Non-normality has a significant effect on the performance of control charts for averages. The design considerations for a control chart for averages must include recognition of the degree of non-normality of the underlying data. The performance of a control chart may be judged on its ability to correctly identify the probabilities of assignable causes of variation and chance causes of variation in a process. This paper examines the effects of non-normality, as measured by skewness and kurtosis, on the performance, and hence the design, of control charts for averages and provides an alternative method of designing charts for averages of data with non-normal distributions.

Non‐Normality and the Design of Control Charts for Averages*

(1975). MIL-STD-414 Sampling Procedures and Tables for Inspection by Variables for Percent Defective. Journal of Quality Technology: Vol. 7, Standards and Specifications, pp. 51-60.

MIL-STD-414 Sampling Procedures and Tables for Inspection by Variables for Percent Defective

Reviews of Standards and Specifications: MIL-STD-414 Sampling Procedures and Tables for Inspection by Variables for Percent Defective

The effect of nonnormality on E(X) and R charts is reported. The effect of departure from normality can be examined by comparing the probabilities that E(X) and R lie outside their three-standard-deviation and two-standard-deviation control limits. Tukey's lambda -family of symmetric distributions is used because it contains a wide spectrum of distributions with a variety of tail areas. The constants required to construct E(X) and R charts for the lambda -family are computed. Control charts based on the assumption of normality give inaccurate results when the tails of the underlying distribution are thin or thick. The validity of the normality assumption is examined by using a numerical example. >

Robustness of mean E(X) and R charts

Optimal acceptance sampling plans for log-location-scale lifetime models using average risks

Acceptance sampling plans based on the normal distribution have been available since 1955 and before. Yet reports of potential users indicate a general lack of enthusiasm for their application. There is the uncertainty of the assumption of the normal distribution, but the difficulties users have encountered are attributable more to the translation from the standardized deviate to proportion defective than with the probabilities involved. Some possible ways of adjusting for this are discussed. Sampling plans for truncated life tests based on the exponential, normal, lognormal, gamma, Weibull, etc., distributions are also available, as are disbribution-free life test plans based on increasing or decreasing failure rate distributions. These are extremely useful and further extensions of these ideas are in the offing. For the normal distribution, plans have been devised which control each tail of the distribution to separate levels. These plans are useful in the very common situation where defectiveness measu...

D. B. Owen

Papers

Summary of Recent Work on Variables Acceptance Sampling with Emphasis on Non-normality