformationBeyond Historical Product Data


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ARA Consulting

Application of Custom Models ForSemiconductor Forecasting

Data Typically Available:Historical Product Demand & Delivery Data

Product Inventory Levels

Product Delinquency

Specific End-Market Forecasts

General Macro-Economic Trends

Customer Product Backlog


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ARA Consulting Application of DSF ForSemiconductor Forecasting

Demand Signal Forecasting (DSF)• Forward-Looking Approach to Custom Models• Utilizes Customer Backlog (VOC) as a Leading Indictor to

Augment Historical Data• But, Customer Backlog Lead Time is Typically Less That What is

Required to Initiate Product Builds – Need ‘Gap Fill’ Forecast

Demand Signal Forecasting (DSF) + Indicator Variables• Can Further Customize Model By Incorporating Indicator Variables• Example: Inventory Levels, Delinquency, End-Market Forecasts,

and Macro-Economic Trends to Further Refine & Customize Model


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ARA Consulting

DSF Application Example Background

• Customer’s Backlog is Often a Weak Forward Looking Signal Beyond OneMonth; i.e. 30 Day Backlog Usually Reliable, 60 and 90 Day BacklogUsually Subject to Significant Changes

• Manufacturing Cycle Times Range From ~90 Days (Si Start to Ship) to 15– 30 Days (Wafer Bank to Ship)

• Mis-Match Between Backlog Signal Timing & Mfg Cycle Time Can BeManaged With Inventory Staging, But at a Cost

• But, Tradeoff Inventory Risk vs. Customer Delinquency/Satisfaction

Demand Signal Forecasting Generations• Gen 1: Backlog as Leading Indicator Variable (Elias 2000 Thesis)• Gen 2: Mid-Range Backlog Imputation in a Transfer Function Based

Custom Model to Create a Better Leading Indicator (Elias and Alvarez,2014 Unpublished Work)

DSF Gen 2 Addresses Mis-Match Between Customer BacklogTiming as a Useful Leading Indicator & Mfg Cycle Time


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ARA Consulting

D = DemandC = Custom DSF2E = EWMA

DSF2 Applied to High Volume Consumer Product• One Product• One Customer• One Market Segment


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ARA Consulting DSF2 Model Results

D = DemandC = Custom DSF2e = Error


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ARA Consulting DSF Gen 2 – First Step

00.10.20.30.4

1 2 3 4 5 6 7

Weighting by AgeDSF2 Looks Backward and DevelopsOptimal ARIMA Model Based on PastDemand and Past Forecast Errors


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ARA Consulting

DSF Gen 2 – Second Step

DSF2 Then Looks Forward and Uses aTransfer Function to Blend in Backlog

0

0.2

0.4

1 2 3 4 5 6 7

Weighting by Age

Backlog

0

0.2

0.4

1 2 3 4 5 6 7

Weighting by Age

forecasts:Yt+1, Yt+2, Yt+3

(Idealized)


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ARA Consulting Forecast Benchmarks DSF2 Compared to Four Alternate Forecasting Methods:

• Exponentially Weighted Moving Averages (EWMA), with AutomatedSmoothing Coefficient Optimization

• Holt-Winters Seasonal Decomposition• Auto-Regressive Integrated Moving Average (ARIMA), with Monthly

MAPE-Optimal Model Parameterization• Sales and Operational Planning (S&OP) Consensus Forecasting

Forecast Methods Comparison Metrics:• Bias % (Cum Actual – Cum Forecast)*100/Cum Actual• Mean Absolute Percent Error (MAPE)• Normalized Inventory Dollar Maximum Delinquency and Final Period

Delinquency or Inventory Level• Forecast Performance Graphs Showing Head-to-Head Results


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ARA Consulting

Forecast Method Comparisons:Statistical Metrics

Rank Method Bias MAPE5 S&OP 58% 63%4 EWMA -1.3% 55%3 Holt-Winters -9.6% 42%2 ARIMA -7.9% 34%1 DSF Gen 2 4.3% 27%

The Custom DSF2 Model Outperformed Both the S&OPConsensus Forecast and the Conventional Statistical Models

Available in Demand Planning Software Packages

Interesting, But Where’s The Money?


