Further Approximate Optimum Inspection Intervals

Abstract. The author derives a general explicit formula and presents an heuristic algorithm for solving Baker’s model. The examples show that this new approximate solution procedure for determining near optimum inspection intervals is more accurate than the ones suggested by Chung (1993) and Vaurio (1994), and is more efficient computationally than the one suggested by Hariga (1996). The construction and solution of the simplest profit model for an exponential failure distribution were presented in Baker (1990), and approximate analytical results were obtained by Chung (1993) and Vaurio (1994). The author will therefore mainly devote the following discussion to the problem of further approximating optimum inspection intervals. Keywords: Exponential Distribution, Inspection, Repair, Cost, Profit, Machine 1. INTRODUCTION Consider a single unit representing a manufacturing system composed of many components. In the following, the author will use the word “machine” to refer to such a single-unit or complex system. Under the superposition of the renewal processes related to the failure of the components, it is reasonable to assume that the ma-chine’s failure distribution is exponentially distributed, see Cox and Smith (1954). In fact, Drenick (1960) mathematically showed that under reasonably general conditions, distribution of the time between failures tends to the exponential as the complexity of machine structure or the time of operation increases. Moreover, many authors such as Davis (1952) and Epstein (1958) found strong empirical justification that this failure law characterizes a wide variety of devices including ball-and-roller bearings, vacuum tubes, bus engines, and many electronic systems. Now suppose that a machine is subject to failures at random with a constant hazard λ per unit time, i.e. follows the exponential failure distribution