Band 28, Heft 2

Demerits control is the traditional tool for monitoring defects of different severity with a single chart. It requires arbitrary assignment of numerical values to the ordinal scale and therefore is theoretically flawed. We assess the error rates of demerits control compared to an alternative based on the proportional odds model only to find that it is not more powerful than traditional demerits.

In this paper, we consider acceptance sampling plans assuming a half exponential power life distribution and a life test that is truncated at a preassigned time. For various acceptance numbers, confidence levels and values of the ratio of the true mean lifetime to the specified mean life, we determine the minimum sample size necessary to ensure a certain mean lifetime. The operating characteristic function of the sampling plans and the associated producer's risks are derived and also discussed. We illustrate the use of the acceptance sampling plans based on displayed tables with some numerical examples.

One of the most fundamental issues in estimation theory about accuracy of an unbiased estimator is computing or approximating its variance. Very often, the variance has a complicated form or cannot be computed explicitly. In this paper, we consider two well-known lower bounds for the variance of unbiased estimator, namely the Bhattacharyya (1946, 1947) and the Kshirsagar (2000) bounds for some versatile families of distributions in statistics and especially in reliability analysis. We consider the generalized gamma (GG), inverse Gaussian, Burr type XII and Burr type III distributions, and derive for these distributions, general forms of Bhattacharyya and Kshirsagar matrices. Additionally, we evaluate different Bhattacharyya and Kshirsagar bounds for the variance of estimators of some functions of relevant parameters and arrive at proposal which of the bounds should be used in given situations.

In this paper we develop an order k version of the alternative hyper-Poisson distribution of Kumar and Nair (Statistica, 2012) and study some of its important properties such as its probability mass function, first moment, variance and recurrence relations for its probabilities, raw moments and factorial moments. The estimation of the parameters of this class of distribution by various methods of estimation is also considered and demonstrated with the help of a real data set.

In this paper a new bivariate distribution called Marshall–Olkin–Morgenstern-bivariate-Weibull distribution is introduced and studied. Two different models of minification processes with the above bivariate distribution as stationary marginal distribution are developed. It is shown that the process is strictly stationary. The properties of the process are derived. The expressions for reliability under stress-strength analysis when the components are in series and parallel are obtained. The process is extended to p th order as well as k -variate cases.

Adaptive control charts deliver significantly better performances than that of static control charts. However, the frequent switches between sampling interval lengths and/or between sample sizes can be a complicating factor in the administration of these charts. This factor is totally absent for the adaptive chart proposed in this paper. The proposed chart is an X ̅ chart with variable control and warning limits (VCWL). Expressions for the performance measures for this chart are developed. The methods presented are general and can be applied to other Shewhart control charts. The performances of VCWL X ̅ charts are compared numerically with that of static X ̅ charts. It is observed that the idea of VCWL significantly improves the performances of X ̅ charts in detecting small to moderate shifts in the process mean without affecting that in detecting large shifts.

This paper introduces a transmuted generalized inverted exponential distribution. We generalize the two parameter generalized inverted exponential distribution using the quadratic rank transmutation map proposed by Shaw et al. (2007) to develop a transmuted generalized inverted exponential distribution. The properties of the transmuted generalized inverted exponential distribution are discussed. We derive the moments and examine the order statistics. Moreover, the maximum likelihood estimators for the parameters is briefly investigated and the information matrix is derived.

Since the first acceptance sampling plans have been developed 80 years ago, a number of selection principles have emerged. The majority of these principles are characterized by the fact that they look upon producer and consumer as two opposing parties. However, in many occasions, e.g., in final inspection, producer and consumer represent the same party and, therefore, the used sampling plan should not make an attempt to discriminate between their interests. In this case the interest is to avoid wrong decisions, i.e., reject product of sufficient quality and accept product of insufficient quality. Thus, the natural objective in these cases is to use overall risk for a wrong decision as optimization criteria. In this paper, a table and procedure are given for finding the Modified Quick Switching Systems QSS  −  m ( n ; C N ,  C T ) involving minimum sum of producer's and consumer's risks for specified Acceptable Quality Level and Limiting Quality Level using weighted Poisson distribution.

Process capability is defined as inherent variability of a process which is running under chance cause of variation only. Process capability index is measuring the ability of a process to meet the product specification limit. Generally Cp and Cpk have been widely used as statistical tools to assess the manufacturing process performance. These indices provide numerical measures on process precision, process accuracy and process performance. The multivariate process capability indices, which are used for evaluation of processes with correlated quality characteristics are considered as new emerging research area. In this paper, we describe an approach of estimating multivariate process capability indices assuming multivariate g-and-h distribution and illustrate their performance using simulated and practical data set.

Acceptance sampling is one of the celebrated techniques in quality assurance. The application of acceptance sampling methodology has been widespread in the industrial environment and the concept is being used primarily for incoming or receiving inspection. It is concerned with inspection of one or more samples drawn randomly from a lot or lots of finished products or materials and with decision making regarding lots on the basis of the information contained in the sample(s) about the quality of the products. A sampling plan under acceptance sampling is a rule that precisely specifies the parameters of the sampling process and acceptance/rejection criteria and may be one of two categories, viz., attributes and variables. The theory of acceptance sampling plans by attributes is based on the implicit assumption that the production process from which lots are formed is stable and the lot or process fraction nonconforming is a constant. However, the lots formed from a process, in practice, have quality variations, which occur due to random fluctuations, and thereby the proportion of non-conforming units in the lots will vary continuously. Hence, in such cases, a framework of Bayesian methodology, which uses prior information on the process variation for making decisions about the submitted lots, can be employed as an alternative to conventional plans. Such plans are called Bayesian acceptance sampling plans. In this paper, Bayesian single sampling plans by attributes are developed under the conditions of Poisson distribution for sampling information and gamma distribution for prior process information. The methodology for determining the plan parameters based on unity values with operating ratio as a measure of discrimination is discussed. The procedures for the determination of an optimum plan and for the construction of operating characteristic curve are also presented. The Bayesian plans are compared with the plan under conventional method through an illustration.