Richard L. Marcellus

Bayesian monitoring to detect a shift in process mean

A Bayesian analogue of the Shewhart X-bar chart is defined and compared with cumulative sum charts. The comparison identifies types of production process where the Bayesian chart has better expected performance than the cumulative sum chart. Implementing the Bayesian chart requires more detailed knowledge of the process structure than is required by the best-known types of charts, but acquiring this information can yield tangible benefits. Copyright

Performance Measures for ―X Charts with Asymmetric Control Limits

Theoretical and empirical justification is given for using asymmetric control limits for certain types of production processes. The following are also discussed: the sensitivity of the performance measures to the process and control parameters, the advantages and disadvantages of using asymmetric control limits, and the construction of tradeoff curves to characterize performance. The justification is given in terms of a collection of quantitative performance measures for ―X charts with asymmetric control limits. The performance measures quantify the false-alarm frequency, the sensitivity to out-of-control conditions, and the resources required for sampling. Copyright

Operating characteristics of X-bar charts with asymmetric control limits

When the assumptions behind the Shewhart chart are not met, policies other than the traditional 3-sigma limits may enable speedier and more economical detection of process change. If a process has unequal probabilities of downward and upward shifts, downward shifts of differing magnitude from upward shifts, and/or standard deviations after downward shifts different from those after upward shifts, then increases in the in-control average run length and decreases in the out-of-control average run length are simultaneously achievable with control limits placed at unequal distances from the process mean. The magnitude of these improvements is investigated for several types of process. The results are then extended to median charts for processes with output that is not normally distributed.

Scheduling identical jobs on uniform parallel machines with random processing times

Abstract For the problem of scheduling identical jobs on a set of uniform parallel machines with random processing times, methods are given for optimizing the expected sum of weighted completion times and the probability of meeting a common due date.

Performance Measures for a Single-Change-Point Nonstationary Control Chart Policy

Single-change-point policies are defined as control chart policies where the charting procedures are changed exactly once at a preselected time. A special class of these policies is studied, namely those where decisions whether or not to look for an assignable cause are always based on a single sample. For these policies, the paper presents average run lengths, the expected number of false alarms per production cycle, the expected number of samples, the expected number of sampled items, and the expected time required to detect an assignable cause. Theoretical conditions are given for the single-change-point policies to have a better performance than stationary policies. In addition, numerical exploration reveals that the largest improvements occur when assignable causes result in a relatively small shift in the mean and the expected occurrence time of the assignable cause is relatively small with a low variability. This, along with previous work by other authors, shows that extensive investigation of nonstationary policies would be worthwhile. The results may be directly extended to all charts of Shewhart type.

On Statistical Process Control Design

A foundation is laid for making the characterization of physical relationships among design variables, process parameters, and performance variables a primary focus of designing statistical process control (SPC) systems. Such characterizations will make it possible to construct and investigate collections of performance measures that managers can use to evaluate and choose policies. An example model is given that describes the interacting sources of variability in an SPC system using X-bar and standard deviation charts. This is followed by a collection of performance measures, examples of how they can be investigated through trade-off curves, and an illustration of interplay between the example model and the behavior of a real system.

A markov renewal approach to the poisson disorder problem

In the Poisson disorder problem, a decision maker observes a Poisson process whose intensity changes at some random time. After the change, the process is considered to be in a state of disorder. The decision maker wishes to use one action before disorder and another, different, action after disorder. However, the change to disorder produces no direct discernible evidence — the decision maker perceives only the events of the Poisson process. The decision to switch from one action to the other must be based exclusively on the evidence provided by these observed events. For many cost functionals, an optimal policy is to change actions when the probability of disorder (given all past observations) rises above a certain level. Considering a certain Markov renewal process embedded in the disorder process yields new information about such policies.