Summary Report on the Statistically Based Analysis
of Probabilities of Fixture Use in Households
January 22, 2014
On September 18, 2013, Aquacraft delivered to IAPMO a MS Access database in accordance
with the proposal contract. The task group held weekly conference calls when possible since the
September deliverable (9 conference calls within 12 weeks), along with dozens of email
correspondence. For several weeks, the task group explored and tested the database to verify
mathematical accuracy. Several conference calls were held with Aquacraft addressing preliminary
system problems and errors. As a result, the Access database underwent four iterations for
improvements. To date, the Access database is not complete in verification. The fixture count needs to
be reconciled in the various summaries and queries. There are noted discrepancies between the fixture
surveys and the actual data. An accurate fixture count is necessary to derive the probabilities of use.
Also, the task group requested verification that all of the vacationing homes have been eliminated from
the datasets. Including unoccupied vacationing homes in the analysis increases the fixture count and
will skew the outcome. These items have yet to be resolved with a revised updated Access database.
Test examples have been conducted using the CA Single Family dataset. When exporting the
data into the MS Excel template provided in the proposal where the task group formulas could be
applied to the data, the probabilities differed from the probabilities derived from the Access query. This
may indicate mathematical inconsistency within the Access database. This has yet to be explored more
fully.
Although the Access database will display the average hits per hour per fixture for the 24 hour
duration, is not able to select the peak hours (greatest hits) for querying purposes. Hence, the
probabilities are based on hourly averages over the full 24 hour period. The task group realized that T
(average time in seconds between successive operations of a fixture) is therefore no longer a random
variable, but becomes an hourly constant. T must remain a random variable since it changes throughout
the day. There must be a busy observation window to derive a probability of single fixture use per
home. This busy observation window is not consistent with each home and must be detected for each
home. This issue of the database assuming T is constant creates the problem that a fixture may not be in
use during the selected busy time. How is that fixture accounted for? These issues are yet unresolved
when applied particularly to the single home.
Problems were detected with the number of leaks showing strong diurnal patterns and the
number of daily hits per capita extraordinarily high in homes with few occupants in the Westminster
data set. Aquacraft was to examine the data set and report to the task group on its findings. The task
group may need to revisit “Faucets, Leaks, and Other” and see how Aquacraft assesses those categories
in the raw data (what is the line of demarcation to disaggregate a leak from Other or a short burst
duration of a faucet). Faucet hits seem high (in one dataset, a particular hour shows 2116 faucet hits and
3473 leak hits). Aquacraft will need to investigate what percentage of the hits in these categories are
actually disaggregated trail flows from other fixtures in the raw data. This is unresolved.
The task group requested Aquacraft to query the q-value (water flow of a fixture in gpm) and pvalue (probability a single fixture is in use) for individual high-efficiency fixtures to complete one of the
tables in the UPC proposal. This led to the problem of defining high-efficiency for each fixture and
selecting the appropriate parameters to query. Ranges in flow rate or volume needed to be selected to
agree with WaterSense parameters for toilets and showers. Faucets are problematic to define highefficiency parameters. Bathtubs were excluded from high-efficiency parameters. Appliances became
problematic since Energy Star uses a water factor, a ratio of capacity and water volume, parameters not
applicable to the Access database. Also, Aquacraft’s survey did not identify Energy Star appliances, only
distinguishing clothes washers as top load or front load. AHAM was contacted for assistance in defining
the parameters of high efficiency clothes washers and dishwashers, and if it is possible to do so with
respect only to volume of water. Results of this inquiry are still pending. Once the high-efficiency
parameters are determined, Aquacraft will need to adjust the high-efficiency query in the Access
database accordingly.
The Wistort method in the UPC proposal was more closely scrutinized by the task group once
having familiarity with the database. A criterion was developed to determine when the Wistort method
can be used. The criterion indicates that the Wistort method should not be used for single family homes.
It is more applicable to multi-family homes and it is yet to be determined what the low-end boundary is,
i.e. the minimum number of multi-family units for the Wistort method to be accurate. Therefore, the
task group has decided for two distinct approaches; one approach for the single family dwelling and
another approach for multi-family dwellings.
Because of these and other unanswered questions about the correct approach, the task group
was unable to complete a revised proposal for the 2015 UPC by January 3, 2014. It has been understood
by the task group in the beginning that the submitted proposal was only a placeholder to be later
revised pending satisfactory results from statistical mining and formulating probable estimates of water
demand. These results have not been achieved within the limited time allotted. Given another six
months, the task group is confident that the results will not only prove satisfactory, but exceed
expectations for applicability in the UPC. The task group is eager to continue moving forward and submit
a substantial proposal for the next code cycle.