27/10/2017 Department of Veterinary and Animal Sciences Department - PDF document

27/10/2017 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences Outline Filtering techniques applied for monitoring of daily gain in slaughter pigs: Monitoring methods – revisited • Introduction • Basic monitoring • Shewart control charts Anders Ringgaard Kristensen • DLM and the Kalman filter • Simple case • Seasonality • Online monitoring • Used as input to decision support Slide 2 Average daily gain, slaughter pigs ”E-kontrol”, slaughter pigs Quarterly calculated production results Presented as a table A result for each of the most recent quarters and aggregated We have: Sometimes comparison with • 4 quarterly results expected (target) values • 1 annual result Offered by two companies: • 1 target value • AgroSoft A/S How do we interpret the results? • Cloudfarms One of the most important key Question 1: How is the figure calculated? figures: Average daily gain Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences How is the figure calculated? First finding: Observation error The basic principles are: • Total (live) weight of pigs delivered: xxxx * All measurements are encumbered with uncertainty (error), • Total weight of piglets inserted: −xxxx ** but it is most prevalent for the valuation weights. • Valuation weight at end of the quarter: +xxxx *** • Valuation weight at beginning of the quarter: −xxxx *** We define a (very simple) model: • Total gain during the quarter yyyy κ = τ + e o , where: Daily gain = (Total gain)/(Days in feed) • κ is the calculated daily gain (as it appears in the report) Registration sources? τ is the true daily gain (which we wish to estimate) • • e o is the observation error which we assume is normally distributed • * Slaughter house – rather precise N(0, σ o 2 ) • ** Scale – very precise The structure of the model (qualitative knowledge) is the • *** ??? – anything from very precise to very uncertain equation The parameters (quantitative knowledge) is the value of σ o (the standard deviation of the observation error). It depends on the observation method. Slide 5 Slide 6 1

27/10/2017 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences Observation error Second finding: Randomness The true daily gains τ vary at random. κ = τ + e o , e o ~ N(0, σ o 2 ) Even if we produce under exactly the same conditions in two τ successive quarters the results will differ. We shall denote the What we measure is κ phenomenon as the “sample error”. What we wish to know is τ We have, τ = θ + e s , where The difference between • e s is the sample error expressing random variation. We assume e s » N(0, σ s 2 ) the two variables is • θ is the underlying permanent (and true) value undesired noise This supplementary qualitative knowledge should be reflected κ We wish to filter the noise in the stucture of the model: κ = τ + e o = θ + e s + e o away, i.e. we wish to The parameters of the model are now: σ s og σ o estimate τ from κ Slide 7 Slide 8 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences Sample error and measurement error The model in practice: Preconditions The model is necessary for any meaningful interpretation of calculated production results. θ What we measure is κ The standard deviation on the sample error, σ s , depends on the natural What we wish to know is θ individual variation between pigs in a herd and the herd size. The difference between the The standard deviation of the observation error, σ o , depends on the measurement method of valuation weights. two variables is undesired For the interpretation of the calculated results, it is the total uncertainty, σ , noise: that matters ( σ 2 = σ s 2 + σ ο τ 2 ) • Sample noise Competent guesses of the value of σ using different observation methods (1250 pigs): • Observation noise • Weighing of all pigs: σ = 3 g We wish to filter the noise Stratified sample: σ = 7 g • away, i.e. we wish to estimate • Random sample: σ = 20 g κ θ from κ • Visual assessment: σ = 29 g Slide 9 Slide 10 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences The model in practice: Interpretation Different observation methods Calculated daily gain in a herd was 750 g, whereas θ the expected target value was 775 g. Shall we be worried? It depends on the observation method! A lower control limit (LCL) is the target minus 2 τ times the standard deviation, i.e. 775 – 2 σ Using each of the 4 observation methods, we obtain the following LCLs: • Weighing of all pigs: 775 g – 2 x 3 g = 769 • Stratified sample: 775 g – 2 x 7 g = 761 κ κ κ κ • Random sample: 775 g – 2 x 20 g = 735 • Visual assessment: 775 g – 2 x 29 g = 717 σ = 3 g σ = 7 g σ = 20 g σ = 29 g Slide 12 Slide 11 2

27/10/2017 Department of Veterinary and Animal Sciences Third finding: Dynamics, time Modeling dynamics Daily gain, slaughter pigs We extend our model to include time. At time n we model the calculated result as follows: 950 κ n = τ sn + e on = θ + e sn + e on 900 850 Only change from before is that we know we have a new result each 800 quarter. g 750 We can calculate control limits for each quarter and plot everything in a 700 diagram: A Shewart Control Chart … 650 600 θ 2. quarter 97 3. quarter 97 4. quarter 97 1. quarter 98 2. quarter 98 3. quarter 98 4. quarter 98 1. quarter 99 2. quarter 99 3. quarter 99 4. quarter 99 1. quarter 00 2. quarter 00 3. quarter 00 4. quarter 00 1. quarter 01 2. quarter 01 τ 4 … τ 1 τ 2 τ 3 Quarter Daily gain in a herd over 4 years. Is this good or bad? κ 1 κ 2 κ 3 κ 4 Slide 14 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences A simple Shewart control chart: Weighing all pigs Simple Shewart control chart: Visual assessment Daily gain, slaughter pigs Daily gain, slaughter pigs 950 950 900 900 850 850 800 800 g g 750 750 700 700 650 650 600 600 2. kvartal 97 3. kvartal 97 4. kvartal 97 1. kvartal 98 2. kvartal 98 3. kvartal 98 4. kvartal 98 1. kvartal 99 2. kvartal 99 3. kvartal 99 4. kvartal 99 1. kvartal 00 2. kvartal 00 3. kvartal 00 4. kvartal 00 1. kvartal 01 2. kvartal 01 2. kvartal 97 3. kvartal 97 4. kvartal 97 1. kvartal 98 2. kvartal 98 3. kvartal 98 4. kvartal 98 1. kvartal 99 2. kvartal 99 3. kvartal 99 4. kvartal 99 1. kvartal 00 2. kvartal 00 3. kvartal 00 4. kvartal 00 1. kvartal 01 2. kvartal 01 Period Period Periode Periode Observed gain Expected Observed gain Expected Upper control limit Lower control limit Upper control limit Lower control limit Slide 15 Slide 16 Department of Veterinary and Animal Sciences Department of Veterinary and Animal Sciences Interpretation: Conclusion More findings: κ n = θ + e sn + e on Something is wrong! The true underlying daily gain in the herd, θ , may Possible explanations: change over time: • The pig farmer has serious problems with fluctuating • Trend daily gains. • Seasonal variation • Something is wrong with the model: The sample errors e sn may be auto correlated • Structure – our qualitative knowledge • Temporary influences • Parameters – the quantitative knowledge (standard The observation error e on is obviously auto deviations). correlated: • Valuation weight at the end of Quarter n is the same as the valuation weight at the start of Quarter n +1 Slide 17 Slide 18 3