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Seeq Version: R21.0.43.03 but the solution is applicable to previous versions as well. The Profile Search Tool is great for specifying a profile in Signal A and then looking for occurrences of that profile throughout time. In the screenshot below I've used Profile Search to identify when the Compressor Power Area A resembles the shape of a chair. For basics about how to use the tool check out the Seeq KB article Profile Search. However, what if I want to look for that same profile on another signal? In the screenshot below, I've added a second signal, Compressor Power Area G. I'd like to identify when the "chair" profile I previously specified for Compressor Power Area A is present in Compressor Power Area G. I can do this by using the profileSearch() function in Seeq Formula. Here is how... 1. Start with the Chair in Area A condition I previously made and use Duplicate to Formula. The duplicated formula looks like (note that $cpA refers to Compressor Power Area A): profileSearch($cpA, toTime("2019-09-02T15:43:30.135Z"), toTime("2019-09-03T06:28:09.629Z"), 98, 0.5, 0.3, 0.3) 2. Modify the formula to add $cpG (Compressor Power Area G) to the start of the function. This is an optional argument in Profile Search which allows us to use the profile identified on signal $cpA and look for when it occurs on signal $cpG. For more information on the Profile Search function, check out the documentation available in the Formula Tool. $cpG.profileSearch($cpA, toTime("2019-09-02T15:43:30.135Z"), toTime("2019-09-03T06:28:09.629Z"), 98, 0.5, 0.3, 0.3) Here is a screenshot of what it looks like in the Formula Tool: 3. View the final result. In this example two "chairs" where identified in Area G.

Overview This method will provide a simple visualization of externally determined control limits or help you accurately calculate new control limits for a signal. Using these limits we will also create a boundary and find excursions for how many times and for how long a signal deviates from the limits.These created signals can be used in follow-on analysis search for periods of abnormal system behavior. In this example we will be creating average, +3 Std Deviation and -3 Standard Deviation boundaries on a Temperature Signal. Setup Signals In the Data tab, select the following: Asset → Example → Cooling Tower 1 → Area A Signal → Temperature Option 1: Manually Define Simple Control Limits From the Tools tab, navigate to the Formula tool. The Formula can be used to easily plot simple scalar values. If you already have calculated values for the upper and lower limit just enter them in the formula editor with their units as shown in the screenshot below. Formula - Simple Upper Limit 103F Formula - Simple Lower Limit 70F Option 2: Calculate The Control Limits From the Tools tab, navigate to the Formula tool. In formula we are going to define the time period over which we want to calculate our control limits as well as the math behind those limits. Step 1 - Calculate the upper limit Variables Name Item Type $Series Temperature Signal Formula $calcPeriod = capsule("2018-01-01T00:00:00-06:00","2018-05-01T00:00:00-06:00") $tempAve = $Series.average($calcPeriod) $tempStdDev = $Series.standardDeviation($calcPeriod) $tempAve + 3*$tempStdDev Description of Code $calcPeriod → This is the time range over which we are going to calculate the average and standard deviation of our signal. The start and end time of our period must be written in ISO8601 format (Year - Month - Day "T" Hour : Minutes : Seconds . Fractional Seconds -/+ Timezone) $tempAve → Intermediate variable calculating the average of the temperature signal over our calculation period $tempStdDev → Intermediate variable calculating the standard deviation of the temperature signal over our calculation period $tempAve + 3*$tempStdDev → Example control limit calculation Step 2 - Duplicate your formula to calculate the lower limits Click the info icon in the details pane next to your calculated upper limit signal. From the info panel select duplicate to create a copy of the formula. With this copy simply edit the formula to calculate the lower limit. $calcPeriod = capsule("2018-01-01T00:00:00-06:00","2018-05-01T00:00:00-06:00") $tempAve = $Series.average($calcPeriod) $tempStdDev = $Series.standardDeviation($calcPeriod) $tempAve - 3*$tempStdDev **Alternate method number three -- if you wanted $calcperiod to actually changed based on the previous month or week of operation you could use signal from condition based off a periodic condition to achieve this solution. Step 3 - Visualize Limits as a Boundary Using the Scorecard Metric to connect the process variable and upper and lower limits. Select Temperature as your item to measure. Add threshold for your upper and lower limits. Default is to add a fixed value. By clicking on the scalar icon to the left of the green "x", you can select a signal as your threshold limit. You can change the colors of the different threshold or color only the area between the threshold as shown below. Once you click execute, you will see a new scorecard metric with the shaded area between the boundaries and the original signal. Step 4 - Create Capsules when Outside the Boundary Using the Value Search tool, create a condition for when the signal is outside the limit signals. Name your new condition, select temperature as the input signal, select <> not between, click on the scalar icon to select a signal as your limit, and use the upper and lower limit signals as your upper and lower limit, respectively. Step 5 - Create a Scorecard to Quantify How Often and How Long Boundary Excursions Occur Create a Scorecard to count how many and how long and what % of total time these excursions are occurring. Create each metric using the Scorecard Metric tool and the Count, Total Duration and Percent Duration statistics. Use a Condition Based scorecard to get weekly or monthly metrics. Step 6 - Plot how these KPIs are Changing Over Time By creating a signal which plots these KPIs over time we can quantify how our process variable is changing relative to these limits. To begin, determine how often you would like to calculate the KPI per Hour/Day/Week/Month and create a condition for those time segments using the Periodic Condition tool. In the screenshot below we are creating a weekly condition with capsules every week. Using the Signal from Condition Tool count the number of Outside Simple Boundary capsules which occur within each weekly capsule. This same methodology can be used to create signals for total duration and % duration just like in the scorecard section above. For each week the tool will create a single sample. The timestamp placement and interpolation method selections will determine how those samples are placed within the week and visualized on the chart. The scorecard metrics that you created above can also be trended over time by switching from Scorecard View to Trend View. Content Verified DEC2023

