Optimum Preventive Maintenance Policies
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...Þ and failures are removed by minimal repair (Barlow and Hunter, 1960, Policy II). As the concepts of minimal repair and especially imperfect maintenance (Pham and Wang, 1996) became more and more established, various extensions and variations of these two policies were proposed. One expansion of the ‘‘periodic replacement with minimal repair at failure’’ policy is the one where a unit receives imperfect PM every T time unit, intervening failures are subject to minimal repairs, and it is replaced after its age has reached ðOþ 1ÞT time units, where O is the number of imperfect PMs which have been done (Liu et al., 1995). O 1⁄4 0 is allowed in this policy, which means the unit will be replaced whenever it has operated for T time units and there will be no imperfect PM for it. The policy decision variables are O and T. Obviously, if O 1⁄4 0, this policy becomes the ‘‘periodic replacement with minimal repair at failure’’ policy. Berg and Epstein (1976) have modified the block replacement policy by setting an age limit. Under this modified policy, a failed unit is replaced by a new one; however, units whose ages are less than or equal to t0 ð06 t0 6 T Þ at the scheduled replacement times kT ðk 1⁄4 1; 2; . . .Þ are not replaced, but remain working until failure or the next scheduled replacement time point. Obviously, if t0 1⁄4 T , it reduces to the block replacement policy. This modified block replacement policy was shown to be superior to the block replacement policy in terms of the long-run maintenance cost rate. Tango (1978) suggests that some failed units be replaced by used ones, which have been collected before the scheduled replacement times. Under this extended block replacement policy, units are replaced by new ones at periodic times kT ðk 1⁄4 1; 2; . . .Þ. The failed units are, however, replaced by either new ones or used ones based on their individual ages at the times of failures. A time limit r is set in this policy, similar to t0 in Berg and Epstein (1976). Under this policy, if a failed unit’ age is less than or equal to a predetermined time limit r, it is replaced by a new one; otherwise, it is replaced by a used one. This policy is different from Berg and Epstein’s because it modifies the ordinary block replacement policy by considering rules on the failed units rather than on the working ones (cf. Berg and Epstein, 1976). Obviously, if r 1⁄4 T , this policy becomes the block replacement policy. Nakagawa (1981a,b) presents three modifications to the ‘‘periodic replacement with minimal repair at failure’’ policy. The modifications give alternatives that emphasize practical considerations. The three policies all establish a reference time T0 and periodic time T . If failure occurs before T0, then minimal repair occurs. If the unit is operating at time T , then replacement occurs at time T . If failure occurs between T0 and T , then: (Policy I) the unit is not repaired and remains failed until T ; (Policy II) the failed unit is replaced by a spare unit as many times as needed until T ; (Policy III) the failed unit is replaced by a new one. In all these three policies, the policy decision variables are T0 and T . Clearly, if T0 T , Policies I, II, and II all become the ‘‘periodic replacement with minimal repair at failure’’ policy. If T0 0, Policy III becomes the block replacement policy. Nakagawa (1980) also makes an expansion to the block replacement policy. In his policy, a unit is replaced at times kT ðk 1⁄4 1; 2; . . .Þ independent of the age of the unit. A failed unit remains failed until the next planned replacement. Another variant of the ‘‘periodic replacement policy with minimal repair’’ policy is also due to Nakagawa (1986), in which the replacement is scheduled at periodic times kT ðk 1⁄4 1; 2; . . .Þ and failure is removed by minimal repair. If the total number of failures is equal to or greater than a specified number n, the replacement should be done at the next scheduled time; otherwise, no maintenance should be done. The decision variable is n and T. In this policy, if n 1⁄4 1, this policy becomes the ‘‘periodic replacement with minimal repair at failure’’ policy. Chun (1992) studies determination of the optimal number of periodic PM’s under a finite planning horizon....
