Institute of Technology Delhi , ( IIT Delhi )

Number: 015-0565 Abstract Title: An integrated model for maintenance planning, process qualityTitle: An integrated model for maintenance planning, process quality control and production scheduling Authors Information: 1. Divya Pandey Research Scholar Department of Mechanical Engineering Indian Institute of Technology Delhi, (IIT Delhi) Hauz Khas, New Delhi India-110016 * Corresponding Author e-mail: [email protected], [email protected], 2. Dr. M.S.Kulkarni Assisstant Professor Department of Mechanical Engineering Indian Institute of Technology Delhi (IIT Delhi) Hauz Khas, New Delhi India-110016 e-mail: [email protected] Fax Number: +911126582053 3. Prof. Prem Vrat Professor of Eminence Management Development Institute Mehrauli Road, Sukhrali, Gurgoan-122007 India e-mail: [email protected] POMS 21 st Annual Conference Vancouver, Canada May 7-May 10, 2010 An integrated model for maintenance planning, process quality control and production scheduling Abstract Performance of a manufacturing system depends on the performance at the shopfloor level. Traditionally, shopfloor level operational policies concerning maintenance, quality and production-scheduling have been considered and optimized independently. However, these three aspects of operations planning may also have an interaction effect on each other and hence need to be considered jointly for improving the manufacturing system performance. In this paper, a model for integrating maintenance and process quality is developed to obtain optimal preventive maintenance interval and control chart parameters that minimize expected cost per unit time. Subsequently, the optimal preventive maintenance interval is superimposed onto the production-schedule in order to determine the optimal job-sequence that will minimize penalty-cost incurred due to schedule delay. An illustrative example is included to compare the performance of the proposed integrated model with the performance obtained by using independent models. Key word: Preventive maintenance, process quality, production scheduling, control chartPerformance of a manufacturing system depends on the performance at the shopfloor level. Traditionally, shopfloor level operational policies concerning maintenance, quality and production-scheduling have been considered and optimized independently. However, these three aspects of operations planning may also have an interaction effect on each other and hence need to be considered jointly for improving the manufacturing system performance. In this paper, a model for integrating maintenance and process quality is developed to obtain optimal preventive maintenance interval and control chart parameters that minimize expected cost per unit time. Subsequently, the optimal preventive maintenance interval is superimposed onto the production-schedule in order to determine the optimal job-sequence that will minimize penalty-cost incurred due to schedule delay. An illustrative example is included to compare the performance of the proposed integrated model with the performance obtained by using independent models. Key word: Preventive maintenance, process quality, production scheduling, control chart Introduction In the context of the manufacturing, there is a need for a manufacturing system to quickly adapt itself to the demand fluctuations (random requests) and to the internal interruptions (machines breakdowns/process failure). In such an environment, the optimal production and maintenance planning, and scheduling and quality control becomes increasingly challenging. There is a large gap in the literature in terms to joint consideration of scheduling, maintenance and process/product quality. For instance, in most models, machines are assumed to be always available during the scheduling horizon; while on the other hand, maintenance planning models seldom consider the impact of maintenance on due dates and quality of the process. This paper has three goals. First, to develop an approach to integrate maintenance planning and process quality control policy. Specifically, the aim is to obtain optimal preventive maintenance interval and control chart parameters that minimize the expected cost per unit time. Subsequently, an approach is proposed in which the optimal preventive maintenance interval obtained is superimposed onto the production-schedule in order to determine the optimal job-sequence that will minimize the penalty-cost associated with schedule delay. Finally, it compares the performance of the proposed integrated model with the methodology that treats these issues independently. The paper is organized as follows: in Section 2, a brief review of relevant literature is presented. In section 3, the problem statement is discussed in detail and in section 4, a solution methodology is presented. In Section 5, a mathematical model for integrated maintenance planning and process quality control policy is developed and a numerical example is presented for illustration. A superimposition model of preventive maintenance interval obtained in section 3 on production schedule is presented in Section 6 along with an illustrative example to show how the proposed approach works. Comparison of the integrated model with the performance obtained by using independent model is given. Some possible extensions of proposed approach are also given. 2. Literature review In the ’80s, researches on production scheduling with machines failures or varying machine capacity started appearing in literature. Many of these researches, such as Pinedo and Rammouz (1988), Adiri et al. (1991), Hirayama and Kijima (1992), Federgruen and Mosheiov (1997), Leung and Pinedo (2004), considered a passive approach toward machine unavailability and focused on how to adjust the production schedule to account for the time when machines are unavailable. It is well known that carrying out preventive maintenance on a machine with increasing failure rate can effectively reduce the occurrence of machine failures and increase the machine availability. Graves and Lee (1999), and Lee and Chen (2000) developed approaches that simultaneously schedule jobs with a single preventive maintenance. They assume that each machine is maintained only once during the planning horizon. Their approaches on production and preventive maintenance scheduling consist of two stages: (1) Determine the interval during which a machine has to be maintained only once to increase its availability. (2) Within the interval found in (1), schedule the jobs and the single preventive maintenance simultaneously. Cassady and Kutanoglu (2003) compared the optimal value of total weighted tardiness under integrated production scheduling with preventive maintenance planning with that under separate production scheduling and preventive maintenance planning. They assume that the uptime of a machine follows a Weibull distribution; the machine is minimally repaired when it fails; and the