Designing quality inspection in short-run assembly processes of wrapping machines

Manufacturing companies are increasingly focused on producing high-quality, fault-free products that meet customer needs. Defects in the final product, particularly those generated during production processes, can have a dramatic impact on the product itself, both in terms of quality and cost. From this perspective, designing inspection procedures that are effective in detecting defects occurring in different stages of production has always been a great challenge and a pivotal factor in being competitive in the market. In recent years many authors have focused on defects generated during assembly processes and, in particular, many of these studies confirm that the human factor plays a critical role in causing defects. Studies in the electromechanical field have shown that defects caused by operators during assembly operations can be predicted through design complexity factors (based on process, design, and human factors). Recently, these defect prediction models have been used to obtain reliable predictions of defects probabilities in short-run assembly manufacturing processes, for which traditional statistical process control (SPC) techniques are not appropriate. By combining these probabilities with different parameters related to the effectiveness and cost of inspection, the best inspection strategies can be evaluated and selected according to the requirements imposed by the manufacturer. The research here presented investigates the development of a probabilistic model of defect generation specific for assembly processes of wrapping machines, and the subsequent exploitation for designing effective and affordable inspection strategies. The production of wrapping machines can be classified as a short-run assembly process due to the high degree of customization, to such an extent that each machine may be considered almost unique. Moreover, the total number of such customized machines produced in a year, typically, does not reach one hundred units. Accordingly, due to the limited historical data available and the mentioned difficulty in applying the main SPC techniques, the planning of product quality inspections represents a remarkable problem in this industrial sector. In this view, this study aims to answer the following Research Questions (RQ): RQ1: Is there a relationship between process or design complexities and the generation of defects in the assembly processes of wrapping machines? RQ2: If such a relationship exists, which is the most suitable mathematical model to describe it? RQ3: Is this mathematical model similar to those existing in the scientific literature? RQ4: How the knowledge of the defects that may occur in the process can influence the design of inspection strategies? The proposed analysis focuses on the assembly of a single part of the wrapping machine: the pre-stretching device. The methodology used involves the decomposition of the assembly process into several assembly steps (m), also called workstations, in which a specific operation is performed. For each workstation two complexity parameters are defined, namely the process and the design complexity factors. Then, basing on experimental data, a prediction model relating the observed defects in each workstation and these two factors is defined. In the case of wrapping machines, the exponential behaviour of the model is demonstrated. Consequently, it can be used to obtain reliable estimates of the probabilities of occurrence of defective-workstation-output (pi) in each workstation i. Such probability pi is a physiological characteristic of the process in normal working conditions and concerns the quality of the i th workstation. Each i-th workstation may be inspected using different quality control techniques, according to the typology of defect to be detected. Two types of errors are associated with each i-th inspection: (i) the error of erroneously classifying a good workstation-output as a defective one, which is known as type-I error (αi); and (ii) the error of erroneously classifying a defective-workstation-output as a good one, which is known as type-II error (βi). The probabilities αi and βi are estimated depending on the characteristics of the inspection procedure and the technical skills and/or experience of the inspectors. These parameters (pi, αi and βi) may be combined in a probabilistic model, and two indicators which depict the overall effectiveness and economic convenience of an inspection strategy may be obtained. The first one, D, is the mean total number of defective-workstation-outputs which are erroneously not signaled in all the inspections. Considering that it represents the mean number of defects remaining in the product after the controls, it is an indication of inspection effectiveness. The second one, Ctot, is the total cost of the inspection strategy, which takes into account the cost of the inspection activity, as well as the cost for repairing the defects, both those actually present and due to inspection errors, and the cost of undetected defects, including image loss and after-sales repairs costs. Such indicator easily allows the producer to determine whether the whole-strategy is efficient, i.e., economically affordable. The proposed methodology plays a key role not only in the early design stage of new quality inspections for the assembly of new devices or new wrapping machines, but also in improving existing inspection strategies. In fact, through the use of the two indicators of effectiveness and affordability, the most critical workstations can be easily detected. As a result, inspection engineers are driven to identify alternative control procedures in order to make the inspection strategy more effective and cost-efficient.