Sequential Analysis for a Binomial Proportion Using an Imprecise Prior Distribution

• Activity Number: 515
• Type: Contributed
• Date/Time: Thursday, August 7, 2008 : 10:30 AM to 12:20 PM
• Sponsor: Section on Quality and Productivity
• Author(s): Dennis Oberhelman*+ and Kathleen Whitcomb
• Companies: University of South Carolina and University of South Carolina
• Keywords: sequential sampling ; binomial parameter ; imprecise prior

Abstract

We describe a procedure for constructing a sequential sampling plan for a binomial parameter, p, using a class of conjugate priors defined using the 'intervals of measures' method (DeRobertis and Hartigan, 1981). This approach is useful in cases where only partial prior information is available. Upper and lower expected costs for accepting or continuing to sample are computed for each point on the sampling grid, leading to 'upper' and 'lower' sampling plans. A single sampling plan is then constructed to determine whether to 'accept,' 'reject,' or 'continue' for any point on the sampling grid using the 'P-minimality' decision criterion (Troffaes, 2007). An example of a sampling plan using a class of conjugate priors is presented as well as preliminary simulation results comparing expected costs of plans using precise conjugate priors versus classes of conjugate priors.