Using economically designed Shewhart and adaptive ―X charts for monitoring the quality of tiles

Abstract

This paper presents the economic design ofX control charts for monitoring a critical stage of the main production process at a tile manufacturer in Greece. Two types ofX charts were developed: a Shewhart-type chart with fixed parameters and adaptive charts with variable sampling intervals and/or sample size. Our prime motivation was to improve the statistical control scheme employed for monitoring an important quality characteristic of the process with the objective of minimizing the relevant costs. At the same time we tested and confirmed the applicability of the theoretical models supporting the economic design of control charts with fixed and variable parameters in a practical situation. We also evaluated the economic benefits of moving from the broadly used static charts to the application of the more flexible and effective adaptive control charts. The main result of our study is that, by redesigning the currently employed Shewhart chart using economic criteria, the quality-related cost is expected to decrease by approximately 50% without increasing the implementation complexity. Monitoring the process by means of an adaptiveX chart with variable sampling intervals will increase the expected cost savings by about 10% compared with the economically designed Shewhart chart at the expense of some implementation difficulty.

Evaluation of CUSUM Charts for Finite-Horizon Processes

“…In addition to the Truncated ARL and ATS a potentially useful characteristic of a control chart in short runs, which has already been used in practice by Nikolaidis et al (2007), is the average number of false alarms during the production run, F. For the Shewhart chart, this measure is simply…”

“…To illustrate the model and the measures of performance developed in the previous sections, consider the application presented in Nikolaidis et al (2007), which refers to the monitoring of the tile formation process at a major tile manufacturer in Greece. A critical stage of tile formation is the press operation, which is controlled indirectly through the homogeneity of tile penetrability after stamping.…”

“…According to the analysis of Nikolaidis et al (2007), X is normally distributed with µ 0 = 0.0308 mm and σ = 0.0092 mm. An assignable cause may shift the process mean to µ 1 = µ 0 + δσ = 0.0446 mm (δ = 1.5).…”

Bayesian np control charts with adaptive sample size for finite production runs

“…As a real case application, Nikolaidis et al 21 presented a detailed study for monitoring a critical stage of the main production process at a tiles manufacturer in Greece. To improve the current monitoring of the process, the economically optimal design parameters of the static and Bayesian schemes, given the relevant costs, were provided.…”

The performance of the Shewhart sign control chart for finite horizon processes

“…More complicated control charts based on the Bayes Theorem and the continuous Bayesian updating of the out-of-control operation probabilities have also been proposed by Calabrese [2], Makis [15], Nenes and Tagaras [18], Tagaras [22], Tagaras and Nikolaidis [23] and Celano et al [4]. An application of these control charts to an actual production process is presented in Nikolaidis et al [21].…”