In her biography of J.B. Priestley, Maggie Barbara Gale calls An Inspector Calls "a deceptively conservative one-set, well-made play, where the action all takes place over one evening." Another way of saying this might be to argue that Priestley follows Aristotle's classic unities of time, place, and action. Priestley's play does flirt with theatrical conventions and, of course, follows many of them, to a point, but ultimately challenges many of them.
Why "deceptively conservative"? It is not just because the unities are not really so neat. To be sure, the interesting actions leading to Eva's death happened in times and places other than the evening covered by the play. As for the unity of action, it takes the Inspector to weave the different prior actions together into a coherent narrative, but this narrative is challenged when it is thought that the story might involve different women after all--and the whole existence of the Inspector and the suicide are put into question by the end of the play.
Even more than that, Priestley's play begins as a drawing-room drama but evolves into something that looks more like a murder mystery or a thriller. Nevertheless, neither of those genres has a history of emphasizing the political or sociological messages that Priestley eventually delivers through the character of the Inspector. These other genres focus, naturally, on the death and the investigation, but Priestley is interested in the personal and social conditions that led to the various choices that his characters make.
To understand the precise nature of this comparison with those genres, it might be interesting to look up other plays from those genres from the same period. Consider these:
• Dial M for Murder by Frederick Knott
• The Hollow by Agatha Christie
• The Mousetrap by Agatha Christie (a play in which the policeman makes for an interesting counterpoint to the Inspector)
Here are some key questions:
• What are the key points and messages of the play? Are they central to the plot or peripheral to it?
• Does the play even have an explicit message for the audience? Does the investigator or the wisest character share a wise message, or is the murderer the one with the most interesting thoughts?
• Does the play contain instances of wrongdoing? If so, how many characters are "guilty," and who takes charge of justice?
• What role does authority (in the laws, or embodied by the police or others with power) play in the play's projected morality?
You are likely to find that An Inspector Calls does not have a great deal in common with murder mysteries or thrillers after all. Yet, it is no comedy and does not very well fit the traditional model of a tragedy. Indeed, the Inspector is a kind of truth-teller who provides what a couple of the characters need to reach their moral epiphany and see their social responsibility, yet the presumed leaders of the family, the older generation, suffer no downfall and are quite happy when they find excuses to avoid such an epiphany.
To some degree, perhaps, this somewhat naturalistic, somewhat expressionist play also reminds one of the early twentieth-century trend of the psychological novel, where the interesting things are the conversations and people's nuanced thoughts and reactions to their experiences. Most of all, however, the play fits in the tradition of the novel or play that is written in large part to engage an audience with a social problem. Still, rather than try to figure out where the play might belong in literary history, perhaps readers are served best by reviewing the play on its own merits.