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Cycle Time Mathematics Presented at KLRAT 2013 Troy.magennis@focusedobjective.com

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Conclusions Forecasting using cycle time is proving useful Cycle time follows a Weibull/Lognormal shape – We can estimate the actual distribution with just a minimum and a maximum guess (initially) Controlling the shape of the distribution (narrowing) improves predictability Proposing a way of identifying what risks and delays will have the greatest impact… Commercial in confidence 2

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Prediction Intervals

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Actual Maximum Actual Minimum 1 3 2 Q. What is the chance of the 4 th sample being between the range seen after the first three samples? (no duplicates, uniform distribution, picked at random) 4

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Actual Maximum Actual Minimum 1 3 2 4 Highest sample Lowest sample Q. What is the chance of the 4 th sample being between the range seen after the first three samples? (no duplicates, uniform distribution, picked at random) ? ? ? ?

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Actual Maximum Actual Minimum 1 3 2 4 25% chance higher than highest seen 25% lower than highest and higher than second highest 25% higher than lowest and lower than second lowest 25% lower than lowest seen Highest sample Lowest sample Q. What is the chance of the 4 th sample being between the range seen after the first three samples? (no duplicates, uniform distribution, picked at random) A. 50% % = (1 - (1 / n – 1)) * 100

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Actual Maximum Actual Minimum 1 3 2 12 5% chance higher than highest seen 5% lower than lowest seen Highest sample Lowest sample Q. What is the chance of the 12 th sample being between the range seen after the first three samples? (no duplicates, uniform distribution, picked at random) ? ? A. 90% % = (1 - (1 / n – 1)) * 100 4 5 6 7 8 9 10 11

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# Prior SamplesPrediction Next Sample Within Prior Sample Range 350% 467% 575% 680% 783% 886% 988% 1089% 1190% 1291% 1392% 1593% 1794% 2095% Halved the risk with 3 samples

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Monte Carlo

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Commercial in confidence 10 If a measurement changes over time or is different each time you measure it, it is a DISTRIBUTION Cant apply normal mathematical operators….

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Commercial in confidence 11 Cycle Time Forecasting 1. Easy to Capture Metric 3. Follows Known Distribution Pattern 2. Forecasting using Historical Data (even a little) 4. Forecast at Project or Feature or Story Level

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Sum Random Numbers 25 11 29 43 34 26 31 45 22 27 31 43 65 45 8 7 34 73 54 48 19 12 24 27 21 3 9 20 23 29 187410295 Sum: ….. Historical Story Lead Time Trend Days To Complete Basic Cycle Time Forecast Monte Carlo Process 1. Gather historical story lead-times 2. Build a set of random numbers based on pattern 3. Sum a random number for each remaining story to build a single outcome 4. Repeat many times to find the likelihood (odds) to build a pattern of likelihood outcomes

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How I Quantify Lead Time Reduction Lead Time# Stories / YearThroughput Benefit Current 60% 10% Decrease 717% More 20% Decrease 833% More When no ROI is easily discerned (maintenance teams?) Even a small decrease in Cycle Time has a increased impact on throughput over a year..

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Cycle Time Forecast DateForecast Cost Cash flow to EOY14 (cost saving + revenue) Benefit Current15-Jul-2014$1,000,000$0 + $60,000 = $60,0000% 10% Decrease 27-May-2014$912,500 $87,500 + $90,000 = $177,500 296% Better 20% Decrease 04-Apr-2014$820,000 $120,000 + $145,000 = $265,000 442% Better MonthRevenue April$30,000 May$25,000 June$20,000 July$20,000 Aug-Dec$10,000 Revenue Estimates for product: How I Quantify Cycle Time Reduction Even a small decrease in Cycle Time can have huge a benefit on cash flow over time. This example shows the cost of missing a seasonal uptick in summer sales (revenue estimates shown to the left). Cost per work day is calculated at $2,500 day.

