A Sampling Program to Optimize Manufacturing Plant Operations - By : Fabrice Chilly Ngamaleu,

A Sampling Program to Optimize Manufacturing Plant Operations

sampling plan

Editor’s Note

This article was one of the finalists in the “Ingenious Writers Contest” organized by SARA and Substance ÉTS. It is the popularized summary of an article entitled: Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint, co-authored by Ali Gharbi, Professor in the Department of Automated Manufacturing Engineering, École de technologie supérieure (ÉTS).


Since the industrial age in the early 20th century, the manufacturing industry has been in constant search of revolutionary management and continuous improvement methods to guarantee optimal production costs. Many researchers who have come to the sector are working on developing appropriate solutions.

A sampling program taking into account links between services was develop

Figure 1 Illustration of a manufacturing chain

The first proposed solutions were based on individualistic approaches. They considered only one department within a manufacturing plant. Departments are what makes up a factory: preventive and corrective maintenance, product quality control, supply, customers, etc. These solutions were somewhat simpler to develop and had the advantage of being easy to implement in industry. Their major disadvantage is that they did not take into account the fact that all these departments are interrelated. As a result, the solutions were less efficient and did not allow for the optimal operation of an industry.


Current interest lies in integrated approaches that simultaneously bring together several departments within the system. Although many integrated solutions to date have involved two departments, researchers have been devoting considerable effort for decades to three-department integration approaches. Management models incorporating production planning, maintenance and quality control are examples of this approach. In these models, quality control is done by inspecting all outgoing products from a chain. In other words, all products are checked one by one before warehousing. This is a 100% inspection policy.

However, is this the best approach to quality control, knowing the cost and additional work involved? In their research article, the authors questioned this method by considering a sample-based inspection, known as an acceptance sampling inspection, where a single sample from each lot of outgoing products within the production chain is inspected. Their objective was to develop a solution to minimize production costs and optimize production and maintenance planning, while ensuring customer satisfaction for good quality products.

The sampling program depend on the AOQL adopted by the client

Figure 2 Inspection at a Food Factory


The manufacturing plant studied in the article produces only one type of item. Activities have an impact on performance by gradually degrading facilities. This leads to malfunctions and increases the number of non-compliant products.

To maintain or restore plant performance, the authors considered the following preventive maintenance strategy: minimal repair (troubleshooting) and preventive maintenance performed during the setup preceding the production of each lot. They also considered a complete overhaul, which is major maintenance performed as soon as the defective item rate reaches or exceeds a given threshold.

At the end of the chain, the products are inspected. This involves inspecting the products in a random sample from each lot. If the number of defective items exceeds the acceptance threshold, the lot is rejected and then fully checked to eliminate all defective products. The proportion of defective items is compared to the value of the given threshold, indicating whether a complete system overhaul is required. The size of each outgoing lot and the size of the test sample depend on the average outgoing quality limit (AOQL) accepted by the customers.

Setup time is fixed. Troubleshooting and overhaul times are random events, based on probability distributions. The lot size in the inventory determines the production rate.

Proposed Solution

The authors used an approach well-known to manufacturing process professionals. They began with a mathematical formulation of the problem in which the complex interactions between production, stock, quality and maintenance are analyzed. They also highlighted the components of the total incurred costs, which are the cost of inventory, shortages, setup, maintenance and quality.


Figure 3 System Logic

This first step resulted in approximately thirty mathematical equations. Due to the complexity of the problem, the authors chose simulations over analytical and numerical resolution approaches. They were carried out using C ++ and SIMAN programming languages to transform the mathematical model into a set of discrete and continuous interconnected events. Afterwards, an optimization algorithm was used to obtain optimal values of the decision variables.


Figure 4 Simulation-based optimization procedure


The main contribution of this article is the model developed for the joint optimization of sampling-based production, maintenance and quality as an approach to quality control. Then come the results obtained by applying the developed model to a hands-on case.

The first results were used to validate the simulation model by analyzing the impact of a dozen variables on the problem. A total of twenty-four analyses were conducted to demonstrate the strength of the resulting solution.

The following results are part of a comparative study carried out between the model developed by the authors and models presented in the literature. As mentioned above, quality control in the literature follows a 100% inspection approach (systematic inspection of all products), whereas the approach presented here is to inspect a sample of products from each lot. With the proposed model, the products inspected represent only 17% of the lot, for an AOQL (defective products delivered to customers) of about 0.74%. In the models presented in the literature, 100% of the products are inspected, for a 0% AOQL. Inspection, inventory and shortage costs are higher for these methods, whereas the approach developed by the authors is up to 20.6% more cost efficient. This gain increases with the inspection cost. However, if the AOQL is lowered to a value of less than or equal to 0.1%, both approaches are almost economically equivalent.

The proposed sampling program allows economy up to 20%

Figure 5 Quality control in a factory


The article presents three important contributions, namely:

  • The introduction of a new approach to the quality control sampling plan in the manufacturing industry
  • A new modeling framework for complex relationships between random events
  • An approach that generates considerable savings for the industry (up to 20.6% compared to previous approaches)

The study takes into account only one quality attribute of the product, resulting in an inspection based on a single criterion. The complex nature of existing products does not always match this reality. Indeed, the quality of a shoe, for example, will be assessed both on its comfort, dimensions, mass, etc. A future challenge would be to define a way of selecting the sample within the lot to be inspected, making it possible to include all the quality requirements of the products.

Additional Information

For more information on this research, please see the following reference article: Bouslah, B., Gharbi, A., Pellerin, R. (2016). “Integrated production, sampling quality control and maintenance of deteriorating production systems with AOQL constraint.” Omega, Volume 61, pages 110-126.

Field(s) of expertise :

Optimal Control 

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