It's time the railways in Britain got to grips with what passengers expect in timekeeping. The present 10-minute threshold described as "on time" for long distance trains and the 5-minute one for local trains is ridiculous. It is derided by passengers as a "lie" and "idoitic" and they're right. When a train is advertised as arriving at 10:07, it should get there at 10:07. 10:16 is not "on time", it's 9 minutes late and we travellers all know it, regardless of what the railway company or the Department for Transport might say.
If there has to be some leeway in train timekeeping for performance monitoring purposes, there should, logically, be a 3-minute rule for all trains. To understand why, we need to understand how a railway produces its product. We have to get, at least, the basics - what the railway offers as a service and how it makes that offer work. We should start by looking at the timetable.
A railway is a service provider. It provides a travel service. It provides the service by producing a stream of moving packages called trains, which are used to transport people along a production line called a track. The intervals between the the moving packages, the trains, are decided on (usually) according to the number of people who want to travel along that particular route at that particular time.
Since most railways don't have so many prospective passengers that they need to provide trains every few minutes they make it easier for passengers by writing a timetable¹. The timetable sets out the times trains are due to appear at each calling point.
Now, there are limitations on the number of trains you can run along one track in one direction. The limits are set by the trains' ability to stop safely. Since trains are heavy, long and often move at quite high speeds they need lots of room to stop. In fact, most trains need about 10 times the stopping distance needed by your car on the road. So the intervals between trains are set for safety reasons, in much the same way as the wise car driver does when he leaves enough room between himself and the car in front in case he has to stop quickly. Train drivers do the same but they are guided by signals.
Signals are provided so that trains drivers can keep their trains a safe distance apart. Signals provide guidance on the state of the line ahead so that the driver can adjust the speed of the train accordingly. On most major routes in Britain, the signals will allow trains to run at about 3 minutes apart, that's 20 trains an hour. In reality, it's slightly fewer trains per hour than this because a margin is allowed for different driving techniques, longer than normal station stops, different types of trains and variable local conditions.
So, our railway production line can send packages, our trains, along the line at 3-minute intervals and this is our basic performance criterion - a 3-minute service interval, or "headway", as we on the railway call it. If we are going to judge our performance properly, we should examine our production line, our train service interval, our so-called headway. If our railway is going to perform according to its capabilities, we should regard any deviation from our 3-minute headway, such as late running, as wrong, because it prevents our train "packages" from passing along our production line at the correct, 3-minute intervals. Put another way, late running reduces our production capability and therefore reduces our performance.
So, any train that runs more than 3 minutes late is occupying the time² belonging to another train and we have therfore lost a unit of production. This is how we should judge our performance - on our time within 3 minutes. Any other value judgement is false, as it ignores the simple unit of production that is the basis of any railway operation, the train headway.
Footnote 1: Generally, if a train service runs at less than 10 minute intervals, a full, published timetable isn't necessary. Of course the railway will produce its own "working" timetable to ensure that trains are run at the correct intervals but it will give the passengers a service frequency of, say, "a train every few minutes" or "a train every 7-8 minutes", so that passengers know what to expect.
Footnote 2: We call the time a train occupies a section of line as its "path". Trains are given a "timetabled path" and many railways use a graphical format for timetables to show how the train paths fit on a time plan.