preventive maintenance restores the machine to a state as good as new. Their results indicate that there is an average of 30% reduction in the expected total weighted tardiness when the production scheduling and preventive maintenance planning are integrated. Leng et al. (2006) and Sortrakul and Cassady (2007) further extended the work of Cassady and Kutanoglu (2003) and proposed Chaotic Partial Swarm Optimization (CPSO) heuristic and GA-based heuristics respectively to solve the integrated mathematical model for single machine production scheduling and PM planning as a multi-objective optimization problem. Similarly, increasing number of practitioners and researchers have recognized that there is a strong relationship between product quality, process quality and equipment maintenance (Ben-Daya and Duffuaa, 1995), and integration of these may be beneficial to organization. But research in this field is still limited. Rahim (1993) determined jointly the optimal design parameters on an -bar control chart and preventive maintenance (PM) time for a production system with an increasing failure rate. Ben-Daya and Rahim (1999,2000); and Rahim (1994) investigated integration of -bar chart and PM, when the deterioration process during in-control period follows a general probability distribution with increasing hazard rate. Cassady et al. (2000) studied an -bar chart in conjunction with an age replacement preventive maintenance policy. Rahim and Ben-Daya (2001) provided an overview of the literature dealing with integrated models for production scheduling, quality control and maintenance policy. Recently, Linderman et al. (2005) developed a generalized analytic model to determine the optimal policy to coordinate Statistical Process Control and Planned Maintenance to minimize the total expected cost. Panagiotidou and Tagaras (2007) have proposed an economic model for the optimization of preventive maintenance interval in a production process with two quality states. While some literature is available for integrating maintenance with scheduling and maintenance with quality, integration of all the three areas i.e. production scheduling, maintenance and quality control has recently started getting attention from the research community (Rahim and Ben-Daya 2001) and hence it presents a good oppurtunity for further research. Nomenclature [ ] 1 FM CM C E Expected cost of corrective maintenance (CM) due to failure mode1 [ ] PM C E Expected cost of preventive maintenance (PM) failure process TCQ E − ] [ Expected total cost of quality due to process failure CM MT Mean Time to CM PR Production rate lp C Cost of lost production LC Labour Cost FCPCM C Fixed cost per CM 1 FM P Probability of occurrence of failure due to failure mode 1 f N Number of failures PM MT Mean Time to PM FCPPM C Fixed cost per PM ] [ I T E Expected in-control period 1 ARL Average run length during in-control period 0 T Expected time spent searching for a false alarm 2 FM P Probability of occurrence of failure due to failure mode 2 eval T Evaluation period c M ARL / 2 Average run length during an out-of-control period due to machine failure E ARL2 Average run length during an out-of-control period due to machine failure τ Mean elapse time from the last sample before the assignable cause to the occurrence of assignable cause when the maintenance and quality policies are integrated s T Time to sample and chart one item 1 T Expected time to determine occurrence of assignable cause reset T Time to perform the resetting of the process which moves out-of-control due to external reason α Type I error probability j CRe Cost of rejection C M R / ) ( δ Probability of nonconforming items produced due to machine failure mode II C M / β Type II error probability due to machine failure mode II E R ) ( δ Type II error probability due to external reasons E β Probability of nonconforming items produced due to external cause reset C Cost of resetting ] ) [( 2 FM CM C E The expected cost of corrective maintenance due to Q M ECPUT * ] [ Expected cost per unit time of integrated maintenance and quality policy 3. Problem Statement Consider a production system consisting of a single machine producing products of the same type with constant production rate of items per hour on a continuous basis (3shifts of 7hrs each, 6 days-a-week). Further, consider a single component operating as a part of machine with time-to-failure following a two parameter Weibull distribution. Let the scale and shape parameters of the distribution be and respectively. Suppose the process can best be evaluated by measuring a key quality characteristic of finished products. Let denotes the measurement of this characteristic for a given product, and assume that is a normal random variable having mean μ and standard deviation σ. The value of μ is referred to as the process mean, and the value of σ is referred to as the process standard deviation. When the process is in-control (operating properly), the process mean is set at its target value. The process mean can instantaneously shift, due to equipment/process failure. After a shift has occurred, the new process mean is given by: μ = μ0+δσ0, where δ is some nonzero real number. After the shift, the process is said to be out-of-control. Usually, the failure which causes this shift is relatively subtle. Therefore, the cause of failure cannot be identified without shutting down the process and performing a close inspection of the equipment. In this paper, two types of equipment failure mode are considered. If failure mode 1 ( ) occurs, then it is immediately detected and the machine has to be stopped. Corrective actions are taken to restore the machine back to the operating conditions. Thus, results in an expected corrective maintenance cost ( [ ] 1 FM CM C E ) comprising of cost of down time, and cost of repair/restoration. However, failure mode 2 ( ) affects the functionality of the machine and causes the process to shift, resulting in an increase in the rejection level, till it is detected. It is assumed that the occurrence of is not immediately detectable but whenever it is detected, the process is stopped immediately and corrective actions are taken to restore the process to the normal conditions. Apart from machine failures due to , process may also deteriorate and shift due to external causes ‘E’ like environmental effects, operators’ mistake, use of wrong tool, etc. The process is also restored if an external causes ‘E’ is detected. Since and E cannot be directly detected, a control chart is used to monitor the quality characteristic ‘ ’. Hence the time to detect and E depends on the power of the control chart. The parameters of this chart are: (h) the time (in hours) between samples, (n) the sample size, and (k) the number of standard deviations of the sampling distribution between the centre line of the control chart and the control limits. The resulting upper and lower control limits for the -chart are given by: