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The purpose of this paper is to investigate a new sampling methodology previously proposed for systems with a known lifetime distribution: the Predetermined Sampling Intervals (PSI) method.

The methodology is defined on basis of system hazard cumulative rate, and is compared with other approaches, particularly those whose parameters may change in real time, taking into account current sample information.

For different lifetime distributions, the results obtained for adjusted average time to signal (AATS) using a control chart for the sample mean are presented and analysed. They demonstrate the high degree of statistical performance of this sampling procedure, particularly when used in systems with an increasing failure rate distribution.

This PSI method is important from a quality and reliability management point of view.

This methodology involves a process by which sampling instants are obtained at the beginning of the process to be controlled. Also this new approach allows for statistical comparison with other sampling schemes, which is a novel feature.

The main purpose of this paper is to present an optimal economic solution for a different adaptive sampling method that is highly intuitive in its nature: the normal sampling intervals (NSI) method.

Considering costs associated with sampling, false alarms and imperfect operation per unit of time, the paper presents a new optimal simple solution that minimizes the expected total cost per cycle. This NSI method involves the density function of the standard normal variable, assuming that the distribution of averages is normal or approximately normal (on the basis of the central limit theorem). It depends on a single scale parameter while other methods depend on various parameters.

When this expected total cost associated with the new NSI method is compared with the fixed (FSI) and variable sampling intervals (VSI) methods, in identical situations, it may be seen that, in general, it is lower (and may be much lower) and, also, that it is lower for a wider range of changes in terms of quality. This feature is particularly important because, in practice, the degree of change that occurs is not known, so this greater robustness in terms of performance is relevant.

In the practice, the minimization of total expected costs is an important point of view in the life of companies, concerning quality and statistical process control (SPC). The paper holds that this NSI method has a great degree of potential, in particular considering that in industrial processes there is growing recourse to automated systems for the collection and analysis of samples, and thus there are no special additional costs associated with labour, management or administration.

The great advantages of this NSI method are its highly intuitive nature and the fact that it enables generally much better results to be achieved as compared with the use of FSI and VSI methods. An optimal economic solution for this NSI method is presented in this paper.

Bayesian networks (BNs) are implemented for monitoring a process via statistical process control (SPC) where attribute data are available on output from the system. The paper aims to discuss this issue.

The BN provides a graphical and numerical tool to help a manager understand the effect of sample observations on the probability that the process is out-of-control and requires investigation. The parameters for the BN SPC model are statistically designed to minimize the out-of-control average run length (ARL) of the process at a specified in-control ARL and sample size.

The BN model outperforms adaptive np control charts in all experiments, except for some cases where only a large change in the proportion of sample defects is relevant. The BN is particularly useful when small sample sizes are available and when managers need to detect small changes in the proportion of defects produced by the process.

The BN model is statistically designed and parameters are chosen to minimize out-of-control ARL. Future advancements will address the economic design of BNs for SPC with attribute data.

The BNs allow qualitative knowledge to be combined with sample data, and the average percentage of defects can be modeled as a continuous random variable. The framework of the BN easily permits classification of the system operation into two or more states, so diagnostic analysis can be performed simultaneously with statistical inference.

The purpose of this paper is to investigate the economic‐statistical design of EWMA charts with variable sampling intervals (VSIs) under non‐normality to reduce the process production cycle cost and improve the statistical performance of control charts. The objective is to minimize the cost function by adjusting the control chart parameters which suffice for the statistical restriction.

First, using the Burr distribution to approximate various non‐normal distributions, the economic‐statistical model of the VSI EWMA charts under non‐normality can be developed. Further, the genetic algorithms will be used to search for the optimal values of parameters of the VSI EWMA charts under non‐normality. Finally, a sensitivity analysis is carried out to investigate the effect of model parameters and statistical restriction on the solution of the economic‐statistical design.

The result of sensitivity analysis shows that a large lower bound of average time to signal when the process is in control increases the control limit coefficient, no model parameter significantly affects the short sampling intervals, and so on.

The economic‐statistical design method proposed in this paper can improve the statistical performance of economic design of control charts and the general idea can be applied to other VSI control charts.

The purpose of this paper is to measure the performance of a sampling method through the average number of samples drawn in control.

Matching the adjusted average time to signal (AATS) of sampling methods, using as a reference the AATS of one of them the paper obtains the design parameters of the others. Thus, it will be possible to obtain, in control, the average number of samples required, so that the AATS of the mentioned sampling methods may be equal to the AATS of the method that the paper uses as the reference.