Background In this Use Case, a user created a condition to identify when the compressor is running. During each Compressor Running capsule, the compressor operates in a variety of modes. The user would like a summary of the modes of operation for each capsule in the form of a new signal that reports all modes for each capsule (i.e. Transition;Stage 1;Transition;Stage 2;Transition, Stage 1;Transition). Method 1. The first step is to resample the string value to only have data points at the value changes. It's possible the signal is already sampled this way, but if it is not, use the following Formula syntax to create a "compressed" signal: $stringSignal.tocondition().setMaximumDuration(3d).transformToSamples($capsule -> sample($capsule.getStart(), $capsule.getProperty('Value')), 4d) 2. Now, you can create a signal that concatenates the string values during each capsule. This is achieved using the following Formula syntax: $compressorRunning.setmaximumduration(10d).transformToSamples($cap-> sample( $cap.getStart(), $compressedStringSignal.toGroup($cap).reduce("", ($s, $capsule) -> $s + $capsule.getvalue())), 7d).toStep()

You can use the start and end times of capsules to create new capsules with an arbitrary time before or after. This is useful when the process expert knows that there is a time period of interest before or after a capsule start or end timestamp. Refer to the example below. Here we have a series for the Area A Compressor Power shown in blue. We have created capsules shown in green for when the compressor is running in the high state, above 30kW. In this example, we want to create a capsule series that starts when the compressor exits the high stage (goes below 30kW) and then ends at exactly 2 hours later (or any other arbitrary time specified by the user). All we need to use is the following Seeq Formula: This formula creates a new set of capsules that start at the end of the “Compressor Power > 30” capsules and end exactly 2 hours later. The functions afterStart(), beforeStart() and beforeEnd() can be used similarly. For example, to create a set of capsules that capture the two hours prior to our “compressor high” condition, we can simply modify the formula above by changing “afterEnd” to “beforeStart.”

