Sequential Methods for Monitoring Declining Quality, with Application to the Long-Term Storage of Seeds

Abstract

SUMMARY The results in this paper were motivated by the problem of monitoring the quality of seeds being stored for long periods under conditions of low temperature and low humidity. Under the assumption of a simple and smooth form of deterioration, a unified procedure is developed which specifies both when and how the seed lot should be inspected. Limits on the probability of reaching a prespecified poor quality are set. The theory is presented in a general form, in the expectation that it will be useful in other applications. Specific details for implementation in seed banks are given, and computer simulations are used to confirm the validity of approximate theory. The quality of some resource is declining with the passage of time from an initially high value, until eventually an unacceptable standard will be reached. Determination of the quality at any particular time can be achieved by inspection, but inspections are expensive and subject to error. This paper addresses two related issues: when to make the inspections, and how to decide when the unacceptable standard has been reached. The methods that will be used are those of hypothesis testing, and not decision theory. It will be assumed that the decline in quality is smooth, and can be represented by a simple model. This research has been motivated by a particular practical context. Seed banks exist to conserve genetic resources through the long-term storage of seeds. Each accession, within the bank is a collection of several thousand seeds of a particular strain stored under homogenous conditions of low temperature and low humidity. Initially the accession will have a high viability: a high proportion of the seeds would germinate if planted. The viability will deteriorate slowly over time until an unacceptably low value is reached. The potential storage life for many plant varieties will be 100 years or more. Inspections take the form of germination tests conducted on samples drawn from the accession. These inspections are time-consuming and expensive in the sense that they deplete the very accessions that are to be conserved. If the viability is found to be unacceptably low, then the stock will be regenerated: some of the seeds will be planted, the crop will be harvested, and new seeds will be collected and stored in place of the old accession. The operation of seed banks is described in Ellis, Tong, and Roberts (1985) and sequential designs for a single inspection are discussed by Whitehead (1981) and Ellis and Whitehead (1987). The theory will be developed in some generality in the hope that other applications for the procedure might be found. It is likely that analogous problems arise in other storage situations. Ecological or medical monitoring might provide other examples.