# Distribution of Discharges

Six Sigma – iSixSigma Forums Old Forums Healthcare Distribution of Discharges

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• #25786

MGrayson
Participant

Good Day:
I’ve been asked to set a target for the percentage of patients discharged from hospital before 11am based on what we want the data to look like.  I’m pretty sure it would be a Poisson distribution with greater than X percentage occurring before 11.  Am I on the right track?  It’s been a while and it’s  slow coming back to me.
M!

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#62450

Eugene Jacquescoley
Participant

Grayson,
Hello. I believe so. Poisson distribution process may assume that the probability of events is small enough to avoid having multiple events at the same time. In your particular case of patient discharge rates; one may also preclude that an expected number of occurences may only depend on the length of the interval over which they are counted.
Hope this helps.
Eugene Jacquescoley

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#62455

Mundorff
Member

Your inquiry really encompasses two separate questions:
1. What percentage of discharges occur by the 11:00 desired time? This is a binary variable, illustrated with a p-chart.
2. What is the distribution of discharges by hour throughout the day (the Poisson distribution you referred to previously)?
The second will give you some idea of how much movement will be necessary to achieve whatever goal is set for the first measure.  For instance, moving a discharge up from noon to 11:00 would be more feasible than moving one from 22:00 up by 11 hours.
After that it is probably a slog to examine those “feasible” post-11:00 discharges by service, by physician, etc. to look for patterns for possible interventions.  It could be (to choose one real-life example from our system), for instance, that the patient is ready to go home at 10:00, but it takes the pharmacy more than one hour to fill discharge prescriptions because of the crunch of morning discharge orders.

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