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Design masterclass 5 Statistics


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as simple as designing for either 100% occupancy or 50% occupancy. Simply generating a random pattern of occupancy


(see Figure 1) shows us that it is unlikely that the office will be fully occupied at any time. However, this simple approach does not give us a suitable basis for determining a design level of occupancy, as it is still easy to argue that random chance can give rise to maximum occupancy. So it can, but with what probability? If we plot the occupancy data as a histogram, we can


fit a Gaussian Distribution curve to it by calculating the mean and standard deviation. It is then helpful to know that, to a close approximation, events more than three standard deviations from the mean occur with a probability of less than 0.15%. So we can now examine the data again and determine


that the occupancy is unlikely to exceed eight people for more than about 0.5% of the time, or eight working hours per year. Conversely, this means that designing the air conditioning for the very few occasions on which the occupancy will exceed eight people will increase the plant size and cost by 25% (assuming the plant size is directly proportional to the occupancy). Understanding these sorts of diversity factors is


Figure 1: Generating a random pattern of occupancies for a notional office of 10 estate agents reveals that 100% occupancy is an unlikely occurrence. In order to determine suitable design occupancy we need to delve further into the statistics. The Gaussian (or Normal) Distribution curve represents the frequency of occurrence of events randomly distributed about a mean (_). The standard deviation (_) is a measure of the spread of the data. Knowing the rule of thumb, that 95% of the data fall within 2_ of the mean and that 99.7% fall within 3_, allows us to quickly establish suitable design parameters and understand the significance of events occurring outside those parameters.


critical in determining the appropriate conditions to which we should be designing. Consider, for example, that this simple diversity applies not only to the fresh air volume and therefore external air gain, but also to the occupancy gain and the casual gains and electrical consumption from computers and task lights. If we don’t get our diversity factors right then the consequences can quickly snowball. These days, of course, we would probably design


the plant for 100% occupancy and then justify the decision by adding variable volume control with some form of occupancy sensor. This will reduce some of the operating inefficiency but we are still stuck with a system which is essentially over-sized for the use to which it is typically put. Now let’s apply a similar statistical method to gain


an understanding of external design temperatures: The Met Office weather record for London shows extremes of –10C and 38C with a mean of 10.5C and a standard deviation of about 6C. If we assume a Gaussian distribution for the temperatures (which is a good approximation), and fit these parameters we can immediately identify some of the key points that have historically been used to define London design temperatures (Figure 2). Temperatures more than three standard deviations


Figure 2: When we apply statistical analysis to weather data, such as the widely available monthly averages and extremes, like this for London, we can begin to appreciate the significance or otherwise of occasional extreme events. To design for these events would result in severe over-sizing of plant and equipment compared to that designed for a more rational balance of cost and risk.


52 CIBSE Journal February 2011


from the mean are likely to be exceeded less than 0.15% of the time, or just 13 hours in an average year. In the summer the majority of these extremes will occur during the working day and so 28C became adopted as the temperature for cooling design. In the winter the majority of the cold extremes will occur at night and so a lower deviation is accepted for commercial buildings leading to the –2C rule of thumb for heating design. If we were to select our cooling plant based on the extremes of temperature that we sometimes


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