Background In this Use Case, a condition was created to identify when a compressor is running. Let's say I'd like to extend each capsule in this condition so that instead of ending when the compressor turns off, it ends when the next compressor running capsule starts. Method The method used depends on the Seeq version. Seeq R21.0.42 and Later Version R21.0.42 introduced the .growEnd() operator; this operator grows capsules in in a condition by extending the end until the start of the next capsule. Earlier Versions (Before R21.0.42) 1. First, create a condition that is the inverse of the Compressor Running condition. This can be achieved using the .inverse() function in Formula 2. Next, extend each Compressor Running capsule so that they overlap with the Downtime capsules. This is achieved using the .move() function in Formula. 3. Finally, combine the Downtime and Compressor Running - Extended conditions use the union logic in the Composite Condition tool.

Goal is to create a string signal that shows the different operation modes in a device at each time. Step 1. Create the sample modes using Values Search Tool, Advanced Search: Value Search Tool, Advanced Search Step 2. Create a continuous condition called “Mode” comprising all three (startup, steady state, shutdown), and assign a property to each capsule to identify the mode. for more information please look at the following link: Set property to a capsule Formula for creating the mode with property condition: $ShutDown = $Shutdown.setProperty("Mode", "ShutDown") $StartUp = $Startup.setProperty("Mode", "StartUp") $steady = $Steady.setProperty("Mode", "Steady") combineWIth($StartUp, $steady, $ShutDown) Step 3. Use the Formula Tool to create a string signal using the "mode with property" condition and shows the mode of the input signal at each time. Here is the formula for creating the string signal (Mode is the Mode with property condition in here) : $inputsignal.transformToSamples( $capsule -> sample($capsule.getStart(), $capsule.getproperty('Mode')), 10d)

FAQ: I've got a signal for which the average and standard deviation are believed to be drifting over time. When I view the average and standard deviation in calendar time, it isn't helpful because they are highly dependent upon the production grade that I am running. Is there a better way that I could be viewing my data to get a sense of the drift of the average and standard deviation by production grade over time? Solution 1: Histogram 1. Add your signal of interest and your production grade code signal to the display. 2. Create a condition for all production grades using formula: $gradeCode.toCondition() 3. Use the Histogram tool to calculate the average reactor temperature during each grade campaign and display them aggregated over production grade, and time. The same methods from step 3 can be applied to get a second histogram of the distribution of the standard deviation of the signal of interest by grade over time. Solution 2: Chain View 1. Add your signal of interest and your operating state signal to the display. 2. Use Formula to create a condition for all operating states: $stateSignal.toCondition() 3. Use the Signal from Condition tool to calculate the average temperature over the all operating states condition. 4. Use the Signal from Condition tool to calculate the standard deviation of temperature over the all operating states condition. 5. Use Formula to calculate two new signals for “Avg + 2 SD” and “Avg – 2 SD”. 6. Filter your all operating states condition for only the state that you are interested in viewing. In this example we want to view only the capsules during which the compressor is in stage 2, for which the syntax is: $AllOperatingStates.removeLongerThan(7d).removeShorterThan(4h).filter($capsule -> $capsule.getProperty('Value').isEqualTo('STAGE 2')) This formula is taking our condition for all operating states, keeping only capsules that are between 4h and 7d in length, then filtering those capsules to include only those for which the value is equal to stage 2. 7. Swap to chain view and view a longer time range.