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...Þ and failures are removed by minimal repair (Barlow and Hunter, 1960, Policy II). As the concepts of minimal repair and especially imperfect maintenance (Pham and Wang, 1996) became more and more established, various extensions and variations of these two policies were proposed. One expansion of the ‘‘periodic replacement with minimal repair at failure’’ policy is the one where a unit receives imperfect PM every T time unit, intervening failures are subject to minimal repairs, and it is replaced after its age has reached ðOþ 1ÞT time units, where O is the number of imperfect PMs which have been done (Liu et al., 1995). O 1⁄4 0 is allowed in this policy, which means the unit will be replaced whenever it has operated for T time units and there will be no imperfect PM for it. The policy decision variables are O and T. Obviously, if O 1⁄4 0, this policy becomes the ‘‘periodic replacement with minimal repair at failure’’ policy. Berg and Epstein (1976) have modified the block replacement policy by setting an age limit. Under this modified policy, a failed unit is replaced by a new one; however, units whose ages are less than or equal to t0 ð06 t0 6 T Þ at the scheduled replacement times kT ðk 1⁄4 1; 2; . . .Þ are not replaced, but remain working until failure or the next scheduled replacement time point. Obviously, if t0 1⁄4 T , it reduces to the block replacement policy. This modified block replacement policy was shown to be superior to the block replacement policy in terms of the long-run maintenance cost rate. Tango (1978) suggests that some failed units be replaced by used ones, which have been collected before the scheduled replacement times. Under this extended block replacement policy, units are replaced by new ones at periodic times kT ðk 1⁄4 1; 2; . . .Þ. The failed units are, however, replaced by either new ones or used ones based on their individual ages at the times of failures. A time limit r is set in this policy, similar to t0 in Berg and Epstein (1976). Under this policy, if a failed unit’ age is less than or equal to a predetermined time limit r, it is replaced by a new one; otherwise, it is replaced by a used one. This policy is different from Berg and Epstein’s because it modifies the ordinary block replacement policy by considering rules on the failed units rather than on the working ones (cf. Berg and Epstein, 1976). Obviously, if r 1⁄4 T , this policy becomes the block replacement policy. Nakagawa (1981a,b) presents three modifications to the ‘‘periodic replacement with minimal repair at failure’’ policy. The modifications give alternatives that emphasize practical considerations. The three policies all establish a reference time T0 and periodic time T . If failure occurs before T0, then minimal repair occurs. If the unit is operating at time T , then replacement occurs at time T . If failure occurs between T0 and T , then: (Policy I) the unit is not repaired and remains failed until T ; (Policy II) the failed unit is replaced by a spare unit as many times as needed until T ; (Policy III) the failed unit is replaced by a new one. In all these three policies, the policy decision variables are T0 and T . Clearly, if T0 T , Policies I, II, and II all become the ‘‘periodic replacement with minimal repair at failure’’ policy. If T0 0, Policy III becomes the block replacement policy. Nakagawa (1980) also makes an expansion to the block replacement policy. In his policy, a unit is replaced at times kT ðk 1⁄4 1; 2; . . .Þ independent of the age of the unit. A failed unit remains failed until the next planned replacement. Another variant of the ‘‘periodic replacement policy with minimal repair’’ policy is also due to Nakagawa (1986), in which the replacement is scheduled at periodic times kT ðk 1⁄4 1; 2; . . .Þ and failure is removed by minimal repair. If the total number of failures is equal to or greater than a specified number n, the replacement should be done at the next scheduled time; otherwise, no maintenance should be done. The decision variable is n and T. In this policy, if n 1⁄4 1, this policy becomes the ‘‘periodic replacement with minimal repair at failure’’ policy. Chun (1992) studies determination of the optimal number of periodic PM’s under a finite planning horizon. Dagpunar and Jack (1994) determine the optimal number of imperfect PMs H. Wang / European Journal of Operational Research 139 (2002) 469–489 473...
