What is the test for determining the admissibility of evidence of past criminal conduct?

The trial court has a sua sponte duty to instruct on factors relevant to a witness's credibility. (People v. Rincon-Pineda (1975) 14 Cal.3d 864, 883-884.) However, it generally does not have such a duty regarding "the limited admissibility of evidence of past criminal conduct." (People v. Collie (1981) 30 Cal.3d 43, 64.) "When evidence is admissible... for one purpose and is inadmissible... for another purpose, the court upon request shall restrict the evidence to its proper scope and instruct the jury

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accordingly." (Evid. Code, 355, italics added, People v. Hernandez (2004) 33 Cal.4th 1040, 1051.)