# How to calculate run-off triangles?

(Note: This is copy of my question on StackOverflow here.)

Reality description: We do have a list of projects. In every project there is a lot of accounts. You can do a lot of actions on every account. I do have the following dimensions and fact table defined (simplified):

``````Dimensions and attributes:
Project
project_key
project_name
industry
number_of_accounts
Distance
distance_key
distance_in_months
distance_in_quarters
Account
account_key
project_key
account_id
Fact Table and attributes:
Action_Fact_Table
project_key
distance_key
account_key
action_id
``````

Now, I would like to use run-off triangle approach to analyze data (it's maybe not the real run-off triangle, but the approach is the same). The most simple triangle would look like:

``````              Distance in Months
Project name|     1    2    3    4    5    6    7    8    9    10
-------------------------------------------------------------------------
Project1   |     5   10   15   20   25   30   35   40   45    50
Project2   |     7   14   21   28   35   42   49   56   63
Project3   |     2    5    8   11   14   20   25   30
Project4   |     0    2    5   10   18   23   40
Project5   |     5   12   18   20   21   30
``````

There is running sum of number of actions by rows. Distance in months shows the distance between date of action and project start date. You can obviously create similar triangle using distance in quarters (or any other period defined in distance dimension).

You can also create triangel for different level of hierarchy in project dimension, e.g. industry (Project1-Project3 = Industry1, Project4-Project5 = Industry2):

``````              Distance in Months
Project name|     1    2    3    4    5    6    7    8    9    10
-------------------------------------------------------------------------
Industry1   |    14   29   44   59   74   92  109  126  108   50
Industry2   |     5   14   23   30   39   53   40
``````

There is also more advanced run-off triangle where you divide running sum of actions by number of accounts. Assume there is the following number of accounts for our projects:

``````Project_name number_of_accounts
-----------------------------
Project1     100
Project2     100
Project3     100
Project4     100
Project5     200
``````

Then I would like to get the following triangle:

``````              Distance in Months
Project    |     1    2    3    4    5    6    7    8    9    10
------------------------------------------------------------------------
Project1  |   .05  .01  .15  .20  .25  .30  .35  .40  .45   .50
Project2  |    .7  .14  .21  .28  .35  .42  .49  .56  .63
Project3  |    .2   .5   .8  .11  .14  .20  .25  .30
Project4  |    .0   .2   .5  .10  .18  .23  .40
Project5  |   .05  .06  .09  .10 .105  .15
``````

This is especially usefull when you would like to compare projects and their actions in case where number of accounts in project is not the same for all projects.

The question is whether it is possible to create such calculation in OLAP. I was thinking I can use number_of_accounts in project table, but I can't figure it out. The other option is to aggregate data in account dimension. I was also not able to find anything using google, maybe because I'm asking wrong question.

The solution to this question is widely applicable in many industries, it is crucial especially in insurance and banking. It can be used everywhere where processes have long performance window and can be tracked by well defined, comparable batches of units.

(We are using PostgreSQL, Saiku, cubes are defined in Schema Workbench)

