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Recently, Ohta et al. [Quality and Reliability Engineering International 17: 439-446, 2001] have studied the economic design of CCC (Cumulative Count of Conforming)- r charts for high-yield processes assuming a fixed hazard rate. Generally, however, the hazard rate is varying over time. With the ageing of a process, the hazard rate gets first gradually smaller, while during the last stage of the wear-out process, the hazard rate increases. For such processes, the Weibull distribution is used to model the circumstances. In this paper, we discuss an economic design of a dynamic CCC – r chart with time-varying parameters. Concretely, we propose a process control model for a Weibull distributed-shock model and determine the initial values and dynamic decision rules for the time-varying parameters of the CCC–r chart, that is, the required number of nonconforming observations r , the sampling interval h , and the lower control limit LCL maximizing the expected profit per unit time derived from the process. Finally, we compare the profits obtained applying a dynamic CCC – r chart with those obtained with a traditional static CCC – r chart.

Using a counter example, we show that the formula for computing the Average Run Lengths (ARL) of a moving average control chart (MA) in Wetherill and Brown (1991) is incorrect. However, we conjecture that the formula may provide an upper bound for the ARL of a moving average control chart.

Wu and Spedding [Journal of Quality Technology 32: 32-38, 2000] have proposed the synthetic control chart to detect small shifts in process mean. In this paper, for the same problem, we propose a control chart called ’Group Runs’ (GR) control chart, which is a combination of Shewhart's chart and an extended version of conforming run length chart. It is numerically verified that, the GR chart gives a significant reduction in out of control ATS as compared to those of the synthetic control chart and chart when in-control ATS is not smaller than a certain number. Steady state performance of the GR chart is also better. Hence, GR chart turns out to be economical to detect small shifts in the process mean.

Process Capability indices have become popular for describing how well a process meets specified tolerances. The lack of affinity with the process nonconformance probability p and the difficulty of dealing with the sampling distribution of their natural estimators affect greatly the use of the traditional indices as C p , C pk , C pm and C pkm . In this paper, a capability index is proposed which is calibrated to the nonconformance probability. Moreover, Bayesian inference procedures under multinomial sampling are developed for simplifying application of the index in industry.

In [v. Collani, Theoretical Stochastics, Heldermann Verlag, 2004] and [v. Collani, Empirical Stochastics, Heldermann Verlag, 2004] Stochastics, the Science of Prediction is re-established, its basic concepts are developed and fundamental stochastic procedures are introduced. Stochastics is defined as the branch of science which deals with the aspect of “uncertainty”. As uncertainty constitutes a major problem in all area of life, the principles developed in stochastics are universally valid. This paper deals with production processes in the framework of stochastics. In the first part, the fundamental concept of stochastics, the Bernoulli-Space, is briefly introduced as an appropriate description of the real uncertainty aspect. Next two types of stochastic procedures are identified: The first consists of making statements concerning the indeterminate future, and the second deals with making statements concerning the determinate, but unknown past. The second part of this paper is devoted to production processes. It is shown that traditional SPC methods lost there significance within modern production environments which are characterized by an ever increasing degree of automation and by objectives which differ considerably from those during the pre-computerized times. The larger degree of complexity of the new process environment and the more demanding aims require new advanced means for dealing with uncertainty. By means of examples it is illustrated how stochastic methods comply with the needs of modern production processes.

In this paper, we propose a new bivariateWeibull distribution and derive estimation and test procedures based on censored samples with common covariates. The study of bivariate Weibull was motivated by interesting biometrical applications. The maximum likelihood estimators for the model parameters are obtained together with a test of significance.

In reliability analysis, it is preferable to complete an experiment of data collection in a short time due to constraints concerning energy, money or other resources. In this paper we propose a relative measure called relative expected experimental time (REET) for a life testing experiment when the corresponding random lifetime follows a log-logistic distribution. This may be of help for assessing the savings in experimental time by using a censored sample instead of a complete sample. We demonstrate relative saving measure by means of some probability distribution. A method of assessing the suitability of a specified probability model is also suggested.

Frequent wastage or exit of personnel are common in many administrative and production oriented organizations. Once the accumulated number of exits from the organization reaches a certain threshold level, it could be viewed as a “breakdown point”. The time to attain breakdown point is an important characteristic for the management of the organization. In this paper, a shock model approach is proposed to obtain the expectation and variance of the time to attain the threshold level. Numerical and graphical illustrations are provided to illustrate the practical use of the model.

Most maintenance models assume perfect maintenance, where a system becomes as good as new after each maintenance action. However, in reality system's performance deteriorates over time. This work investigates a system's performance when subjected to failures which are imperfectly repaired. Two cases are regarded: Maintenance by repair and replacement and maintenance by probabilistic repair and replacement. The objective is to asses the system's long run behavior by deriving closed expressions for its operational probability.

This article investigates the problem of minimizing the average fraction inspected (AFI) for a combined continuous lot by lot acceptance sampling plan. A solution procedure is developed to find sub-optimal sampling plan parameters that will meet the average outgoing quality limit (AOQL) requirement, while guaranteeing a small AFI when the process average ( > AOQL) is known.

Since the first acceptance sampling plans have been developed almost 80 years ago, a number of selection principles have emerged. The majority of these principles is 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 the overall risk for a wrong decision as optimization criteria. This is the case with so-called “minimum risks sampling plans”, which are reviewed in this paper so as to make them better known to those responsible for quality control.

Resistivity of resin plays a vital role for trouble free performance of electrostatic application of resin based paints. Low resistivity results in electrical shorting and high resistivity leads to poor deposition of paints due to insufficient charge pick up. Hence resin resistivity should be maintained within a specified range. The present study was undertaken in a reputed paints manufacturing enterprise. The concerned firm was not able to maintain the resistivity value within the desired specification. They were consistently getting low resistivity. It was decided to study on identifying significant factors for controlling resistivity through experimentation. A 2 3 full factorial experiment was conducted with three factors phthalic anhydride%, water collection time, and solvent distillate collection time, each varying at two levels. The experiment could not be replicated due to time constraint. After analysing the data, using Bayesian method of posterior probability plot the main effect of water collection time and solvent distillate collection time were found to be significant at 5% level of significance. Considering expected values of resistivity at different levels of significant factors, optimum levels were arrived at so as to achieve the expected average resistivity value closed to the target value. Taking experimental error into account a 95% confidence interval was obtained which was lying within the desired specification. Confirmatory trials were made for few batches. Since the results of confirmatory trials were satisfactory the recommendations were accepted by plant management. As a result of implementation of the recommendations of the present study the concerned firm was able to get the value of resin resistivity within the specification.