Lead time distribution in unreliable production lines processing perishable products

Abstract

The integrated analysis of quality and production logistics in manufacturing systems has recently attracted increasing interest among researchers and industrialists. It has been shown that several links exist among the manufacturing system design and the product quality, which are dominated by complex dynamic interactions. However, these interactions have never been addressed in manufacturing systems producing perishable products. The quality characteristics of perishable products deteriorate over time. Several examples of this phenomenon are found in the food industry, in semiconductor manufacturing, and in polymers forming processes. If the time parts spend in the system exceeds a certain threshold the inventory becomes obsolete and defective parts need to be scrapped. A similar problem is also found in highly dynamic supply chains. In this paper, we provide an analytical method to model the dynamics of this phenomenon in a buffered two-machines line with general Markovian machines. The main contribution is a method for the calculation of the lead time distribution, that allows us to derive predictions of the effective throughout and scrap rate. In case of two-state machines the approach leads to symbolic expressions while in case of general Markovian machines numerical solutions can be obtained. Numerical results provide relevant insights on the problem and show counterintuitive behaviors paving the way to the design of buffers for product quality

Lead-time oriented production control policies in two-machine production lines

“…We consider a system in which: i) the first machine has a single failure mode with parameters p 1,1 = 0.01 and r 1,1 = 0.1; ii) the second machine is characterized by three failure modes that occur with probability p 2,1 = 0.01, p 2,2 = p 2,3 = 0.005, and are repaired with probability r 2,1 = 0.1, r 2,2 = 0.05 and r 2,3 = 0.01 respectively; iii) the number of Kanbans is fixed at B = 50 items. As already shown in (Colledani et al, 2014b), under the single stage Kanban control policy (top box of Figure 1) the lead time distribution in a two machine line is characterized by a bi-modal distribution that has peaks at time units 1 and B − 1. The magnitudes of these peaks depend on the difference of the efficiencies of the two machines.…”

“…The lead time of a part can be computed following the approach described in Colledani et al (2014b) for lines with machines of general complexity and in Shi and Gershwin (2012) for lines with up-down machines. In this paper we give a brief overview of this approach.…”

Formal analysis of production line systems by probabilistic model checking tools

“…In other words, knowing the state of the system when a given part enters, we can calculate the probability that it will be ready (exits the system) in a given number of time units. Also in [9] a way to calculate lead time distributions is proposed. In that work however the lead time of a random part is determined assuming no knowledge on the state of the system when the part enters.…”

“…In this paper we consider production line models composed of buffers and unreliable machines with Markov behavior. Building on previous works dealing with the same or similar models (see, e.g., [1], [2], [7]- [9]), in this paper we introduce an integrated framework for formal modeling and performance analysis of such systems. Our proposal is to describe the system with a well-known and widely applied model checking tool called PRISM [13] which allows for specifying the system in terms of a DTMC, expressing and calculating performance indices, and verifying complex temporal properties of the model [11].…”