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Forecast Method Comparisons:Financial Metrics

Rank Method MaxDelinquency

Period End Inventoryor (Delinquency)

Period EndMonths Inventory

5 S&OP $17M ($14M) n/a4 EWMA $9.5M $12M 6 Months3 Holt-Winters $3M $14M 7 Months2 ARIMA $2M $11M 5.5 Months1 DSF Gen 2 $3M $3M 1.5 Months

Bottom Line High ROI:Less Delinquency/Missed Sales & Higher Customer Satisfaction

Less Inventory Build/Working Capital, Reduced Inventory ExposureIn Reality Implications More Severe as Assumed that 100% of Delinquency

‘Catch-up’ Builds are Sold; Typically Some Portion Gets Cancelled Resulting inLost Sales and Therefore Even More Excess Inventory

Note: Semiconductor Industry ASP ~$1.25, For Illustrative Purposed Normalized Unit ASP Set to $1 and Normalized Units to 1M/Month


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D = DemandC = Custom DSF2E = EWMA

DSF2 vs. EWMA Forecast


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D = DemandC = Custom DSF2H = Holt-Winters

DSF2 vs. Holt-Winters Forecast


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D = DemandC = Custom DSF2A = ARIMA

DSF2 vs. ARIMA Forecast


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ARA Consulting

D = DemandC = Custom DSF2S = S&OP Fcst

DSF2 vs. S&OP Lead 3 Forecast


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ARA Consulting Inventory Observations

S&OP: Keeps Predicting Product’s Demise – Never Caught Up With DemandEWMA: Slow to Respond - Initially Delinquent Then Over-Builds

Holt-Winters: Moderate Bullwhip Effect Evident – Builds-Delinquent-BuildsARIMA: Starts Off Reasonably, Doesn’t Respond to Final Rapid Drop

DSF2: Starts Off Reasonably, By Utilizing Customer Backlog Keeps From Overbuilding

Delinquent SupplyExcess Inventory


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ARA Consulting ConclusionForecasting System Designed to Quickly Track Changes in Behavior

Can Create “Noisy” Forecasts During Periods of Relative Stability

Forecasting System Designed to Give Smooth Forecasts WillTypically Lag True Changes

If Only Looking Back, There is No Reliable Way to Forecast What WillHappen When Established Patterns or Relationships Change

It Follows That Without Forward Looking Data/Information,Quantitative Methods & Corresponding Predictions are Only as

Reliable as The Stability of Patterns Modeled in Their Past History

This is Where Demand-Signal ForecastingComes In


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ARA Consulting CaveatsKeep Modeling Approach “As Simple as Possible, But Not Simpler”

Custom Models Take Work, The DSF2 Model in This Example Took~40 Hrs Hours to Develop & 1 Hr/Mth Maintenance

While Modest Within Overall Costs Associated With an S&OP Effortand Very High ROI, the Optimal Method Depends on The Situation

DSF2 Was The Optimal Approach in This Example (And Others), ButThat Will Not Be True in All Situations

In Course of This Work, Multiple Custom Models Were Utilized ForDifferent Products; In All But One Case The Statistical Models Out-

Performed the S&OP Consensus Forecast

DSF2 Works Best When Customer Order Patterns are Subject toRapid Changes and Historical Data is Insufficient to Provide a Good

Predictor of the Future

Therefore, ….


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ARA Consulting

One Size Does NotFit All


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Optimal Forecasting Method Depends onMany Variables

Segmentation Often Used to MatchForecasting Method to Product Category

Best to Use Simplest/Lowest Cost“Acceptable” Method (Forecast Value Add)


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ARA Consulting

Conventional Segmentation

Forecasting Technique vs. Product Category(After Demand Driven Forecasting)


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Recommended Segmentation Variables:Product Lifecycle PositionVolume (Pareto Principle)Degree of Intermittency

Margin

Semiconductor Segmentation

Fast Ramp

Slow Ramp

Delayed Ramp

New Product Mid-Life Product

Top 20 Low VolumeSteady State

Fast Ramp

Slow Ramp

Controlled EOL

EOL Product

Low VolumeIntermittent

Build toOrder

(Lead Times13 – 16Weeks)

Low Margin

BTO

High Margin

Bank to Fcst& FTO

Bank to Fcst

Finish toOrder (FTO)

(Lead Times4– 6 Weeks)


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RecommendedConsiderNot Required or Inapplicable

When to Use Custom Model

Fast Ramp

Slow Ramp

Delayed Ramp



Fast Ramp

Slow Ramp

Controlled EOL

EOL Product


Build toOrder


Low Margin

BTO

High Margin

Bank to Fcst& FTO

Bank to Fcst




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ARA Consulting

Top “20”Typically 50 – 80% of a Company’s or Business Unit’s Revenue

Bank to Fcst: Custom Models Worth The Effort; Heuristics Need to Be UnderstoodFinish to Order (FTO): Theoretically No Fcst Required; Lead 1 Backlog Could be Used to

