Finite Horizon Production Research Articles

The efficiency of CUSUM schemes for monitoring the multivariate coefficient of variation in short runs process

Current monitoring technologies emphasize and address the issue of monitoring high-volume production processes. The high flexibility and diversity of current industrial production processes make monitoring technology for small batch processes even more important. In multivariate process monitoring, a broader applicability exists in multivariate coefficients of variation (MCV) based monitoring schemes due to the lower restriction of the process. In view of the effectiveness of MCV monitoring and with the aim to achieve further performance improvement of current MCV monitoring schemes in a finite horizon production, we additionally introduce two one-sided cumulative sum (CUSUM) MCV schemes. In the case of deterministic and random shifts, the design parameters of the proposed schemes are obtained via an optimization procedure designed by the Markov chain method and the corresponding performance is analysed based on different run length (RL) characteristics, including the mean and the standard deviation. Simulation comparisons with existing exponentially weighted moving average (EWMA) MCV schemes show that the proposed CUSUM MCV schemes are more efficient in monitoring most of the shifts, including the deterministic and random shifts. Finally, to demonstrate the benefits of the new monitoring schemes, a comprehensive case study on monitoring a steel sleeve manufacturing process is conducted.

Distribution-free control charts for monitoring scale in finite horizon productions

Distribution-free (also known as nonparametric) control charts have been shown to be useful for on-line monitoring of lot production within a finite horizon production (FHP) process. Despite the partial process knowledge at the beginning of production in a FHP process, a distribution-free control chart can be started without any restrictive assumption about the underlying distribution of the quality characteristic. In this work, three nonparametric Shewhart-type control charts are investigated to monitor the unknown scale parameter in FHP processes based on some well-known nonparametric tests for scale. To this end, the violation of the assumption of equal medians of the reference and the test population distributions is investigated and a fourth control chart based on the Moses test, which does not require this assumption, is considered. An extensive numerical analysis is performed to examine chart performance based on some metrics suitable in the FHP setting. A real industrial example is presented to show a practical implementation of the investigated charts. Conclusions and future research ideas are provided.

EWMA monitoring schemes for MCV in short production runs with an application to the steel sleeve manufacturing process

In industries, multi-variety and small batch processes are extremely common due to the fact that the production process is moving towards flexible manufacturing to meet the increasing demand of consumers for individualized products. In recent years, monitoring techniques based on the multivariate coefficients of variation (MCV) have been widely developed owing to their applicability in assessing the relative variability of multivariate processes. It is worth noting that few of these studies have targeted monitoring the MCV in a short production run context. In this paper, two new one-sided MCV monitoring schemes are proposed by adopting the exponentially weighted moving average (EWMA) scheme in a finite horizon production. Based on the Markov chain approach, the performance measures, including the truncated average run length (TARL) and truncated standard deviation of the run length (TSDRL), of the EWMA MCV schemes are derived. Moreover, the superiority of the proposed monitoring schemes is illustrated by comparing their performance with that of the conventional Shewhart MCV monitoring schemes in a short production run context. The results show that increasing the batches enhances the advantages of the EWMA monitoring schemes over the Shewhart schemes. Finally, the superiority of the proposed EWMA monitoring scheme is illustrated by a real steel sleeve manufacturing case study.

A number‐between‐events control chart for monitoring finite horizon production processes

AbstractIn this paper, we present a number‐between‐events (NBE) control chart for monitoring the fraction nonconforming in finite horizon production (FHP) processes and related specific performance measures. When monitoring fractions nonconforming in FHP processes, the common binomial ‐chart has two crucial limitations: the underlying distributional assumptions are violated when dealing with low‐volume production and a scarce efficiency in the case of processes characterized by a low fraction nonconforming. Thus, an efficient monitoring of FHP processes requires the selection of the correct underlying statistical model: in this case, a distribution from the hypergeometric family of discrete statistical distributions. An efficient statistical monitoring of processes with low fractions nonconforming can be achieved by means of discrete time‐between‐events (TBE) control charts, which count the number of units up to the appearance of a fixed number of nonconforming units in the sample. Here, we present a discrete TBE‐chart, denoted as NBE‐chart, based on the negative hypergeometric distribution that meets numerous requirements of efficient monitoring of FHP processes. The proposed control chart can be conveniently used for both low‐volume and mass production in processes with frequent changeovers.

One-sided Shewhart control charts for monitoring the ratio of two normal variables in short production runs

Monitoring the ratio of two normal random variables plays an important role in several manufacturing environments. In addition, the traditional control charts that have been developed for infinite production horizons can not function effectively to detect anomalies in short production runs. In this paper, we tackle this problem by proposing two one-sided Shewhart-type charts to monitor the ratio of two normal random variables for a finite horizon production. The statistical performance of the proposed charts is investigated using the truncated average run length as a performance measure in short production runs. In order to help the quality practitioner to implement these control charts, we have provided ready-to-use tables of the control limit parameters. An illustrative example from the food industry is given for illustration.

A distribution-free Shewhart-type Mann–Whitney control chart for monitoring finite horizon productions

Distribution-free control charts have been proposed in recent years to monitor processes with insufficient information about the distribution of observations. A promising field of application of these charts is the small production of finite batches of products, where the number of scheduled inspections is limited to a few tens. Following the machine reconfiguration after a process set-up, the quality practitioner cannot rely on past production runs to get knowledge about the distribution of the observations: this scenario can be referred to as the Case U (Unknown) condition in statistical process monitoring. Here, we investigate the issues related to the implementation of Mann–Whitney (MW) type control charts for monitoring the location in a finite horizon production (FHP) process. The practitioner-to-practitioner variability is considered while designing the control limits. The in-control and out-of-control chart performances are investigated over a wide set of scenarios and some graphical tools are proposed to help practitioners during the decision-making process. A comparison with the Shewhart Sign control chart for FHP processes is also presented. An illustrative example is provided to demonstrate the implementation of the proposed chart on a real industrial dataset.

