Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Bed turnover rate and turnover interval function

T = f(D, B_bar); TI = g(n, B_bar, U, D); T = h(o, L_bar); TI = k(o, L_bar); c_D = m(C_bed, T)

Maps the discharges, available beds and occupied bed-days of a period to the two measures reported as bed turnover: the turnover rate, the number of patients each bed served, and the turnover interval, the average time a bed stands empty between one patient and the next. It also expresses both through bed occupancy and average length of stay, and spreads the annual cost of a staffed bed over the patients it served. The records follow the notation of the Bed Turnover article. The throughput identity linking annual discharges to beds, occupancy and average length of stay is held on the Average Length of Stay page (HE-FM-ALOS-002) and is referenced here, not repeated.

  • Bed turnover rate from discharges and average available beds

    T = D / B_bar

    Divides the discharges of a period, including deaths, by the average daily number of available beds over the same period. The result is the number of patients each bed served, a partial productivity ratio of one output, discharges, to one input, beds. NHS Wales reports it as the bed use factor (indicator IP03). B_bar is the mean of the daily bed counts, which the computational function under this formula derives from those counts.

  • Bed turnover interval from available and occupied bed-days

    TI = (n * B_bar - U) / D

    Divides the bed-days on which available beds stood empty in a period by the number of discharges, giving the average time a bed is empty between one patient leaving and the next arriving. n times B_bar is the available bed-days. NHS Wales reports the same quantity as the bed turnover interval (indicator IP04), written as average unoccupied beds times days in the period, divided by deaths and discharges.

  • Annual bed turnover rate from occupancy and average length of stay

    T = 365 * o / L_bar

    Expresses the annual turnover rate through bed occupancy and average length of stay. It follows from dividing both sides of the throughput identity on the Average Length of Stay page (HE-FM-ALOS-002) by the number of beds, with o equal to U divided by 365 times B_bar and L_bar equal to U divided by D. A high turnover rate can come from short stays, from full beds or from both, so the rate is ambiguous on its own. On a Pabón Lasso chart, which plots T against o, each line from the origin joins points with the same L_bar.

  • Bed turnover interval from occupancy and average length of stay

    TI = L_bar * (1 - o) / o

    Expresses the turnover interval through occupancy and average length of stay. Adding the stay and the interval gives 365 divided by the annual turnover rate, so each bed cycles through one stay and one empty interval per patient, and the stay is the share o of that cycle. On a Barber-Johnson diagram, which plots L_bar against TI, lines from the origin join points of equal occupancy and diagonals with equal intercepts join points of equal turnover.

  • Fixed bed cost per discharge from the bed turnover rate

    c_D = C_bed / T

    Spreads the annual cost of a staffed bed that does not vary with patient numbers over the patients the bed served in the year, as in top-down costing. A higher turnover rate lowers this average only because the same cost is shared among more patients; whether cash is saved depends on what happens to the freed capacity.