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Monitor performance in real time: By continuously observing throughput, users can quickly respond to performance variations and adjust resources accordingly.
Diagnose problems: Quickly identifying spikes or dips in throughput helps locate bottlenecks or periods of overload in a system.
Predict future trends: By studying the evolution of flow rates over a long period of time, users can anticipate future resource needs or prepare adjustments to maintain optimal flow.
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Quartiles: Analyze the Distribution of the Performance of Your Flow
Quartiles divide the data into four equal parts, allowing us to understand how it is distributed.
They are particularly useful for getting an overview of the performance distribution in a process.
Definition of Quartiles
Q1 (First quartile): 25% of data is below this value.
Q2 (Median or second quartile): 50% of the data is lower than this value.
Q3 (Third quartile): 75% of data is below this value.
Inter-quartile ranges (IQR) can also be used to detect outliers.
The IQR will represent the lower and upper limits admissible to have a predictable flow distribution. These are the famous mustaches. Values falling outside must be considered as outliers and analyzed.
The IQR is defined as Q3−Q1.
A common rule is to consider any value outside of Q1 − 1.5 × IQR and Q3 + 1.5 × IQR as an outlier.
Example of calculating Quartiles
Sort data in ascending order: 17; 18; 19; 19; 20; 20; 21; 22; 23; 24
Calculate the First Quartile – Q1 by identifying the Cycle time of 25% of the measurements – Result: Q1 = 19
Calculate the Second Quartile, i.e. the Median, representing 50% of the measured cycle times – Result Q2 = 20
Odd List: When the number of measures is odd, take the middle value
Even List: When the number of measurements is even, as in our example, add the 2 central values and divide them by 2. The result represents the Median.
Calculate the Third Quartile – Q3, representing 75% of measurements taken – Result: Q3 = 22
Identify the Whiskers, i.e. the lowest value and the highest value measured – Result:
Calculate the inter-quartile (IQR)
IQR = Q3 – Q1 = 22 – 19 = 3
Low limit = Q1 – 1.5IQR = 19 + 1.53 = 14.5
High limit = Q3 + 1.5IQR = 22 + 15*3 = 26.5
Utility
Quartiles are often used to visualize the distribution of data and identify points where the majority of values fall. This allows you to see where the central values are (using the median) and identify gaps or outliers.
Let's take the example of a development team that delivers tickets every two weeks. By analyzing the number of tickets delivered over multiple periods, quartiles give us insight into the distribution of deliveries. This helps understand how many tickets are delivered in the bottom 25%, middle 50%, and top 25%.
UCL/LCL: Keeping your Process under Control
Control limits (UCL and LCL) are statistical thresholds used in control charts. They allow a process to be monitored to detect anomalies and determine whether it is stable.
UCL (Upper Control Limit): Upper control limit.
LCL (Lower Control Limit): Lower control limit. These limits are typically set at 3 standard deviations above and below the mean, meaning that 99.73% of the data should fall within this range in an “in control” process.Utilité
Control limits are ideal for detecting anomalies in a process. If any data falls outside of these limits, it may indicate a problem that requires investigation (such as an unexpected change in performance).
UCL/LCL : Comment les calculer ?
Les limites de contrôle (UCL/LCL) sont utilisées dans les cartes de contrôle pour surveiller un processus. Elles sont basées sur la moyenne et l’écart-type, et définissent une plage de variation normale. Elles sont calculées en appliquant la règle des 3-sigma, soit trois écarts-types au-dessus et en dessous de la moyenne.
UNPL/LNPL: Understanding Natural Variability
Unlike UCL and LCL, natural process limits (UNPL and LNPL) are not based solely on statistical calculations, but rather on a thorough understanding of the process and accepted tolerances.
UNPL (Upper Natural Process Limit): Natural upper limit.
LNPL (Lower Natural Process Limit): Natural lower limit. These limits reflect the natural range of variation of the process, defined by accepted specifications or tolerances, not by statistical deviations alone.
Utility
Natural limits are particularly useful when you have a good empirical understanding of the process or when specific tolerances must be met (for example, industry standards or customer requirements). They help avoid overreacting to small variations while ensuring that the process operates within the defined acceptable range.
Example
1 – Data collection and distribution analysis
In general, the first step is to identify whether the process follows a normal distribution or not. Natural boundaries can sometimes be calculated differently depending on the distribution of the data.
2 – Determine acceptable tolerances (or specifications)
UNPL/LNPL can be based on accepted tolerances or performance specifications defined by business needs, customer requirements or internal standards. If these tolerances exist (for example, a team expects to deliver between 15 and 25 tickets per iteration), they can directly guide the calculations.
If specifications or tolerances are already established, natural limits can be set accordingly. For example, if the team considers that by delivering less than 16 tickets or more than 26, it is deviating from its normal behavior, then:
LNPL = 16
UNPL = 26
3 – Calculate natural limits based on observed variability
If you do not have pre-established tolerances, you can calculate UNPL/LNPL based on historical process data.
3.1 – Calculate the median or an adjusted average
The median is often used instead of the mean if the process has outliers or asymmetric variations. This gives a central measurement less influenced by extreme values.
In our case, the median of tickets delivered over 10 periods is:
Median = 20
If you use the average, it is: Average(xˉ) = 20.3
3.2 – Calculate the natural range of variability
The natural variability of the process is often estimated from the interquartile range (IQR), which measures the dispersion between the lowest 25% of data and the highest 25%.
For our example, the quartiles are as follows:
Q1 (1st quartile)=19: 25% of tickets delivered are less than or equal to 19.
Q3(3rd quartile)=22: 75% of tickets delivered are less than or equal to 22.
The interquartile range (IQR) is: IQR = Q3−Q1 = 22−19 = 3
3.3 – Calculate natural limits
A common method is to multiply the IQR by a factor, often 1.5×IQR, to identify the acceptable range of variation.
Thus, the natural limits can be calculated as follows:
UNPL = Q3+1.5×IQR = 22+1.5×3 =22+4.5 = 26.5
LNPL= Q1−1.5×IQR = 19−1.5×3 = 19−4.5 = 14.5
3.4 – Adjust limits based on observations and specifications
Once the initial limits are calculated, you can adjust them based on empirical observations or process goals.
For example, if your team finds that delivering fewer than 16 tickets or more than 26 tickets is unacceptable, you could set the UNPL/LNPL respectively to those values, even if the calculations indicate a slight variation.
You see, based on this example, that the UNPL and the LNPL are very complementary to the measurement with the Quartiles by integrating the limits not to be exceeded to remain in a stable system.
Predictability Analysis
The Predictability analysis makes it possible to measure the quality of the flow and the level of confidence in its use for projections.
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