A more robust performance measure to compare sampling methods because in many cases the period of time where the process is in control is greater than the out of control period. With this performance measure the paper compares different sampling methods through the average total cost per cycle, in systems with Weibull lifetime distributions: three systems with an increasing hazard rate (shape parameter β=2, 4 and 7) and one system with a decreasing failure rate (β=0, 8).

In a usual production cycle where the in control period is much larger than the out of control period, particularly if the sampling costs and false alarms costs are high in relation to malfunction costs, the paper thinks that this methodology allows us a more careful choice of the appropriate sampling method.

To compare the statistical performance between different sampling methods using the average number of samples need to be inspected when the process is in control. Particularly, the paper compares the statistical and economic performance between different sampling methods in contexts not previously considered in literature. The paper presents an approximation for the average time between the instant that failure occurs and the first sample with the process out of control, as well.

The purpose of this paper is to develop a cost model by the variable sampling interval and optimization of the average cost per unit of time. The paper considers an economic–statistical design of the X̅ control charts under the Burr shock model and multiple assignable causes were considered and compared with three types of prior distribution for the mean shift parameter.

The design of the modified X̅ chart is based on the two new concepts of adjusted average time to signal and average number of false alarms for X̅ control chart under Burr XII shock model with multiple assignable causes.

The cost model was examined through a numerical example, with the same cost and time parameters, so the optimal of design parameters were obtained under uniform and non-uniform sampling schemes. Furthermore, a sensitivity analysis was conducted in a way that the variability of loss cost and design parameters was evaluated supporting the changes of cost, time and Burr XII distribution parameters.

The economic–statistical model scheme of X̅ chart was developed for the Burr XII distributed with multiple assignable causes. The correlated data are among the assumptions to be examined. Moreover, the optimal schemes for the economic-statistic chart can be expanded for correlated observation and continuous process.

The economic–statistical design of control charts depends on the process shock model distribution and due to difficulties from both theoretical and practical aspects; one of the proper alternatives may be the Burr XII distribution which is quite flexible. Yet, in Burr distribution context, only one assignable cause model was considered where more realistic approach may be to consider multiple assignable causes.

This study presents an advanced theoretical model for cost model that improved the shock model that presented in the literature. The study obviously indicates important evidence to justify the implementation of cost models in a real-life industry.

The purpose of this paper is to propose a novel condition-based maintenance (CBM) policy with two sampling intervals for a system subject to stochastic deterioration described by the Cox’s proportional hazards model (PHM).

In this paper, the new or renewed system is monitored using a longer sampling interval. When the estimated hazard function of the system exceeds a warning limit, the observations are taken more frequently, i.e., the sampling interval changes to a shorter one. Preventive maintenance is performed when either the hazard function exceeds a maintenance threshold or the system age exceeds a pre-determined age. A more expensive corrective maintenance is performed upon system failure. The proposed model is formulated in the semi-Markov decision process (SMDP) framework.

The optimal maintenance policy is found and a computational algorithm based on policy iteration for SMDP is developed to obtain the control thresholds as well as the sampling intervals minimizing the long-run expected average cost per unit time.

A numerical example is presented to illustrate the whole procedure. The newly proposed maintenance policy with two sampling intervals outperforms previously developed maintenance policies using PHM. The paper compares the proposed model with a single sampling interval CBM model and well-known age-based model. Formulas for the conditional reliability function and the mean residual life are also derived for the proposed model. Sensitivity analysis has been performed to study the effect of the changes in the Weibull parameters on the average cost.

The results show that considerable cost savings can be obtained by implementing the maintenance policy developed in this paper.

Unlike the previous CBM policies widely discussed in the literature which use sequential or periodic monitoring, the authors propose a new sampling strategy based on two sampling intervals. From the economic point of view, when the sampling is costly, it is advantageous to monitor the system less frequently when it is in a healthy state and more frequently when it deteriorates and enters the unhealthy state.

The purpose of this paper is to counter autocorrelation by designing the chart, using warning limits. Various optimal schemes of modified chart are proposed for various sample sizes (n) at levels of correlation (Φ) of 0.00, 0.475 and 0.95. These optimal schemes of modified chart are compared with the double sampling (DS) chart, suggested by Costa and Claro (2008).

The performance of the chart is measured in terms of the average run length (ARL) that is the average number of samples before getting an out-of-control signal. Ultimately, due to the effect of autocorrelation among the data, the performance of the chart is suspected. The ARLs at various sets of parameters of the chart are computed by simulation, using MATLAB. The suggested optimal schemes are simpler schemes with limited number of parameters and smaller sample size (n=4) and this simplicity makes them very helpful in quality control.