Test data (PostgreSQL syntax, let me know if you need something else)

``````--drop table if exists project cascade;
create table project (
project_key int primary key,
project_name character varying,
industry character varying,
number_of_accounts int
);

--drop table if exists distance cascade;
create table distance (
distance_key int primary key,
distance_in_months int,
distance_in_quarters int);

--drop table if exists account cascade;
create table account (
account_key int primary key,
project_key int references project (project_key)
);

--drop table if exists action_fact_table cascade;
create table action_fact_table (
project_key int references project (project_key),
distance_key int references distance (distance_key),
account_key int references account (account_key),
action_id int
);

-- project data
insert into project values (1,'Project1','Industry1',100);
insert into project values (2,'Project2','Industry1',100);
insert into project values (3,'Project3','Industry1',100);
insert into project values (4,'Project4','Industry2',100);
insert into project values (5,'Project5','Industry2',200);

-- distance data
insert into distance values(1,1,1);
insert into distance values(2,2,1);
insert into distance values(3,3,1);
insert into distance values(4,4,2);
insert into distance values(5,5,2);
insert into distance values(6,6,2);
insert into distance values(7,7,3);
insert into distance values(8,8,3);
insert into distance values(9,9,3);
insert into distance values(10,10,4);
insert into distance values(11,11,4);
insert into distance values(12,12,4);

-- account data
/* let me know if you need insert statement for every row */
insert into account (
select generate_series (1,100), 1 union all
select generate_series (101,200), 2 union all
select generate_series (201,300), 3 union all
select generate_series (301,400), 4 union all
select generate_series (401,600), 5
);

insert into action_fact_table values(1,1,90,10001);
insert into action_fact_table values(1,1,32,10002);
insert into action_fact_table values(1,1,41,10003);
insert into action_fact_table values(1,1,54,10004);
insert into action_fact_table values(1,1,45,10005);
insert into action_fact_table values(1,2,22,10006);
insert into action_fact_table values(1,2,29,10007);
insert into action_fact_table values(1,2,41,10008);
insert into action_fact_table values(1,2,89,10009);
insert into action_fact_table values(1,2,15,10010);
insert into action_fact_table values(1,3,32,10011);
insert into action_fact_table values(1,3,100,10012);
insert into action_fact_table values(1,3,72,10013);
insert into action_fact_table values(1,3,80,10014);
insert into action_fact_table values(1,3,10,10015);
insert into action_fact_table values(1,4,12,10016);
insert into action_fact_table values(1,4,45,10017);
insert into action_fact_table values(1,4,83,10018);
insert into action_fact_table values(1,4,42,10019);
insert into action_fact_table values(1,4,33,10020);
insert into action_fact_table values(1,5,22,10021);
insert into action_fact_table values(1,5,27,10022);
insert into action_fact_table values(1,5,59,10023);
insert into action_fact_table values(1,5,32,10024);
insert into action_fact_table values(1,5,70,10025);
insert into action_fact_table values(1,6,32,10026);
insert into action_fact_table values(1,6,5,10027);
insert into action_fact_table values(1,6,15,10028);
insert into action_fact_table values(1,6,70,10029);
insert into action_fact_table values(1,6,43,10030);
insert into action_fact_table values(1,7,59,10031);
insert into action_fact_table values(1,7,9,10032);
insert into action_fact_table values(1,7,99,10033);
insert into action_fact_table values(1,7,79,10034);
insert into action_fact_table values(1,7,31,10035);
insert into action_fact_table values(1,8,56,10036);
insert into action_fact_table values(1,8,34,10037);
insert into action_fact_table values(1,8,48,10038);
insert into action_fact_table values(1,8,79,10039);
insert into action_fact_table values(1,8,42,10040);
insert into action_fact_table values(1,9,10,10041);
insert into action_fact_table values(1,9,10,10042);
insert into action_fact_table values(1,9,49,10043);
insert into action_fact_table values(1,9,61,10044);
insert into action_fact_table values(1,9,49,10045);
insert into action_fact_table values(1,10,99,10046);
insert into action_fact_table values(1,10,69,10047);
insert into action_fact_table values(1,10,84,10048);
insert into action_fact_table values(1,10,99,10049);
insert into action_fact_table values(1,10,3,10050);
insert into action_fact_table values(2,1,182,10051);
insert into action_fact_table values(2,1,127,10052);
insert into action_fact_table values(2,1,197,10053);
insert into action_fact_table values(2,1,174,10054);
insert into action_fact_table values(2,1,187,10055);
insert into action_fact_table values(2,1,144,10056);
insert into action_fact_table values(2,1,160,10057);
insert into action_fact_table values(2,2,155,10058);
insert into action_fact_table values(2,2,153,10059);
insert into action_fact_table values(2,2,119,10060);
insert into action_fact_table values(2,2,188,10061);
insert into action_fact_table values(2,2,125,10062);
insert into action_fact_table values(2,2,147,10063);
insert into action_fact_table values(2,2,123,10064);
insert into action_fact_table values(2,3,136,10065);
insert into action_fact_table values(2,3,163,10066);
insert into action_fact_table values(2,3,187,10067);
insert into action_fact_table values(2,3,138,10068);
insert into action_fact_table values(2,3,168,10069);
insert into action_fact_table values(2,3,132,10070);
insert into action_fact_table values(2,3,138,10071);
insert into action_fact_table values(2,4,158,10072);
insert into action_fact_table values(2,4,171,10073);
insert into action_fact_table values(2,4,153,10074);
insert into action_fact_table values(2,4,141,10075);
insert into action_fact_table values(2,4,182,10076);
insert into action_fact_table values(2,4,165,10077);
insert into action_fact_table values(2,4,143,10078);
insert into action_fact_table values(2,5,190,10079);
insert into action_fact_table values(2,5,181,10080);
insert into action_fact_table values(2,5,163,10081);
insert into action_fact_table values(2,5,134,10082);
insert into action_fact_table values(2,5,145,10083);
insert into action_fact_table values(2,5,190,10084);
insert into action_fact_table values(2,5,198,10085);
insert into action_fact_table values(2,6,137,10086);
insert into action_fact_table values(2,6,133,10087);
insert into action_fact_table values(2,6,135,10088);
insert into action_fact_table values(2,6,103,10089);
