Double Checking for Two Error Types

auditing;confidence limit;double inspection;error types;inspection errors;quality control;repeated checks

Modified Normal Demand Distributions in (R,S)-Inventory Models

To model demand, the normal distribution is by far the most popular; the disadvantage that it takes negative values is taken for granted.This paper proposes two modi.cations of the normal distribution, both taking non-negative values only.Safety factors and order-up-to-levels for the familiar (R, S)-control system are derived and compared with the standard values corresponding with the original normal distribution.demand;inventory control

Simulating an (R,s,S) Inventory System

inventory control;simulation models;reorder point;fill rate

New proposals for the validation of trace-driven simulations

simulation;simulation models;operations research

Double Checking for Two Error Types

Auditing a large population of recorded values is usually done by means of sampling.Based on the number of incorrect records that is detected in the sample, a point estimate and a confidence limit for the population fraction of incorrect values can be determined.In general it is (implicitly) assumed that the auditor does not make mistakes while judging the correctness of the values. However, in practice this assumption does not necessarily hold: auditors are human and can make errors.To take this possibility into account, a subsample of the audited records is checked once more by a second auditor who is assumed never to make mistakes.The information obtained from these two samples should be combined to derive an estimate for the error rate in the population.The starting point for this type of double checking was Moors et al.(2000).Only one possible error type was considered: auditors could only miss (fail to detect) existing errors.For the case of random sampling, the maximum likelihood estimator as well as an upper confidence limit for the error rate were derived.The present paper gives extensions in two directions.Firstly, a second error type is introduced: the auditor may consider a correct value as an error.Again, the sample information of both auditor and infallible expert is combined to give point and interval estimates for the fraction of errors in the population.Secondly, a Bayesian analysis is presented for both the model with one error type and the extended model.auditing;Bayesian statistics;quality control;sampling;error analysis

Exact Fill Rates for (R, s, S) Inventory Control With Gamma Distributed Demand

For the familiar (R; s; S) inventory control system only approximate expressions exist for the fill rate, i.e. the fraction of demand that can be satisfied from stock.Best-known are the approximations derived from renewal theory by Tijms & Groenevelt (1984), holding under specific conditions; in particular, S ¡ s should be reasonably large.They considered, more specifically, the cases of normally and gamma distributed demand.Here, an exact expression for the fill rate is derived, holding generally in the situation that demand has a gamma distribution with known integer-valued parameters, while lead time is constant.This formula is checked through extensive simulations; besides, detailed comparisons are made with Tijms & Groenevelt's approximation.demand;inventory control;simulation

Two-Step Sequential Sampling for Gamma Distributions

estimation bias;extended sampling;sample extension;stochastic sample size;two-step sampling;statistical distribution