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Pearn et al. (Kotz and Johnson, Journal of Quality Technology 24: 216–233, 1992) proposed the process capability index C pmk , and investigated the statistical properties of the natural estimator for stable normal processes with constant mean μ . Chen and Hsu (Communications in Statistics: Theory and Methods 24: 1279–1291, 1995) showed that under general conditions the asymptotic distribution of the natural estimator is normal if μ ≠ m , and is a linear combination of the normal and the folded-normal distributions if μ = m , where m is the mid-point between the upper and the lower specification limits. Write (Theory & Methods 27: 1781–1789; 1998) derived the probability density function of the natural estimator under normality assumption. In this paper, we consider a new estimator for stable processes under a more general and realistic condition in which the information P ( μ ≥ m ) = p , 0 ≤ p ≤ 1, is given. We investigate the statistical properties of the new estimator. We obtain the exact distribution, the cumulative distribution function, and the probability density function under normality assumption. We also calculate the expected value and the mean square error of the new estimator for some commonly used parameters.

Process capability indices C p and C pk are widely used in statistical quality control to assess the capability of a process. These indices are defined, based on the assumption that the quality characteristic follows a normal distribution. In this paper two new capability indices are considered, which do not depend on any distributional assumptions. The estimation and asymptotic properties of the estimators of these indices are investigated. Two examples are given to illustrate the importance of the given indices and their computational procedures.

This paper presents statistical inference procedures from S pn , a process capability index for asymmetrical processes proposed by Boyles. From the frequentist perspective, a conservative lower confidence bound is given. From the Bayesian perspective, the SIR algorithm is used to obtain the posterior distribution of S pn . Both procedures are illustrated by simulations and examples.

A Markov Renewal Process ( MRP ) is used to obtain the time dependent probabilities and the availability of a K -out-of- N :G system with exponential failures and general repairs. A special case of Erlang-2 repairs is provided to illustrate the results.

A rational selection of a probability distribution constitutes a major problem. Often a distribution function is selected which fits well to the observed data. In other cases the availability of statistical methods determines the model. Finally, in many fields of application there are certain traditional practices concerning the selection of probability distributions. This paper treats exemplarily how a probability distribution can be selected by considering the available information about a given situation on the one hand and taking into account the amount of ignorance on the other hand.

Murthy and Sarma (Assam Statistical Review 12: 1–5, 1998) proposed and studied two biased estimators for the expectation of the normal distribution N ( μ , σ 2 ) when the coefficient of variation is known and is given by . Their estimators for small samples were found to be erroneous on account of a simplification and an analytical error. In this note, these errors are pointed out and corrected. For the corrected estimator the values of the relative efficiency for and sample size n = 2(1)25(5)100 are calculated and displayed in a table.

Some recent studies have proved that charts with variable sample size ( VSS ) detect moderate or larger shifts in normal and stable processes more quickly than the Standard Shewhart ( SS ) chart. But the statistical efficiency of charts, the speed at which they detect smaller shifts of the process mean are poor. In this paper a special type of Markov dependent sample size ( MDSS ) chart is discussed that can detect even small shifts faster than other matched charts. Additionally, conditions are outlined which make the MDSS chart signal similar as the SS or VSS chart during the in-control period. Numerical illustrations indicate that the MDSS chart is substantially more efficient than SS and VSS charts.

In this paper, standard Cusum charts with head start value zero are compared with fast initial response (FIR) Cusum charts proposed by Lucas and Crosier (Technometrics 24: 199–205, 1982) from the viewpoint of the false alarm probability function. The focus in this comparison is conservativeness. The concept of conservativeness is based on the relationship between the in-control ARL and the false alarm probability function by regarding the Cusum statistic as a Markov process. The comparison shows that standard Cusum charts are conservative in contrast to FIR Cusum charts. Moreover, the concept of false alarm probability function provides an easy probabilistic interpretation of the in-control ARL .

A major resource for quality exists at Lockheed Martin Aeronautics - Fort Worth with the average age of the workers approaching 50 years with over 20 years employment. Realizing the asset present within this highly experienced work force became a major effort for improving quality at this plant. Tapping this resource occurred both in an assessment of the perception of factors that led to a successful quality initiative and in an ergonomics effort that focused on meeting the capabilities of the worker in the workplace. These programs were integrated for a holistic approach to continuous improvement. This paper will review the specifics of the ergonomics program that increased quality and productivity and reduced injuries along with their associated costs. The conditions that led to this approach, the elements of the ergonomics program, specific ergonomic innovations with the realized savings, and the results of a quality survey that verified the human oriented approach will be reported in this discussion.