bayesian inference

Acceptance Sampling models have been widely applied in companies for the inspection and testing the raw material as well as the final products. A number of lots of the items are produced in a day in the industries so it may be impossible to inspect/test each item in a lot. The acceptance sampling models only provide the guarantee for the producer and consumer that the items in the lots are according to the required specifications that they can make appropriate decision based on the results obtained by testing the samples. Acceptance sampling plans are practical tools for quality control applications which consider quality contracting on product orders between the vendor and the buyer. Acceptance decision is based on sample information. In this research, dynamic programming and Bayesian inference is applied to decide among decisions of accepting, rejecting, tumbling the lot or continuing to the next decision making stage and more sampling. We employ cost objective functions to determine the optimal policy. First, we used the Bayesian modelling concept to determine the probability distribution of the nonconforming proportion of the lot and then dynamic programming is utilized to determine the optimal decision. Two dynamic programming models have been developed. First one is for the perfect inspection system and the second one is for imperfect inspection. At the end, a case study is analysed to demonstrate the application the proposed methodology and sensitivity analyses are performed.

In order to perform Preventive Maintenance (PM), two approaches have evolved in the literature. The traditional approach is based on the use of statistical and reliability analysis of equipment failure. Under statistical-reliability (S-R)-based PM, the objective of achieving the minimum total cost is pursued by establishing fixed PM intervals, which are statistically optimal, at which to replace or overhaul equipments or components. The second approach involves the use of sensor-based monitoring of equipment condition in order to predict occurrence of machine failure. Under condition-based (C-B) PM, intervals between PM works are no longer fixed, but are performed only “when needed”. It is obvious that Condition Based Maintenance (CBM) needs an on-line inspection and monitoring system that causes CBM to be expensive. Whenever this cost is infeasible, we can develop other methods to improve the performance of traditional (S-R)-based PM method. In this research, the concept of Bayesian inference was used. The time between machine failures was observed, and with combining Bayesian Inference with (S-R)-based PM, it is tried to determine the optimal checkpoints. Therefore, this approach will be effective when it is combined with traditional (S-R)-based PM, even if large number of data is gathered.