How does Priestley create tension in the play An Inspector Calls?

Priestley creates tension by making the play a mystery which unravels slowly, entangling the Birling family members.

Strangely, the Inspector is unknown to Mr. Birling, who is familiar with the police. Purposely, Inspector Goole only questions one person at a time because, as he says,

"...what happened to her may have determined what happened to her afterwards, and what happened to her afterwards may have driven her to suicide."

It seems that each person in the Birling house plays a role in the death of Eva Smith, and no one sees her photograph until the Inspector allows him or her to do so. The Inspector speaks first to Mr. Birling, who fired Eva after she went on strike for higher wages; then the Inspector talks to Birling's daughter, Sheila, who in jealousy had the young woman dismissed from a dress shop. The young woman then changed her name and tried to have men take care of her; soon, she met Gerald, Sheila's fiance, who put her up in a friend's apartment and became her lover.

When she hears Gerald relate what has happened, Sheila says  to him,  

"Why—you fool—he [the Inspector] knows! ...And I hate to think how much he knows that we don't know yet. You'll see, you'll see....We all started so confidently until he started asking questions."

Tension becomes so great between Sheila and Gerald that Sheila returns the engagement ring to Gerald, telling him, "You and I aren't the same people who sat down to dinner."

Of course, the greatest tension is created among the family members when they learn that the cold-hearted Mrs. Birling refused Eva Smith the aid of her Brumley Women's Charity Organization. When Eric learns that Eva was refused, he blames his mother for Eva's death as well as the death of the baby—"your grandchild," he tells her. Sheila, too, is upset with the mother.

Clearly, the family members are equally guilty of the girl's demise as they have each acted selfishly and even arrogantly. The greatest irony, however, is that they discover what types of persons they all are behind their veneers of respectability.