Use case: A piece of equipment has a start-up sequence in which it goes through different discrete states sequentially before completing the sequence and reaching steady state. When the equipment is off, the state is 0. When the equipment enters the start-up sequence it cycles through states 1-6 in the pattern "1-2-3-4-5-6". A successful start-up sequence will have all 6 states in the pattern "1-2-3-4-5-6." If a disruption occurs at any point in the start-up sequence the state number will read as state 7, thus a failed start-up sequence could have the pattern "1-7", "1-2-7", "1-2-3-7", etc. This use case describes methods to identify only the successful start-up sequences. Approach 1: If the signal for the state is numeric (e.g. with discrete numeric values of 0-7) 1. Create a new signal that is the running delta of the STATENUMBER signal. Use Seeq Formula and syntax: $statenumbersignal.runningDelta() 2. Create a new condition for all start-up sequences using value search for when the runningDelta signal just created is greater than or equal to zero. 3. Calculate the delta in your STATENUMBER signal over each start-up sequence. This value should always be equal to 6 or 7 as the sequence will either complete successfully (go to 6) or fail and end with a value of 7. Use the signal from condition tool to calculate this. 4. Create a new condition for when this delta in the STATENUMBER signal just created is equal to 6. This must be done in Seeq formula (there is a known issue in using value search for this operation) with the following syntax: $deltaInSTATENUMBERsignal.valueSearch(isEqualTo(6)) Approach 2: If the signal for the state is a string that is easily convertible to a numeric signal. This example is a string with discrete values "STAGE0", "STAGE6", etc. 1. In Seeq formula, use the replace() function with the following syntax: $StringSignalForStateNumber.replace('STATE','') 2. In a new Seeq Formula Window apply the toNumber() function to the signal created in step 1 with the following syntax: $SignalFromStep1.toNumber() - this will create a numeric signal with discrete values of 0-7. Approach 3: If the signal for the state is a string value, not easily converted to a numeric signal or if you wish to proceed using the string signal. 1. Use Value Search to identify STATE6 2. Use Value Search to identify STATE7 3. Use Composite Condition (union operator) to create a combined condition "finalStateinSequence" for the final state in sequence, either STATE6 or STATE7. 4. Use formula to create a condition for all start-up sequences (successful and failed). Syntax: $FinalStateInSequence.inverse().move(0,1h) This formula code is identifying all of the time when the final state in sequence condition is not true and extending those capsules by a short amount of time so that the final state value is contained within the "all start-up sequences" capsules. 5. Use Signal from Condition to identify the ending STATENUMBER value for each of the start-up sequences. 6. Identify your successful start-up sequences by doing a valueSearch in Formula to identify when the ending STATENUMBER is equal to STATE7. Formula syntax: $endingSTATENUMBERsignal.valueSearch(isEqualTo("STATE7")) Content Verified DEC2023

