Risk analysis of life-time acceptance sampling plans under model uncertainties : a thesis submitted for the degree of Master of Science, School of Fundamental Sciences (SFS), Massey University, New Zealand

Abstract

Lifetime acceptance sampling is one of the important branches of quality engineering because lifetime is a critical characteristic of many industrial and agricultural products. Due to budget and time constraints, lifetime acceptance sampling plans usually suffer from the curse of small sample sizes. Given a sufficiently large sample size, the test or sample data can identify its parent distribution easily. However, it is a challenge to find out the parent distribution for small sample sizes, especially when the data comes from a lifetime distribution having a shape parameter. In this thesis, I propose a variables sampling plan, called the M-method plan, to resolve the distribution-data identification issue in lifetime acceptance sampling with small sample sizes. Extensive Monte Carlo simulation studies were carried out to compare the Operating Characteristic (OC) curves of the M-method plans, and two existing alternative plans. Furthermore, I show that the lognormal distribution, which is a shape free lifetime distribution, can be used as a surrogate for Weibull or gamma distributions when the sample size is small. In other words, model uncertainties can be ignored when designing a lifetime acceptance sampling plan under the M-method. The M-method based sampling plan, under the correctly-specified distribution, is compared with various M-method based sampling plans under the scenario of misspecified distributions. Even though the OC curves are distinct from each other significantly depending on the operating procedure, the OC curves can be matched under the proposed method when the parent distribution is fully misspecified as a lognormal distribution for small sample sizes.