On-Line Process Control of the Number of Non-Conformities in the Inspected Item

Abstract

Generally, production systems as automatic welding process, production of ceramic products, making clothes use automatic control and to evaluate the quality of their production processes, they employ on-line process control. The control system consists of a periodic inspection of one item after every m produced items. The number of non-conformities is monitored in the inspected item and if it exceeds the control limit, then it is decided that the process is out-of-control and the process is stopped for adjustment, otherwise the production continues. The process starts in-control with a fixed non-conformities rate and, after an assignable cause, this rate increases leading the system to operate out of control. The process remains in these conditions until the change is detected and the process adjusted. After adjustment, the process returns to operate in-control. The aim of this paper is to present an economic approach to monitor the rate of non-conformities in a production by on-line process control. To design such type of process, an average cost per item produced is achieved through the properties of an ergodic Markov chain and the two required parameters: the inspection interval and the upper control limit are obtained by minimizing the average cost per produced item. A numerical example illustrates the proposal. It was identified the most important factors which result a considerable impact on the average cost per item: the probability of a shift in the parameter of Poisson distribution; cost to send non-conforming items to the customers; the in-control non-conformity rate; the specification limit and the cost of adjustment.

Economical control chart with supplementary rules to monitor the average number of defects

“…The present article extends the work of Vasconcelos et al [17] with two sets of limits (viz., warning and control limits) and an additional stopping process rule based on the policies proposed by Western Electric [18]. Properties involving finite Markov chains with discrete state space to determine an optimum strategy of control in a process were used.…”

“…Costs in the current model follow a similar structure to those reported in earlier studies by Taguchi et al [16]; Nayebpour and Woodall [10]; Vasconcelos et al [17]. The following costs are defined: inspection cost per item (C I ), adjustment cost (C a ), production cost of a non-conforming item (C nc ), and the cost of discarding an inspected item (C d ).…”

“…For this Table 1 Cost variations obtained from m 0 , W 0 , C 0 , and h 0 varying one of the parameters or one of the process costs scenario, the optimal cost per item produced is $0.2463. For comparison purposes, an optimum policy of m 0 =57 and C 0 = 6, obtained by Vasconcelos et al [17], with an average cost per item of $0.2658 is the situation obtained for the case in which the warning limit is equal to the control limit (W=C); consequently, h=0. This cost is approximately 8 % higher than the proposed model.…”

“…This policy provides a control strategy that is approximately 8 % more economical (per unit) than the model that solely applies the conventional decision rule proposed by Vasconcelos et al [17]. Our proposal aimed at developing a model that obtains the following optimum parameters: m 0 (the inspection interval), C 0 (the control limit), W 0 (the warning limit), and h 0 (the size of the inspection sequence).…”

“…In his proposal, the number of non-conformities follows a Poisson distribution. Vasconcelos et al [17] developed an on-line process control system to monitor the number of non-conformities in an inspected item. The parameters reflecting the control limit (C) and the interval inspection (m) are determined by optimization.…”