D. B. Owen

Lower confidence limits on process capability indices

Lower confidence limits are derived for the common measures of process capability, usually indicated by Cp, CPU, CPL, and Cpk. The measures are estimated based on a random sample of observations from the process when the process is assumed to be normall..

On the distributions of the estimated process capability indices

The exact distributions of the estimated process capability indices are presented and their means, variances, and mean-squared errors are given. The basic assumption is that the process measurements are taken from a normal distribution. Theresults in this article are useful in evaluating process capability.

Tables for normal tolerance limits, sampling plans, and screening

Tables for Normal Tolerance Limits, Sampling Plans, and Screening. By Robert E. Odeh and D. B. Owen. New York and Basel, Marcel Dekker, 1980. x, 316 p. 26 cm. Unpriced.

Survey of Properties and Applications of the Noncentral t-Distribution

Applications are outlined of the noncentral t-distribution to tolerance limits, to variables sampling plans, to confidence limits on a quantile, to confidence limits on a proportion, to the distribution of the sample coefficient of variation, and to the power of Students t-test. The basic assumption is that there is available a random sample from a normal distribution with mean and variance unknown. Some of the mathematical properties of the noncentral t-distribution are also outlined. An extensive bibliography has been prepared and cross-referenced to several review journals and books. The bibliography covers references to tolerance limits and sampling plans based on the normal distribution whether or not the noncentral t-distribution is directly involved. Some selected references to Students t-distribution are also included.

A table of normal integrals

Integrals of functions of the univariate, bivariate, trivariate and multivariate normal densities are given. Both indefinite and definite integrals are included.

On Bias Reduction in Estimation

Abstract A general procedure for reducing the bias of point estimators is introduced. The technique includes the “jackknife” as a special case. The existing notion of reapplication is shown to lack a desirable bias removal property for which it was originally designed. Proper reapplication is proposed to conform to the general notion of higher order bias elimination and an interesting algorithm for the correct method is defined. Illustrative examples are drawn from ratio estimation, reliability and truncated distributions. The reduced mean square error which attracted some attention to the jackknife is present in the generalization for some applications.

Tables Using One or Two Screening Variables to Increase Acceptable Product Under One-Sided Specifications

A performance variable with a one-sided specification cannot be measured directly, but one or two related variables (called screening variables) can be measured. The screening variables are used to select product in order to raise the proportion of unit..

A study of a new process capabily index

A new process capability index is proposed that takes into account the location of the process mean between the two specification limits, the proximity to the target value, and the process variation when assessing process performance. The proposed index is compared to other indices on several properties. The proposed index is estimated based on a random sample of observations from the production process when the process is assumed to be normally distributed. The 95% lower confidence limits for the proposed index are derived for given sample sizes and its estimates.

Improved Factors for One-Sided Tolerance Limits for Balanced One-Way ANOVA Random Model

Abstract : The authors investigate various techniques for determining a tolerance limit L such that the probability is gamma that at least a proportion P of a population produced in batches exceeds L. First, they evaluate the approach of Lemon for this problem and then present alternative approaches. If the variance ratio is known, one may obtain exact tolerance limits. For settings where the variance ratio is not necessarily known, they describe a procedure, based on the Satterthwaite approximation, for obtaining conservative tolerance limits. (Author)

Variables Sampling Plans Based on the Normal Distribution

Sampling Plans are considered which call for the acceptance of a lot of material if both – ks ≥ L and + ks ≤ U, where L and U are the lower and upper specification limits and where and s are the sample mean and standard deviation and k is an appropriate constant. Some errors that need to be corrected in previous work are pointed out in interpretation of the mathematical formulas before plans of the type described can be properly applied. Tables are given for the constant k under two different circumstances. Table II applies when the sum of the proportions defective in the two tails of a normal distribution is to be controlled. Table III applies when each tail is to be controlled below preassigned values, i.e., so that one can say with probability y that the proportion in the lower tail (below L) of accepted lots does not exceed a preassigned value and simultaneously the proportion in the upper tail (above U) does not exceed its preassigned value. The same constants, in Table III, apply when all the defect...