The suggested optimal schemes of modified chart are compared with the DS chart, suggested by Costa and Claro (2008). It is concluded that the modified chart outperforms the DS chart at various levels of correlation (Φ) and shifts in the process mean. The simplicity in the design of modified chart, makes it versatile for many industries.

Both the schemes are optimized by assuming the normal distribution. But this assumption may also be relaxed to design theses schemes for autocorrelated data. The optimal schemes for chart can be developed for variable sample size and for variable sampling intervals. The optimal schemes can also be explored for cumulative sum and exponentially weighted moving average charts.

The correlation among the process outputs of any industry can be find out and corresponding to that level of correlation the suggested control chart parameters can be applied. The understandable and robust design of modified chart makes it usable for industrial quality control.

The rejection level of products in the industries can be reduced by designing the better control chart schemes which will also reduce the loss to the society, as suggested by Taguchi (1985).

Although it is the extension of previous work but it can be applied to various manufacturing industries as well as service industries, where the data are positively correlated and normally distributed.

The purpose of this paper is to study the performance of the X‐bar chart on the basis of average run lengths (ARLs) for the positively correlated data. The ARLs at various sets of parameters of the X‐bar chart are computed by simulation. The performance of the chart at the various shifts in the process mean is compared with the X‐bar chart suggested by Zang and residual chart proposed by Zang. The optimal schemes suggested in this paper are also compared with variable parameters (VP) chart and double sampling (DS) X‐bar chart suggested by Costa and Machado.

Positively correlated observations having normal distribution are generated with the help of the MATLAB software. The performance of the X‐bar chart in terms of ARLs at the various shifts in the process mean is compared with the X‐bar chart suggested by Zang and residual chart proposed by Zang. The optimal schemes are also compared with VP X‐bar chart and DS X‐bar chart suggested by Costa and Machado.

The suggested optimal schemes of X‐bar chart perform better at the various shifts in the process mean than the X‐bar chart suggested by Zang and residual chart suggested by Zang. It was concluded that, although the suggested schemes for X‐bar chart detect shifts later than the VP and DS X‐bar charts proposed by Costa and Machado, they involved a much smaller number of parameters that are to be adjusted. So the time required for adjustment in case of optimal scheme is very small compared to the VP and DS charts.

The optimal schemes of X‐bar chart are developed for the normally distributed autocorrelated data. But this assumption may also be relaxed to design these schemes for autocorrelated data. Moreover, the optimal schemes for chart can be developed for variable sample size and for variable sampling intervals.

Although it is the extension of previous work, it can be applied to various manufacturing industries as well as service industries where the data is positively correlated and normally distributed.

The purpose of this paper is to introduce a new design of the X¯ chart to catch smaller shifts in the process average as well as to maintain the simplicity like the Shewhart X¯ chart so that it may be applied at shopfloor level.

In this paper, a new X¯ chart with two strategies is proposed which can overcome the limitations of Shewhart, CUSUM and EWMA charts. The Shewhart chart uses only two control limits to arrive at a decision to accept the Null Hypothesis (H₀) or Alternative Hypothesis (H₁), but in the new X¯ chart, two more limits at “K” times sample standard deviation on both sides from center line have been introduced. These limits are termed warning limits. The first strategy is based on chi‐square distribution (CSQ), while the second strategy is based on the average of sample means (ASM).

The proposed X¯ chart with “strategy ASM” shows lower average run length (ARL) values than ARLs of variable parameter (VP) X¯ chart for most of the cases. The VP chart shows little better performance than the new chart; but at large sample sizes (n) of 12 and 16. The VSS X¯ chart also shows lower ARLs but at very large sample size, which should not be used because, as far as possible, samples should be taken from a lot produced under identical conditions. The inherent feature of the new chart is its simplicity, so that it can be used without difficulty at shopfloor level as it uses only a fixed sample size and fixed sampling interval but it is very difficult to set the various chart parameters in VP and VSS X¯ charts.

A lot of effort has been expended to develop the new strategies for monitoring the process mean. Various assumptions and factors affecting the performance of the X¯ chart have been identified and taken into account. In the proposed design, the observations have been assumed independent of one another but the observations may also be assumed to be auto‐correlated with previous observations and performance of the proposed chart may be studied.

The research findings could be applied to various manufacturing and service industries as it is more effective than the Shewhart chart and simpler than the VP, VSS and CUSUM charts.