A case study is presented for construction of the quality control charts with sub- optimum size samples obtained in a commercial brewey after measuring total.
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PAPER
Construction of quality control charts with sub-optimal size samples Mustafa ozilgen A case study is presented for construction of the quality control charts with suboptimum size samples obtained in a commercial brewey after measuring total acidity apparent extract and pH of the wort; alcohol, real extract, carbon dioxide, total acidzty and pH of the bottled beer Logarithmic transformation of the data was employed to construct the quality control charts, and centering of the data between the specification limits was assessed by means of the process capability index values. 0 1998 Elsevier Science Ltd. All rights reserved
INTRODUCTION The Shewhart control (means and range) charts are used in quality control with measured properties, to assure that the means and the range of the individual samples are confined within pre-determined limits (Table I) when the sample means are distributed normally around the population mean (Hubbard, 1990; Miller and Freund, 1985; Oakland and Followell, 1990). The central limit theorem states that ‘regardless of the distribution behavior of the individual values within their own population, distribution Food Engineering Department, University, 06531 Ankara, Turkey.
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East
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of the sample means will approach to the normal distribution as the sample size increases’ (Miller and Freund, 1985). The sample size required to achieve an acceptable near normal distribution of the sample mean around the population mean is usually four or five (Jacobs, 1990). Increasing the sample size to assure the normal distribution of the sample means may not be possible when the sample is scarce, expensive or anlayses are costly, therefore a procedure is needed for the construction of the quality control charts with the sub-optimal size data; and unfortunately there is not sufficient information in the literature discussing this issue. In this study, non-normal distribution of the sample mean values of the quality factors in wort and bottled beer will be
Table 1 Central line and control limit equations for the means and range charts based on normal distribution Lower control limit (LCL) (a)
Central line (CL)
Means chart parameters
LCL, = CL, - 30, (b)
Upper control limit (UCL)
UCL, = CL,+3o,
Range chart parameters
LCL,