Use Case Background Commonly, engineers are interested in calculating limits on a signal based upon the average and standard deviation. Additionally, there may be different modes of operation during which the performance - and limits - is different. This post describes how to develop mode based boundaries for a process signal to identify deviations from the normal or expected behavior. Mode Conditions In this example, I am interested in calculating boundaries on a Compressor Power signal based upon the mode of operation in a Compressor Stage Signal. (Note: These signals are from Example>Cooling Tower 1> Area A of the Example data shipped with each Seeq installation.) The first step is to identify the 3 stages of operation (Off, Running 1 Compressor, Running 2 Compressors) by performing a Value Search on the Compressor Stage signal: Average Compressor Power using Formula Next, I can use the Formula tool to calculate an Average Compressor Power signal, using the following variables and syntax: Variables Name Item Type $Series Compressor Power Signal $High Compressor High Condition $Low Compressor Low Condition $Off Compressor Off Condition Formula // Identify a reference capsule over which the statistic is calculated. You can think of this as the golden batch period or the period in time that we know that the system was operating properly. $refPeriod = capsule("2016-04-01T00:00:00Z","2016-05-01T00:00:00Z") //Cut the single continuous time series signal (Compressor Power) into sections which correspond to the different modes of operation. This gives us three intermediate time series signals which only contain data for the three distinct modes of operation. $highSeries = $series.within($high) $lowSeries = $series.within($low) $offSeries = $series.within($off) // Create three intermediate time series signals, one for each mode of operation. Find the average value of the time series signal during the reference time period for each mode of operation, and then turn that scalar into a time series signal which only exists in the appropriate mode of operation $highAve = $highSeries.average($refPeriod).tosignal().within($high) $lowAve = $lowSeries.average($refPeriod).tosignal().within($low) $offAve = $offSeries.average($refPeriod).tosignal().within($off) // Splice together the three time series signals into a single signal and step interpolate the $finalSeries $finalSeries = $highAve.splice($lowAve,$low,false).splice($offAve,$off,false).toStep() return $finalSeries Boundaries Using Formula To start, let's calculate the upper boundary as the average + 3 std dev. I can use the Formula tool to calculate this upper boundary using the following variables and syntax. Variables Name Item Type $Series Compressor Power Signal $High Compressor High Condition $Low Compressor Low Condition $Off Compressor Off Condition Formula $refPeriod = capsule("2016-04-01T00:00:00Z","2016-05-01T00:00:00Z") $highSeries = $series.within($high) $lowSeries = $series.within($low) $offSeries = $series.within($off) $highAve = $highSeries.average($refPeriod).tosignal().within($high) $highStdDev = $highSeries.standarddeviation($refPeriod).tosignal().within($high) $highBoundary = $highAve + $highStdDev*3 $lowAve = $lowSeries.average($refPeriod).tosignal().within($low) $lowStdDev = $lowSeries.standarddeviation($refPeriod).tosignal().within($low) $lowBoundary = $lowAve + $lowStdDev*3 $offAve = $offSeries.average($refPeriod).tosignal().within($off) $offStdDev = $offSeries.standarddeviation($refPeriod).tosignal().within($off) $offBoundary = $offAve + $offStdDev*3 $finalSeries = $highBoundary.splice($lowBoundary,$low,false).splice($offBoundary,$off,false).toStep() return $finalSeries Similarly, I can calculate the lower boundary as average - 3 std dev using the following variables and Formula syntax. Variables Name Item Type $Series Compressor Power Signal $High Compressor High Condition $Low Compressor Low Condition $Off Compressor Off Condition Formula $refPeriod = capsule("2016-04-01T00:00:00Z","2016-05-01T00:00:00Z") $highSeries = $series.within($high) $lowSeries = $series.within($low) $offSeries = $series.within($off) $highAve = $highSeries.average($refPeriod).tosignal().within($high) $highStdDev = $highSeries.standarddeviation($refPeriod).tosignal().within($high) $highBoundary = $highAve - $highStdDev*3 $lowAve = $lowSeries.average($refPeriod).tosignal().within($low) $lowStdDev = $lowSeries.standarddeviation($refPeriod).tosignal().within($low) $lowBoundary = $lowAve - $lowStdDev*3 $offAve = $offSeries.average($refPeriod).tosignal().within($off) $offStdDev = $offSeries.standarddeviation($refPeriod).tosignal().within($off) $offBoundary = $offAve - $offStdDev*3 $finalSeries = $highBoundary.splice($lowBoundary,$low,false).splice($offBoundary,$off,false).toStep() return $finalSeries Final Results Executing these 3 formulas results in 3 new time series signals: Average Compressor Power, Compressor Power +3sd and Compressor Power -3sd. The Customize menu in the Details Pane can be used to adjust how these signals are visualized on the screen: Content Verified DEC2023

Issues with different devices can lead to shutdowns and failures. In this example we want to monitor the duration of each operation mode of an input signal. This example can be used to monitor all the conditions that can lead to inefficient device performance. In order to monitor all operation modes we need to, 1. Create all the modes using Value Search Tool. a. StartUp (input < 75) b. ShutDown (input > 95) c. SteadyState (75 < input < 95) 2. Create a continuous condition called “Mode” comprising all three (startup, steady state, shutdown), and assign a property to each capsule to identify the mode. for more information please look at the following post: A Guide to Working with Capsule Properties $ShutDown = $Shutdown.setProperty("Mode", "ShutDown") $StartUp = $Start.setProperty("Mode", "StartUp") $steady = $Steady.setProperty("Mode", "Steady") combineWIth($StartUp, $steady, $ShutDown) 3. Finally, calculate the total time per mode using Histogram Tool. For more information on Histogram Tool please see the following link: Histogram Tool Content Verified DEC2023