Schedules of reinforcement: FR, VR, FI, VI

A schedule of reinforcement is the rule that decides which responses get reinforced. Under continuous reinforcement (CRF), every response is reinforced. Under intermittent reinforcement, only some are. Most exam items on this topic come down to naming the schedule from a short description, or predicting the pattern of responding it produces.

The BACB's 6th edition outline has a task on simple schedules (B.9) and one on concurrent, multiple, mixed and chained schedules (B.10).

Two questions name any simple schedule

1. Does the rule count responses or time? Responses → ratio. Time since the last reinforcer → interval.
2. Is the requirement the same every time, or does it vary around an average? Same → fixed. Varies → variable.

CRF is the same as FR 1.

The pattern each one produces

• FR: a high rate of responding, often with a pause after each reinforcer, then a fast run to the next one. People call it "break and run". Example: a warehouse worker paid per 10 boxes packed works fast, then takes a breather after each completed batch.
• VR: a high, steady rate with little pausing, because any response might be the one that pays. Example: a fisher casting a line, where a bite comes after an unpredictable number of casts.
• FI: little responding just after the reinforcer, then a rising rate as the end of the interval nears. On a cumulative record this curve is called the "scallop". Example: checking the oven more and more often as the 20-minute baking time runs out.
• VI: a moderate, steady rate, because the reinforcer could become available at any moment but responding faster doesn't make it come sooner. Example: checking for a reply to a message that could arrive at any time.

A useful check: would responding faster bring the reinforcer sooner? If yes, it's a ratio schedule. If no, it's an interval schedule.

One nuance from the lab: the FI scallop is clearest in averaged data. Baron and Leinenweber (1994) found that individual intervals often looked more like break-and-run, with the scallop emerging when intervals were averaged. Berry, Kangas and Branch (2012) found the scallop took dozens of sessions to develop. For the exam, the textbook pattern is what you need. In practice, don't expect every interval to look like the diagram.

The fixed-time trap

Fixed-interval and fixed-time schedules are not the same.

• On FI 2 min, the reinforcer goes to the first response after 2 minutes. No response, no reinforcer.
• On FT 2 min, the reinforcer is delivered every 2 minutes whatever the person does. No response is needed.

FT and VT schedules are time-based (response-independent) schedules. In applied work they're how noncontingent reinforcement is delivered, which is task G.3, not B.9. If a scenario says "regardless of behavior", it isn't an interval schedule.

Compound schedules (B.10)

Compound schedules combine two or more simple schedules. Three questions sort the B.10 four:

1. Do the schedules run at the same time or one after another? At the same time, for different responses → concurrent. The learner chooses where to respond, and this is where the matching law applies.
2. If one after another, does each component deliver its own reinforcer? Yes → multiple or mixed. No, only the final link does → chained (or tandem).
3. Is each component signalled by its own stimulus? Multiple and chained have a distinct stimulus for each component. Mixed and tandem don't.

Original example of a multiple schedule: a green card on the desk means questions earn tokens on FR 3; a red card means tokens come on VI 1 min. Remove the cards and keep the alternation, and it becomes mixed.

Common traps

• "Every 10 minutes" isn't enough to name a schedule. Check whether a response is required at the end.
• Calling VR "random reinforcement". VR has a defined average. The number of responses varies around it.
• Mixing up mixed and multiple. Look for the signal. No distinct stimulus per component means mixed.
• Confusing concurrent and conjunctive. Concurrent offers choices at the same time. Conjunctive delivers one reinforcer only after two or more requirements are all met.
• Forgetting thinning. Moving from CRF to a leaner intermittent schedule is a common maintenance step, and responding on intermittent schedules usually lasts longer once reinforcement stops.

Practise it

For each scenario, write "count or clock?" and "same or varies?" next to it before you look at the options. Then check whether a response is actually required.

The lessons on B.9: simple schedules of reinforcement and B.10: concurrent, multiple, mixed and chained cover the patterns in depth. The free diagnostic shows where you stand in B. Concepts and Principles.

FAQ

What is the difference between a ratio and an interval schedule? Ratio schedules require a number of responses. Interval schedules require a period of time to pass, then one response.

Which schedule produces the highest rate of responding? Variable ratio typically produces high, steady rates with little pausing, because responding faster brings reinforcement sooner and there's no predictable point to pause.

What is a post-reinforcement pause? A pause in responding just after a reinforcer is delivered. It is typical of fixed schedules, both FR and FI.

Is fixed time the same as fixed interval? No. Fixed interval requires a response once the time is up. Fixed time delivers the reinforcer on a clock regardless of behavior.

Sources

• BACB, BCBA Test Content Outline (6th ed.): https://www.bacb.com/wp-content/bcba-outline-6thEd (tasks B.9, B.10 and G.3)
• Baron, A., & Leinenweber, A. (1994). Molecular and molar analyses of fixed-interval performance. Journal of the Experimental Analysis of Behavior, 61(1), 11–18: https://pmc.ncbi.nlm.nih.gov/articles/PMC1334350/ (break-and-run in individual intervals; the scallop in averaged data)
• Berry, M. S., Kangas, B. D., & Branch, M. N. (2012). Development of key-pecking, pause, and ambulation during extended exposure to a fixed-interval schedule of reinforcement. Journal of the Experimental Analysis of Behavior, 97(3), 333–346: https://pmc.ncbi.nlm.nih.gov/articles/PMC3372956/ (how the FI pattern develops over sessions)