insert into action_fact_table values(2,6,187,10090);
insert into action_fact_table values(2,6,127,10091);
insert into action_fact_table values(2,6,117,10092);
insert into action_fact_table values(2,7,116,10093);
insert into action_fact_table values(2,7,139,10094);
insert into action_fact_table values(2,7,111,10095);
insert into action_fact_table values(2,7,150,10096);
insert into action_fact_table values(2,7,151,10097);
insert into action_fact_table values(2,7,181,10098);
insert into action_fact_table values(2,7,109,10099);
insert into action_fact_table values(2,8,102,10100);
insert into action_fact_table values(2,8,101,10101);
insert into action_fact_table values(2,8,118,10102);
insert into action_fact_table values(2,8,147,10103);
insert into action_fact_table values(2,8,186,10104);
insert into action_fact_table values(2,8,136,10105);
insert into action_fact_table values(2,8,160,10106);
insert into action_fact_table values(2,9,149,10107);
insert into action_fact_table values(2,9,119,10108);
insert into action_fact_table values(2,9,169,10109);
insert into action_fact_table values(2,9,176,10110);
insert into action_fact_table values(2,9,195,10111);
insert into action_fact_table values(2,9,183,10112);
insert into action_fact_table values(2,9,140,10113);
insert into action_fact_table values(3,1,224,10114);
insert into action_fact_table values(3,1,241,10115);
insert into action_fact_table values(3,2,295,10116);
insert into action_fact_table values(3,2,249,10117);
insert into action_fact_table values(3,2,260,10118);
insert into action_fact_table values(3,3,298,10119);
insert into action_fact_table values(3,3,267,10120);
insert into action_fact_table values(3,3,297,10121);
insert into action_fact_table values(3,4,211,10122);
insert into action_fact_table values(3,4,253,10123);
insert into action_fact_table values(3,4,214,10124);
insert into action_fact_table values(3,5,248,10125);
insert into action_fact_table values(3,5,223,10126);
insert into action_fact_table values(3,5,288,10127);
insert into action_fact_table values(3,6,207,10128);
insert into action_fact_table values(3,6,296,10129);
insert into action_fact_table values(3,6,221,10130);
insert into action_fact_table values(3,6,201,10131);
insert into action_fact_table values(3,6,227,10132);
insert into action_fact_table values(3,6,209,10133);
insert into action_fact_table values(3,7,267,10134);
insert into action_fact_table values(3,7,282,10135);
insert into action_fact_table values(3,7,215,10136);
insert into action_fact_table values(3,7,285,10137);
insert into action_fact_table values(3,7,212,10138);
insert into action_fact_table values(3,8,239,10139);
insert into action_fact_table values(3,8,294,10140);
insert into action_fact_table values(3,8,296,10141);
insert into action_fact_table values(3,8,251,10142);
insert into action_fact_table values(3,8,281,10143);
insert into action_fact_table values(4,2,392,10144);
insert into action_fact_table values(4,2,347,10145);
insert into action_fact_table values(4,3,318,10146);
insert into action_fact_table values(4,3,400,10147);
insert into action_fact_table values(4,3,378,10148);
insert into action_fact_table values(4,4,315,10149);
insert into action_fact_table values(4,4,318,10150);
insert into action_fact_table values(4,4,394,10151);
insert into action_fact_table values(4,4,382,10152);
insert into action_fact_table values(4,4,317,10153);
insert into action_fact_table values(4,5,314,10154);
insert into action_fact_table values(4,5,354,10155);
insert into action_fact_table values(4,5,338,10156);
insert into action_fact_table values(4,5,375,10157);
insert into action_fact_table values(4,5,317,10158);
insert into action_fact_table values(4,5,329,10159);
insert into action_fact_table values(4,5,342,10160);
insert into action_fact_table values(4,5,380,10161);
insert into action_fact_table values(4,6,313,10162);
insert into action_fact_table values(4,6,311,10163);
insert into action_fact_table values(4,6,336,10164);
insert into action_fact_table values(4,6,380,10165);
insert into action_fact_table values(4,6,355,10166);
insert into action_fact_table values(4,7,386,10167);
insert into action_fact_table values(4,7,322,10168);
insert into action_fact_table values(4,7,311,10169);
insert into action_fact_table values(4,7,367,10170);
insert into action_fact_table values(4,7,350,10171);
insert into action_fact_table values(4,7,384,10172);
insert into action_fact_table values(4,7,391,10173);
insert into action_fact_table values(4,7,331,10174);
insert into action_fact_table values(4,7,373,10175);
insert into action_fact_table values(4,7,314,10176);
insert into action_fact_table values(4,7,305,10177);
insert into action_fact_table values(4,7,331,10178);
insert into action_fact_table values(4,7,350,10179);
insert into action_fact_table values(4,7,376,10180);
insert into action_fact_table values(4,7,387,10181);
insert into action_fact_table values(4,7,312,10182);
insert into action_fact_table values(4,7,397,10183);
insert into action_fact_table values(5,1,404,10184);
insert into action_fact_table values(5,1,562,10185);
insert into action_fact_table values(5,1,511,10186);
insert into action_fact_table values(5,1,594,10187);
insert into action_fact_table values(5,1,541,10188);
insert into action_fact_table values(5,2,506,10189);
insert into action_fact_table values(5,2,427,10190);
insert into action_fact_table values(5,2,481,10191);
insert into action_fact_table values(5,2,463,10192);
insert into action_fact_table values(5,2,579,10193);
insert into action_fact_table values(5,2,455,10194);
insert into action_fact_table values(5,2,527,10195);
insert into action_fact_table values(5,3,465,10196);
insert into action_fact_table values(5,3,562,10197);
insert into action_fact_table values(5,3,434,10198);
insert into action_fact_table values(5,3,401,10199);
insert into action_fact_table values(5,3,464,10200);
insert into action_fact_table values(5,3,500,10201);
insert into action_fact_table values(5,4,554,10202);
insert into action_fact_table values(5,4,600,10203);
insert into action_fact_table values(5,5,483,10204);
insert into action_fact_table values(5,6,552,10205);
insert into action_fact_table values(5,6,565,10206);
insert into action_fact_table values(5,6,586,10207);
insert into action_fact_table values(5,6,544,10208);
insert into action_fact_table values(5,6,436,10209);
insert into action_fact_table values(5,6,531,10210);
insert into action_fact_table values(5,6,409,10211);
insert into action_fact_table values(5,6,524,10212);
insert into action_fact_table values(5,6,564,10213);
``````

