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Suppose that a machine is subject to failures at random with constant probability of p per unit time, and that the only way of telling whether the machine has failed is to test it. Given the above assumptions, presents a simplified equation to determine how often a machine should be inspected.

Discusses the economic designs of np charts for a single assignable cause. Develops a simple algorithm to get the optimum designs of np charts. Twenty numerical examples show that the algorithm is very efficient and accurate indeed.

Presents two production models for maintaining current control of an industrial process under the surveillance of an np‐control chart. The first model assumes that the process is not allowed to continue in operation during the search for the assignable cause. The second assumes that the process is allowed to continue in operation during the search for the assignable cause. Develops two simple algorithms, which are implementable in real time on a personal computer, to get the optimum designs of np‐charts. Twenty‐six numerical examples show that the algorithms are very accurate and efficient.

In 1973, Goel and Wu presented an algorithm for the economic design of cusum charts to control the mean of a process with a normally distributed quality characteristic. They employed the two‐dimensional pattern search technique to determine the optimal values of the sample size, the sampling interval and the decision limit. Proposes a search algorithm required to use the one‐dimensional pattern search technique to get the optimal values of design parameters instead of the two‐dimensional pattern search technique. So, our search algorithm is not only accurate and efficient but also simpler to solve than that of Goel and Wu.

When the system fails, the decision to repair or replace a failed unit may depend on the estimated repair cost. Such an idea is called repair limit replacement policy. The repair limit is a limit on the amount of money which can be spent on the repair of a system. The repair limits thus provide an economic replacement policy. Examines optimal repair‐cost limits for a Weibull‐distributed time to failure and an exponentially distributed repair cost. Derives bounds for the optimal repair cost limit that minimizes the average cost per unit time for repairs and replacement. With those bounds, develops a simple algorithm to obtain the optimal repair‐cost limit. Gives numerical examples to illustrate the algorithm.

Examines optimal cost limits for a Weibull‐distributed time to failure and an exponentially distributed repair‐cost limit policy which minimizes the average cost per unit time for repairs and replacement. Presents numerical examples to illustrate the algorithm.

Considers a system consisting of several different elementary components. Presents an algorithm to determine the optimal inspection policy for this system. Numerical examples reveal that this algorithm works very well.

Considers the inventory system using the assumptions that the demand rate is deterministic and follows a linear trend, that the rate of deterioration is constant and that shortages are allowed. Many researchers solve this inventory system from the heuristic point of view. Essentially, their solutions are just suboptimal. Proposes an optimal model for determining the optimal inventory replenishment policy for this inventory system. Some numerical examples show that the heuristic method will sometimes result in significant cost penalties.