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Shape and Impact of Cycle-Time & Scope

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Commercial in confidence 16 Note: Histogram from actual data

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Commercial in confidence 17

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Likelihood… Commercial in confidence 18

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Total Story Lead Time 30 days Story / Feature Inception 5 Days Waiting in Backlog 25 days System Regression Testing & Staging 5 Days Waiting for Release Window 5 Days Active Development 30 days Pre Work 30 days Post Work 10 days

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Binary Permutations Commercial in confidence 20 Risk 1 Risk 2 Risk 3 Risk 4 Risk 5 Risk 6 Risk 7 Risk 8 Risk 9 Risk 10 No Yes No YesNo Yes No YesNo ……………… Yes

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Why Weibull Now for some Math – I know, Im excited too! Simple Model All units of work between 1 and 3 days A unit of work can be a task, story, feature, project Base Scope of 50 units of work – Always Normal 5 Delays / Risks, each with – 25% Likelihood of occurring – 10 units of work (same as 20% scope increase each)

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Normal, or it will be after a few thousand more simulations

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Base + 1 Delay

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Base + 2 Delays

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Base + 3 Delays

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Base + 4 Delays

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Base + 5 Delays

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Commercial in confidence 28 Scale – How Wide in Range. Related to the Upper Bound. *Rough* Guess: (High – Low) / 4 Shape – How Fat the distribution. 1.5 is a good starting point. Location – The Lower Bound KEY POINT: WITH JUST MIN AND MAX THE CURVE CAN BE INFERRED

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Changing Cycle Time Shape

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Commercial in confidence 31 Teams following this curve WILL be able to predict more predictability because forecast range will be tighter When forecasting, the wider the curve, the MORE higher value numbers will occur

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Binary Permutations Commercial in confidence 32 Risk 1 Risk 2 Risk 3 Risk 4 Risk 5 Risk 6 Risk 7 Risk 8 Risk 9 Risk 10 No Yes No YesNo Yes No YesNo ……………… Yes EVERY RISK OR DELAY YOU CAN REMOVE REDUCE COMBINATIONS BY 2 n

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Order of Priority for Improvement Prioritized list of blockers and delay states Balanced to include most frequent & biggest delay Order Risks and Delays by weighted impact Impact = Frequency Risk or Delay Type x Duration This will remove the most combinations of delay and shrink the area of our distribution giving biggest benefit of predictability Commercial in confidence 33

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Mining Cycle Time Data

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Mining / Testing Cycle Time Data Commercial in confidence 35 Capture Data Scatter Plot Histogra m Fit Shape

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Cycle Time Capture Practices Clearly understand from where and to where Capture begin and end date; compute the number of days in-between Does cycle time include defect fixing? Are there multiple types of work in the same cycle time data – Stories – Defects – Classes of Service Commercial in confidence 36

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Things that go wrong… Zero values Repetitive (erroneous) values Batching of updates Include/exclude weekends Project team A staff raided impacting their cycle time (Team A up, team Bs down) Work complexity changes Team skill changes Commercial in confidence 37

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Commercial in confidence 38 Many low values. Often zero or values below what makes sense. Check the most frequent low values. Multiple modes. In this case two overlapping Weibulls. Often due to multiple classes of service, or most often - defects versus stories.

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Commercial in confidence 39 Scale – How Wide in Range. Related to the Upper Bound Shape – How Fat the distribution. Location – The Lower Bound

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Estimating Distributions using Historical Data

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What Distribution To Use... No Data at All, or Less than < 11 Samples (why 11?) (why 11?) – Uniform Range with Boundaries Guessed (safest) – Weibull Range with Boundaries Guessed (likely) 11 to 50 Samples – Uniform Range with Boundaries at 5 th and 95 th CI – Weibull Range with Boundaries at 5 th and 95 th CI – Bootstapping (Random Sampling with Replacement) More than 100 Samples – Use historical data at random without replacement – Curve Fitting Commercial in confidence 41

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Sampling at Random Strategies If you pick what samples to use, you bias the prediction… Strategies for proper random sampling – – Use something you know is random (dice, darts) – Pick two groups using your chosen technique and compute your prediction separately and compare – Dont pre-filter to remove outliers – Dont sort the data, in fact randomize more if possible Commercial in confidence 42

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Commercial in confidence 43 Concurrent WIP Sample : Find the smallest and the biggest or take at least 11 samples to be 90% sure of range Estimating Concurrent Effort from Cumulative Flow Chart

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20%40% 60%80%

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Commercial in confidence 45 Scope Creep Over Time Look at the rate new scope is added over time

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