Journal of Statistical Computation and Simulation Vol. 80, No. 2, February 2010, 143–157 Food shelf life: estimation and optimal design Ross A. Larsen † , G. Bruce Schaalje*, and John S. Lawson Department of Statistics, BrighamYoung University, Provo, Utah, USA (Received 15 May 2008; final version received 13 October 2008 ) Shelf life is a speciﬁed percentile of the time-until-spoilage distribution of a food product. This paper investigates statistical properties of various estimators of shelf life and develops a genetic algorithm for ﬁnding near-optimal staggered designs for estimation of shelf life. MLEs and their associated conﬁdence intervals for shelf life have smaller bias, better performance, and better coverage than the corresponding ad hoc regression-based estimates. However, performance of MLEs for common sample sizes must be evaluated by simulation. The genetic algorithm, coded as an SAS macro, searched the design space well and generated near-optimal designs as measured by improvement to a simulation-based performance measure. Keywords: genetic algorithm; adaptive design; staggered design; Weibull; censoring 1. Introduction Shelf life estimation in food science [1] involves statistical methods for estimating speciﬁed percentiles of the time-until-spoilage distribution of a food product [2]. The data typically come from a planned experiment in which food items are tested for spoilage at storage times that are sometimes speciﬁed in advance, but are more commonly selected adaptively using ‘staggered sampling’ designs [1,3]. Ad hoc estimation methods based on linear regression, popular in the past [4] , are often still used [5]. Methods based on maximum likelihood have been studied more recently [2,6]. Confusingly, some researchers use the ad hoc method but incorrectly refer to it as the maximum likelihood procedure [1]. In medical survival or industrial reliability studies, observations can be either uncensored or censored [7]. Censoring is usually relatively rare, often due to dropout or study termination. However, in shelf life studies, all observations are censored in some way. The ad hoc shelf life estimation methods either ignore the censoring [4] or make additional adjustments to compensate for the censored nature of the data [5]. In spite of this, shelf life estimates based on these methods often seem reasonable. *Corresponding author. Email: schaalje@byu.edu † Present address. Department of Educational Psychology, TexasA&M University, College Station, TX, USA ISSN 0094-9655 print/ISSN 1563-5163 online © 2010 Taylor & Francis DOI: 10.1080/00949650802549135 http://www.informaworld.com Downloaded by [University of Arizona] at 13:28 25 May 2016