Minimization of expected total SPC cost by optimizing deployed manpower

This article proposes a control chart (referred to as M-chart) that minimizes the expected total cost by optimizing the amount of allocated manpower (equipped with adequate measuring instrument) in a statistical process control (SPC) scheme, as well as the sample size, sampling interval and control limits of the control chart. Unlike in the economic chart designs, most input specifications required by the design of an M-chart can be easily determined by practitioners. More importantly, the use of the M-chart will not in any sense increase the difficulties for operators to run and understand the control chart. The design of an M-chart also takes into account the probability distribution of the random process shifts. An example shows that the M-chart can reduce the total cost by about 70 percent, on average, compared to the conventional control charts. It is also found that, in most SPC schemes, the allocated amount of manpower is far less than needed and, consequently, the total cost can be significantly reduced by increasing SPC manpower. Even though the M-chart is discussed in detail only for the X_ chart detecting mean shifts, the general idea can be applied to many other charts (e.g., the CUSUM and EWMA charts) and to monitoring both process mean and variance.