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The expectation of a random variable is its average value, where each value is weighted according to the probability that it comes up. The expectation is also called the expected value or the mean of the random variable. For example, suppose we select a student uniformly at random from the class, and let R be the student’s quiz score. Then E [R] is just the class average —the first thing everyo...

To model the lifetime of a device, increasing Markov chains are used. The transition probabilities of the chain are as follows: pi, j = p if j = i+δ, and pi, j = 1− p if j = i+2δ. The mean time to failure of the device, namely the mean number of transitions required for the process, starting from x0, to take on a value greater than or equal to x0 + kδ is computed explicitly. A second version of...

Purpose – The purpose of the paper is to develop a conceptual framework that integrates the technology and commercial issues early at the design stage to minimize warranty costs in the most effective and efficient manner and also to develop a model for optimization of warranty with specific focus on reliability and warranty policies. Design/methodology/approach – The critical issues in warranty...

We study a problem of allocating divisible jobs, arriving online, to workers in a crowdsourcing setting which involves learning two parameters of strategically behaving workers. Each job is split into a certain number of tasks that are then allocated to workers. Each arriving job has to be completed within a deadline and each task has to be completed satisfying an upper bound on probability of ...

The recent manufacturing environment is characterized as having diverse products due to mass customization, short production lead-time, and unstable customer demand. Today, the need for flexibility, quick responsiveness, and robustness to system uncertainties in production scheduling decisions has increased significantly. In traditional job shops, tooling is usually assumed as a fixed resource....