Asymmetric control limits for small samples

YAZICI B., Kan B.

QUALITY & QUANTITY, cilt.43, sa.5, ss.865-874, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 5
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1007/s11135-008-9193-8
  • Dergi Adı: QUALITY & QUANTITY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus
  • Sayfa Sayıları: ss.865-874
  • Anahtar Kelimeler: Control charts, Non-normality, Skewness correction (SC), Individuals control charts (I Chart), Skewed distributions, CONTROL CHARTS, NONNORMALITY, XBAR
  • Anadolu Üniversitesi Adresli: Evet

Özet

When designing control charts, it is usually assumed that the measurement in the subgroups are normally distributed. The assumption of normality implies that the control limits for a chart for sample averages will be symmetrical about the centerline of the chart. However, the assumption of an underlying normal distribution of the data may not hold in some processes. If the measurements are asymmetrically distributed then the decision maker may choose different actions. One thing that can be done is to consider the degree of skewness. If the nature of the underlying distribution is skewed, then the traditional Shewhart individuals chart may not be valid. This paper presents a technique for constructing appropriate asymmetric control limits when the distribution of data cannot be assumed to be a normal distribution. Meanwhile, it proposes a skewness correction method for the generated Burr, lognormal and exponential distributions. Some numerical calculations are generated for n = 2, 3, 4 by using MATLAB.