Joint Shewhart control charts for location and scale monitoring in finite horizon processes

Small production runs are becoming increasingly important in the manufacturing environment thanks to the technology advancements allowing products to be customized at competitive costs. Similarly, increasing flexibility in high volume production can allow for frequent and rapid changeovers from one part code to another to meet the lean principles. These manufacturing processes are characterized by finite production horizons. To assure high quality standards of products during a finite horizon production, implementing an efficient on-line process monitoring is a critical issue. In this paper we compare the performance of several control charts jointly monitoring location and scale for observations with a location-scale distribution in a finite horizon process where a limited number of inspections is scheduled. For an investigated set of symmetric distributions, our results show that the joint control charts implementing a signed-rank SR statistic and either the Downton’s D estimator or the average absolute deviation MD from median generally perform the best. An example illustrates the implementation of the control charts on a simulated dataset.

One-Sided Shewhart-type Charts for Monitoring the Coefficient of Variation in Short Production Runs

Monitoring the coefficient of variation is an effective approach to Statistical Process Control when the process mean and standard deviation are not constant but their ratio is constant. Until now, research has not investigated the monitoring of the coefficient of variation for short production runs. Viewed under this perspective, this paper proposes a new method to monitor the coefficient of variation for a finite horizon production by means of one-sided Shewhart-type charts. Tables are provided for the statistical properties of the proposed charts when the shift size is deterministic. Two illustrative examples are given in order to illustrate the use of these charts on real data.

Solving a finite horizon EPQ problem with backorders

This paper presents an alternative approach to solve a finite horizon production lot sizing model with backorders using Cauchy-Bunyakovsky-Schwarz Inequality. The optimal batch size is derived from a sequence number of batches. We prove that a constant batch size policy with one fill rate is better than the variable batch sizes with variable fill rates. Finally, a practical approach is proposed to find the optimal solutions for a discrete planning horizon and discrete batch sizes.

A partial backlogging production-inventory lot-size model for deteriorating items with time-varying production and demand rate over a finite time horizon

In this article, I extend Balkhi ((2001), ‘On a Finite Horizon Production Lot Size Inventory Model for Deteriorating Items: An Optimal Solution’, European Journal of Operational Research, 132, 210–223), by considering a generalised mathematical production-inventory model for deteriorating items with partial backlogging. The demand, production and backlogging rates are assumed to be continuous and varying with time. The objective is to find the optimal production restarting and stopping time to keep the total relevant cost as low as possible. To ascertain the optimal solution exists, the conditions for the total relevant cost in the system which attains its global minimum are provided. In addition, based on the minimum total relevant cost, an alternative among the proposed four cases is also suggested. Finally, a numerical example and sensitivity analysis is illustrated and some management insights are presented.

A finite horizon production model with variable production rates and constant demand rate

In this paper we present a finite horizon single product single machine production problem. Demand rate and all the cost patterns do not change over time. However, end of horizon effects may require production rate adjustments at the beginning of each cycle. It is found that no such adjustments are required. The machine should be operated either at minimum speed (i.e. production rate = demand rate; shortage is not allowed), avoiding the buildup of any inventory, or at maximum speed, building up maximum inventories that are controlled by the optimal production lot size.

On a finite horizon production lot size inventory model for deteriorating items: An optimal solution

A generalized production lot size inventory model for deteriorating items over a finite planning horizon is considered. The demand, production, and deteriorating rates are assumed to be known and continuous functions of time. Shortages are allowed and completely backlogged. The conditions under which the system total cost attains its (unique) global minimum are derived. An example which illustrate the applicability of theoretical results is also introduced.

Expansion formulae for characteristics of cumulative cost in finite horizon production models

We consider the expected value and the tail probability of cumulative shortage and holding cost (i.e. the probability that cumulative cost is more than a certain value) in finite horizon production models. An exact expression is provided for the expected value of the cumulative cost for general production functions. This expression is then used to compute the optimal production rate when the production function is linear. An expansion formula (whose coefficients can be obtained recursively) is provided for the tail probability. Examples are given to illustrate the results.

Stability measures for rolling schedules with applications to capacity expansion planning, master production scheduling, and lot sizing

This contribution discusses the measurement of (in-)stability of finite horizon production planning when done on a rolling horizon basis. As examples, we review strategic capacity expansion planning, tactical master production scheduling, and operational capacitated lot sizing. An iterative method to dampen the nervousness is presented.

A Deterministic Multi-Period Production Planning Model with Piecewise Concave Production and Holding-Backorder Costs

A single product, finite horizon production planning model with known requirements is considered. Production and holding-backorder cost functions are assumed to be piecewise concave, thereby allowing an arbitrarily close approximation to a wide range of cost functions which one might encounter in practice. In each period production, inventories and backlogged orders may not exceed prescribed levels. Production (inventory) breakpoints are the endpoints of the intervals over which the production (holding-backorder) cost functions are concave. It is shown that there is an optimal production schedule which has the property that between successive periods in which ending inventories are at inventory breakpoint levels there is at most one period in which production is not at a production breakpoint level. This property, which is an extension of recent results obtained by Florian and Klein [Florian, Michael, Morton Klein. 1971. Deterministic production planning with concave costs and capacity constraints. Management Sci. 18 (1, September) 12–20.] and Love [Love, Steven F. 1973. Bounded production and inventory models with piecewise concave costs. Management Sci. 20 (3, November) 313–318.], suggests a straight-forward dynamic programming algorithm for obtaining an optimal solution.