Sample cube (Mondrian):

``````<Schema name="RunoffTriangleSchema">
<Cube name="RunoffTriangleCube" visible="true" cache="true" enabled="true">
<Table name="action_fact_table" schema="public">
</Table>
<Dimension type="StandardDimension" visible="true" foreignKey="project_key" name="Project">
<Hierarchy name="Project" visible="true" hasAll="true">
<Table name="project" schema="public" alias="">
</Table>
<Level name="Industry" visible="true" column="industry" uniqueMembers="false">
</Level>
<Level name="Project Name" visible="true" column="project_name" uniqueMembers="false">
</Level>
</Hierarchy>
</Dimension>
<Dimension type="StandardDimension" visible="true" foreignKey="distance_key" name="Distance">
<Hierarchy name="Distance" visible="true" hasAll="true">
<Table name="distance" schema="public" alias="">
</Table>
<Level name="Distance In Quarters" visible="true" column="distance_in_quarters" uniqueMembers="false">
</Level>
<Level name="Distance In Months" visible="true" column="distance_in_months" uniqueMembers="false">
</Level>
</Hierarchy>
</Dimension>
<Dimension type="StandardDimension" visible="true" foreignKey="account_key" name="Account">
<Hierarchy name="Account" visible="true" hasAll="true">
<Table name="account" schema="public">
</Table>
<Level name="Account Key" visible="true" column="account_key" uniqueMembers="false">
</Level>
</Hierarchy>
</Dimension>
<Measure name="CountActions" column="action_id" aggregator="count" visible="true">
</Measure>
</Cube>
</Schema>
``````
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