MACHINE EFFICIENCY

Machine Efficiency

Machine Efficiency

One of the key methods for process quality control is the control chart technique, which may be considered as a graphical expression of statistical hypothesis testing. Since 1924 when Dr. W. A. Shewhart presented the first control chart , various control chart techniques have been developed and applied in process control. The major function of control charting is to detect the occurrence of assignable causes so that the necessary corrective action may be taken before a large number of non-conforming products are manufactured. When a control chart is used to monitor a process, three parameters should be determined: the sample size (n), the sampling interval between successive samples (h), and width of control limits (k). Shewhart suggested 3-sigma control limits as action limits and sample sizes of four or five, leaving the interval between successive samples to be determined by the practitioner.

Duncan proposed the first economic control chart design model for determining the sample size (n), the interval between successive samples (h), and the width of control chart limit (k) which minimise the average cost when a single out-of-control state (assignable cause) exist. Duncan's cost model includes the cost of sampling and inspection, the cost of defective products, the cost of false alarms, the cost of searching for assignable causes, and the cost of process correction. However, various assumptions regarding manufacturing processes and their cost and operating parameters have been made since Duncan's model. Numerous authors have made a wide variety of changes to Duncan's modelling assumptions to better reflect different situations encountered in manufacturing. For example, There are situations where process failure mechanism can be non-exponential (Weibull distribution; Hu , Banerjee and Rahim , and others, gamma distribution; Hajaj et al. , and so on). In some case, there are different assignable causes which shift the process mean by different amounts, also, different cost and restoration procedures required to repair the process for different shifts (Duncan , Jaraidi and Zhuang ). In some models an assumption is made where, the process is stopped while out-of-control signals are being investigated (Knappenberger and Grandage ). Some reviews of the early works on economic design of classical control charts can be found in and . Additionally, there are economic control charts for attributes .

Duncan's model makes the following assumptions: there are only two states for the process: the in-control state (E(X) = µ = µ0) and an out-of- control state defined by µ = µ0 ± ds; there is a single assignable cause for the shift in the mean to the out-of-control state. The process starts in the in-control state; the time to the next occurrence of the assignable cause is an exponentially distributed random variable with mean 1/?; and if a point plots outside the control limits (that is, if either or if ), the process remains in operation during the search for the assignable cause . The optimisation procedure and the determination of optimum economic control chart parameters in Duncan's model have been explained previously in . Input and output parameters are presented in this model ...