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...Þ and failures are removed by minimal repair (Barlow and Hunter, 1960, Policy II). As the concepts of minimal repair and especially imperfect maintenance (Pham and Wang, 1996) became more and more established, various extensions and variations of these two policies were proposed. One expansion of the ‘‘periodic replacement with minimal repair at failure’’ policy is the one where a unit receives imperfect PM every T time unit, intervening failures are subject to minimal repairs, and it is replaced after its age has reached ðOþ 1ÞT time units, where O is the number of imperfect PMs which have been done (Liu et al., 1995). O 1⁄4 0 is allowed in this policy, which means the unit will be replaced whenever it has operated for T time units and there will be no imperfect PM for it. The policy decision variables are O and T. Obviously, if O 1⁄4 0, this policy becomes the ‘‘periodic replacement with minimal repair at failure’’ policy. Berg and Epstein (1976) have modified the block replacement policy by setting an age limit. Under this modified policy, a failed unit is replaced by a new one; however, units whose ages are less than or equal to t0 ð06 t0 6 T Þ at the scheduled replacement times kT ðk 1⁄4 1; 2; . . .Þ are not replaced, but remain working until failure or the next scheduled replacement time point. Obviously, if t0 1⁄4 T , it reduces to the block replacement policy. This modified block replacement policy was shown to be superior to the block replacement policy in terms of the long-run maintenance cost rate. Tango (1978) suggests that some failed units be replaced by used ones, which have been collected before the scheduled replacement times. Under this extended block replacement policy, units are replaced by new ones at periodic times kT ðk 1⁄4 1; 2; . . .Þ. The failed units are, however, replaced by either new ones or used ones based on their individual ages at the times of failures. A time limit r is set in this policy, similar to t0 in Berg and Epstein (1976). Under this policy, if a failed unit’ age is less than or equal to a predetermined time limit r, it is replaced by a new one; otherwise, it is replaced by a used one. This policy is different from Berg and Epstein’s because it modifies the ordinary block replacement policy by considering rules on the failed units rather than on the working ones (cf. Berg and Epstein, 1976). Obviously, if r 1⁄4 T , this policy becomes the block replacement policy. Nakagawa (1981a,b) presents three modifications to the ‘‘periodic replacement with minimal repair at failure’’ policy. The modifications give alternatives that emphasize practical considerations. The three policies all establish a reference time T0 and periodic time T . If failure occurs before T0, then minimal repair occurs. If the unit is operating at time T , then replacement occurs at time T . If failure occurs between T0 and T , then: (Policy I) the unit is not repaired and remains failed until T ; (Policy II) the failed unit is replaced by a spare unit as many times as needed until T ; (Policy III) the failed unit is replaced by a new one. In all these three policies, the policy decision variables are T0 and T . Clearly, if T0 T , Policies I, II, and II all become the ‘‘periodic replacement with minimal repair at failure’’ policy. If T0 0, Policy III becomes the block replacement policy. Nakagawa (1980) also makes an expansion to the block replacement policy. In his policy, a unit is replaced at times kT ðk 1⁄4 1; 2; . . .Þ independent of the age of the unit. A failed unit remains failed until the next planned replacement. Another variant of the ‘‘periodic replacement policy with minimal repair’’ policy is also due to Nakagawa (1986), in which the replacement is scheduled at periodic times kT ðk 1⁄4 1; 2; . . .Þ and failure is removed by minimal repair. If the total number of failures is equal to or greater than a specified number n, the replacement should be done at the next scheduled time; otherwise, no maintenance should be done. The decision variable is n and T. In this policy, if n 1⁄4 1, this policy becomes the ‘‘periodic replacement with minimal repair at failure’’ policy. Chun (1992) studies determination of the optimal number of periodic PM’s under a finite planning horizon. Dagpunar and Jack (1994) determine the optimal number of imperfect PMs H....
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...Under this policy, a unit is always replaced at its age T or failure, whichever occurs first, where T is a constant (Barlow and Hunter, 1960)....
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...Þ and failures are removed by minimal repair (Barlow and Hunter, 1960, Policy II). As the concepts of minimal repair and especially imperfect maintenance (Pham and Wang, 1996) became more and more established, various extensions and variations of these two policies were proposed. One expansion of the ‘‘periodic replacement with minimal repair at failure’’ policy is the one where a unit receives imperfect PM every T time unit, intervening failures are subject to minimal repairs, and it is replaced after its age has reached ðOþ 1ÞT time units, where O is the number of imperfect PMs which have been done (Liu et al., 1995). O 1⁄4 0 is allowed in this policy, which means the unit will be replaced whenever it has operated for T time units and there will be no imperfect PM for it. The policy decision variables are O and T. Obviously, if O 1⁄4 0, this policy becomes the ‘‘periodic replacement with minimal repair at failure’’ policy. Berg and Epstein (1976) have modified the block replacement policy by setting an age limit. Under this modified policy, a failed unit is replaced by a new one; however, units whose ages are less than or equal to t0 ð06 t0 6 T Þ at the scheduled replacement times kT ðk 1⁄4 1; 2; . . .Þ are not replaced, but remain working until failure or the next scheduled replacement time point. Obviously, if t0 1⁄4 T , it reduces to the block replacement policy. This modified block replacement policy was shown to be superior to the block replacement policy in terms of the long-run maintenance cost rate. Tango (1978) suggests that some failed units be replaced by used ones, which have been collected before the scheduled replacement times....
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