Optimal Use of Control Charts for Controlling Current Production

Abstract

A model is developed consisting of all the costs incurred when fraction-defective control charts are utilized to control current production: cost of sampling, cost of not detecting a change in the process, cost of false indication of change, and cost of re-adjusting detected changes. It is suggested that such control charts can be utilized in an optimal way, if those combinations of sample size, frequency of sampling and extent of control limits from process average will be used that provide the minimum total cost. It is further suggested that, by applying any specific cost data to this model, these optimal decision values can be easily evaluated by computer enumeration.

The development of a destructive sampling method designed for high quality production processes (DSM-HQ)

“…One of the main negotiable aspects of the method is tied to the risk of a defective unit reaching the customer which is also related to the potential cost savings to the producer. The development of DSM-HQ begins with a cost model similar in concept to the economic SPC developed by Girshick and Rubin (1952), Duncan (1956), Ladany (1973), Lorenzo and Vance (1986), Von Collani (1988) and many others. The complexity and poor statistical properties of economic SPC as noted by Keats et al (1997) have been avoided or recognized in the development and specification of DSM-HQ by incorporating negotiable aspects of the procedure in the place of optimality and special algorithms.…”

Optimal combined set-up and calibration policy

“…Substituting (2) in (3), we obtain P(D,,) = 1 -p {LSLx -__ta.o-bn (4) and the expected number of non-conforming units produced during a cycle of N repetitions, E(D), assuming one product produced per repetition, is:…”

“…In the context of controlling the process with a control chart, Duncan [1] determined a process cost minimisation sampling procedure (distance of control limits, sample size, and frequency of sampling) for sample-mean and sample-range charts, so that in a randomly changing process out-of-control indication signalled the need to search for assignable causes, and eventually to reset the process. Ladany [2] determined a similar steady-state approach in conjunction with fraction defective control charts. Moreover, Ladany and Bedi [3] examined his results to determine when fixed time-interval scheduled set-ups should be used, as opposed to non-scheduled resets, and then in [4] investigated dynamic transient state policies.…”

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

“…The first work that deals with a control chart for a process with a finite horizon was by Ladany [13], who studied the economic optimization of a simple Shewhart type p-chart for short runs. This early work was extended by Ladany and Bedi [14], who introduced a similar model where the duration of the production run was also a decision variable.…”