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# Which Distribution & Analysis - Half hourly interval of ticket inflow

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#### Mayank Trivedi

Greetings All,

Attached sheet contains half hourly interval of ticket inflow, number of dispatches and tickets closed for teh month of June(all days).

I am trying to understand what distribution does the inflow of tickets follow? I used minitab and it told me the distribution is lognormal. Do let me know how it I am correct adn if there is a better method of doing the analysis using all data points.

I have a total of 13 resources and how should they be staffed to ensure maximum tickets are dispatched and worked on?

The number of tickets closed are a combination of tickets closed automatically and tickets closed becasue someone has worked upon them. The ratio is about 3:1.

The purpose of my study is to find out adequate staffing numbers and efficient way of working.

Regards

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#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Lognormal may be reasonable since it terminates at zero (does not allow negative numbers). Theoretically, the distribution should be Poisson, though this may be what is referred to as a "Non-Homogeneous Poisson Process" since likely the average rate varies by time of day.

I'll take a look at this at home over the weekend. Can't do this at work while on the US taxdollar.

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
That is an interesting set of data. There does look to be a rough sine wave through the daily cycle, and low levels on the weekends.

I'd suggest fitting a non-homogeneous poisson process through the data, with a sine wave through the 48 1/2 hour increments, with the amplitude varying based upon day of week. Then set the control limits around that curve fit at plus and minus three times the square root of the centerline. This could be done in a few hours work in Excel (using the optimization module to get the sine wave amplitudes). I don't know about miniTab.