ejb 3.1 spec [4.8.4 Singleton Error Handling] says that "Errors occurring during Singleton initialization are considered fatal and must result in the discarding of the Singleton instance."
I tried to raise a system exception in the @PostConstruct method of a singleton bean. Logs show the deployment error. But I then can access and call the singleton methods.

– Full paragraph 4.8.4: -----------------------------
Errors occurring during Singleton initialization are considered fatal and must result in the discarding of the Singleton instance. Possible initialization errors include injection failure, a system exception thrown from a PostConstruct method, or the failure of a PostConstruct method container-managed transaction to successfully commit. If a singleton fails to initialize, attempted invocations on the Singleton result in an exception as defined by Section 3.4.3 and Section 3.4.4.
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I tested to raise a system exception (throw new RuntimeException()) in the @PostConstruct method.

– Logs show the error -------------------------------
ERROR [AbstractKernelController] Error installing to Start: name=startup-singleton-initiator:topLevelUnit=ts.ear,unit=testSingletonEjb.jar,bean=counter aliases=[startup-singleton-initiator:bean=counter,topLevelUnit=ts.ear,unit=testSingletonEjb.jar] state=Create: java.lang.RuntimeException: Could not invoke PostConstruct on the newly created bean instance
at org.jboss.ejb3.singleton.impl.container.SingletonEJBInstanceManagerImpl.create(SingletonEJBInstanceManagerImpl.java:137) [:1.0.0-alpha-28]
...
Caused by: testsingleton.exn.SE // class SE extends RuntimeException{}
at testsingleton.ejb.CounterEjb.pc(CounterEjb.java:28)

DEPLOYMENTS IN ERROR:
Deployment "startup-singleton-initiator:topLevelUnit=ts.ear,unit=testSingletonEjb.jar,bean=counter" is in error due to the following reason(s): testsingleton.exn.SE
at org.jboss.deployers.plugins.deployers.DeployersImpl.checkComplete(DeployersImpl.java:1228) [:2.2.0.GA]
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However, it is after that possible to access the singleton through a JNDI lookup and successfully call its methods.