Statistical process control Control charts Autocorrelation

Key Words
Statistical process control; Control charts; Autocorrelation; Nonconforming units.
Introduction
Industrial processes often have complex behaviors, including autocorrelation, where successiveunits are related to the previous one. When such an autocorrelation exists, standard control charts may exhibit an increased frequency of false alarms. There is an increased likelihood that the data will exhibit autocorrelation in systems where the process time is longer than the time between sample collection (I). Autocorrelation, especially in samples for units produced closer together in time, may result from many factors, including work shift and operator rotations, mechanic or technician changes, and functions within the machinery itself. Several researchershave examined control chart behavior in the presence of autocorrelation (1-8). If process measurements are autocorrelated, then standard constructions of control charts will violate the assumption that samples are independent (9). The type 1 error rate for control charts is sensitive to autocorrelated data; thal is, control charts are subject to increased false alarms and, hence, shorter average
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Copyright
@ 2000 by Marcel Dekker, Inc.
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NEMBHARDAND NEMBHARD and samples of containers are generally extracted every other hour (and occasionally hourly) on each shift. The first shift operates 18 h and the second shift operates6 h. Correspondingly, the sample size is nine for first shift and three for second shift. Table I presents the number of nonconformities for each category observed in 172 consecutive samples of containers. Most often, the sample size is 12, but, occasionally, more samples were extracted if operators suspected problems (samples 36, 69, 114, 123, 126, 130, and 158). Fewer samples were extracted if the process was shut down earlier or if the operator simply did not take it (samples 50, 100,101,105,122,124, 134,137-141,146,148,151, 160163, 167, and 169). Quality rating systems have been developed for many industrial situations to define, classify, and evaluate nonconformities. Classification systems are provided in various military and International Organization for Standardization (ISO) standards to describe quality, dependent on the complexity and use of the product. For our investigation, we group nonconformities into three classesas follows: Class A-critical: a nonconformity that will result in a hazardous or unsafe condition when used or nonconformity that will obstruct the full capabilities of the product Class B-major: a nonconformity that is likely to result in a failure or retard the use of the product in its end use. Class C-minor: a nonconformity other than critical or major that is not likely to affect the usability of the product in its eTlduse. This system is based on a slight modification of those in standard texts (2,10). Demerits weights are assigned to each of these classifications, where it is assumed that the nonconformities in one category are independent of nonconformities in another category ( I ). Numerical weights may be a function of costs, such as repair, replacement, or operating costs based on Iong-term nonconformity rates, or-£ustomer requirements. Typically, weights increase as the degree of severity increases (e.g., a weight of 9 for critical and a weight of 1 for minor). The actual weights used for the containers in this study were wA = 10, WB= 3, and WL'= I, for outer-, middle-, and inner-seal leaks, respectively. These weights were decided on by company management to reflect their current relative levels of concern for each failure type. These weights may be readily replaced with weights based on economic analyses once such information becomesavailable.
Quality Engineering, 13(2), 179-190 (2000-01)
A DEMERITS CONTROL FOR AUTOCORRELATED
David A. Nembhard and Harriet Black
CHART DATA
Nembhard
Department of Industrial Engineering University of Wisconsin-Madison 1513 University Avenue Madison, Wisconsin 53706-1572
run lengths (ARL). Even at low levels of correlation, dramatic disturbances can occur in the chart properties ( I). In this article, we develop a moving-centerline demerits (MCD) control chart and construct such a chart for nonconformities data from an industrial production system. The MCD chart is an extension of the demerits control chart ( U chart). We note that the u chart is typically referred to in the literature as a nonconformities per unit chart. We use the capital letter U to indicate that a demerits system has been applied to the u chart. The MCD chart is distinct, however, in that it is appropriate to use with autocorrelated data. An effective remedial measure, when autocorrelation is present, is to build a model that accounts explicitly for the autocorrelative structure of the time series. One approach for control charting with autocorrelated data recommends maintaining two charts: one for plotting the dimensions of the process with the original time-series model and another traditional ~hart for the residuals of a fitted time-series model. Given an appropriately fitted time-series model, the residuals should not be correlated. Thus, meaningful fluctuations in the process, due to assignable causes,will be captured in the residuals. However, the time and resource limitations often involved in industry applications may make this approach unmanageable. An alternative approach is to maintain a single control chart that is equivalent to the two-chart approach using time-