Aid Decision Making When Order “Smoothing” Required for Production Purposes


Fast Ramp

Slow Ramp

Delayed Ramp



Fast Ramp

Slow Ramp

Controlled EOL

EOL Product


Build toOrder


Low Margin

BTO

High Margin

Bank to Fcst& FTO

Bank to Fcst




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ARA Consulting

Low Volume Steady StateHigh Margin: Consider Custom Models as Necessary; Could Be Very High ROI

“Boxed” Statistical Models May Be Acceptable (Low Effort) for Bank to Fcst

Low Margin: Build to Order (BTO)


Fast Ramp

Slow Ramp

Delayed Ramp



Fast Ramp

Slow Ramp

Controlled EOL

EOL Product


Build toOrder


Low Margin

BTO

High Margin

Bank to Fcst& FTO

Bank to Fcst




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ARA Consulting

Low Volume IntermittentStatistical Models Probably Won’t Work Well or Worth the Effort

Best to Keep as BTO


Fast Ramp

Slow Ramp

Delayed Ramp



Fast Ramp

Slow Ramp

Controlled EOL

EOL Product


Build toOrder


Low Margin

FTO

High Margin

Bank to FcstFTO

Bank to Fcst




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ARA Consulting

Treat Statistical Forecasting as a “Black Box” atYour Peril

Understanding The Story Behind The Data is aRequirement For Effective Forecasting

You Do Need to Understand the Heuristics

You Don’t Need to Understand the ComputationalDetails

Customized Demand Signal ForecastingModel is Demonstrated to Provide

Significant Financial Benefit


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ARA Consulting

PDCA: Demand ForecastingPlan

(Methods & Data)

Do(Forecast Compilation)

Check(Team Review)

Act(Adjust & Learn)


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ARA Consulting

Approaches to Forecasting

Three Categories of Forecasting Models(Logility – Seven Methods That Improve Forecast Accuracy)


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ARA Consulting

ARIMA = Auto Regressive Integrated Moving Average

ARIMAX

ARIMA + eXogenous variables

Advanced Statistical Algorithm That Produces ForecastsBased Upon Weighted Nonlinear Combinations of PastRealizations, Past Errors, and Future Leading Indicators

Let’s Look at ARIMA a more in Detail ...

Custom Modeling Background


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ARA Consulting

ARIMA Looks at These Two Series:1. The past demand values (D)2. The past forecast error values (e)

Future Forecasts Are Weighted Combinations ofPast Values of These Two Series ... How It WeightsThese Values is The Trick

D = Demande = Error

norm

aliz

ed u

nits

/mon

th


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Rolling Average Weighting ARIMA Makes Future Predictions Based Upon Weighted

Combinations of Past Values Let’s Explore Weighting Options... A Rolling Average Weights Past Predictions Based Upon Equal

Weights of Past Observations:

0

0.2

0.4

1 2 3 4 5 6 7

Weighting by Ageage weight

1 0.252 0.253 0.254 0.255 06 07 0


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EWMA Weighting An Exponentially Weighted Moving Average (EWMA) Weights Past

Predictions Based Upon Weights That Follow an Exponentially DecayingValue

Weights Can Be Tuned By Selection of Decay Factor, But They MustAlways Be Monotonically Decreasing With Age Of Observation

0

0.05

0.1

0.15

0.2

1 2 3 4 5 6 7

Weighting by Ageage weight1 0.162 0.1283 0.10244 0.081925 0.0655366 0.0524297 0.041943


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ARA Consulting

ARIMA Weighting An Autoregressive Integrated Moving Average (ARIMA) Weights Past

Observations and Past Forecast Errors Based Upon Weights That AreCalculated From Maximum Likelihood Estimation (MLE) Criteria

This Permits Weights to Assume Any Values Required; Constrained Only toSum to Unity

ARIMA’s Use of MLE For Parameter Estimation Gives it TheoreticalStatistical Optimality Qualities That EWMA and Holt-Winters Do Not Have

0

0.1

0.2

0.3

0.4

1 2 3 4 5 6 7

Weighting by Ageage weight1 0.252 0.143 0.384 0.075 0.046 0.097 0.03

statistical forecasting for the semiconductor industry

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