An Economic Reliability Test Plan: Log-Logistic Distribution R. R. L. KANTAM  , G. SRINIVASA RAO  & B. SRIRAM   Department of Statistics, Acharya Nagarjuna University, India and  Department of Statistics, J.K.C. College, Guntur-522006, India ABSTRACT Sampling plans in which items that are put to test, to collect the life of the items in order to decide upon accepting or rejecting a submitted lot, are called reliability test plans. The basic probability model of the life of the product is specified as the well-known log-logistic distribution with a known shape parameter. For a given producer’s risk, sample size, termination number, and waiting time to terminate the test plan are computed. The preferability of the test plan over similar plans existing in the literature is established with respect to cost and time of the experiment. KEY WORDS: Log-logistic distribution, reliability test plan, producer’s risk, acceptance sample number Introduction Acceptance sampling plans in Statistical Quality Control are concerned with accepting or rejecting a submitted lot of a large size of products on the basis of the quality of the pro- ducts inspected in a sample taken from the lot. If the quality of the product is the lifetime of the product, then a sample of such products, considered to be representive of the observed life times of the products are put forward for testing. If a decision to accept or reject the lot, subject to the risks associated with the two types of errors (rejecting a good lot/ accepting a bad lot), is possible then such a procedure is termed ‘Acceptance sampling based on life test’ or ‘Reliability test plans’. It requires specifications of a probability model governing the life of the products, since an exponential distribution is a central distribution in reliability studies. The log-logistic distribution has been studied in detail by Shah & Dave (1963) and Tadikamalla & Johnson (1982). Survival models based on logistic and log-logistic distributions haven been given by O’Quigley & Struthers (1982). The log- logistic distribution has been considered by Ragab and Green (1984), Balakrishnan & Malik (1987) with reference to moments of order statistics and linear unbiased estimation of location and scale parameters. Truncated life tests of this type are developed by Sobel & Tischendrof (1959) for exponential distribution. Gupta & Groll (1961) constructed similar sampling plans based on gamma life test sample data. Goode & Kao (1961) constructed sampling plans based on the Weibull distribution. Kantam & Rosaiah (1998) suggested Journal of Applied Statistics Vol. 33, No. 3, 291–296, April 2006 Correspondence Address: G. Srinivasa Rao, Department of Statistics, J.K.C. College, Guntur-522006, India. E-mail: gaddesrao@yahoo.com 0266-4763 Print=1360-0532 Online=06=030291–6 # 2006 Taylor & Francis DOI: 10.1080=02664760500445681