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From the perspective of business history, this chapter presents an overview of the development of the tourism sector in South America, placing special emphasis on the Peruvian case. The chapter explores various topics related to the tourism chain, such as hotel networks, the role of the state, tour operators, micro- and small enterprises, linkages between tourism and sustainability, the formation of clusters in the sector, and interactions between different entrepreneurs in the chain. Special emphasis is placed on the Peruvian case, especially when it comes to discussing the role of micro- and small enterprises in the sector.

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.

The aim of this paper is to present a synthetic chart based on the non‐central chi‐square statistic that is operationally simpler and more effective than the joint X¯ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes.

The approach used is based on the non‐central chi‐square statistic and the steady‐state average run length (ARL) of the developed chart is evaluated using a Markov chain model.

The proposed chart always detects process disturbances faster than the joint X¯ and R charts. The developed chart can monitor the process instead of looking at two charts separately.

The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately.

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 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.

This paper presents economic and economic–statistical designs of the adaptive exponentially weighted moving average (AEWMA) control chart for monitoring the process mean. It also aims to compare the effect of estimated process parameters on the economic performance of three charts, which are Shewhart, exponentially weighted moving average and AEWMA control charts with economic–statistical design.

The optimal parameters of the control charts are obtained by applying the Lorenzen and Vance’s (1986) cost function. Comparisons between the economic–statistical and economic designs of the AEWMA control chart in terms of expected cost and statistical measures are performed. Also, comparisons are made between the economic performance of the three competing charts in terms of the average expected cost and standard deviation of expected cost.

This paper concludes that taking into account the economic factors and statistical properties in designing the AEWMA control chart leads to a slight increase in cost but in return the improvement in the statistical performance is substantial. In addition, under the estimated parameters case, the comparisons reveal that from the economic point of view the AEWMA chart is the most efficient chart when detecting shifts of different sizes.

The importance of the study stems from designing the AEWMA chart from both economic and statistical points of view because it has not been tackled before. In addition, this paper contributes to the literature by studying the effect of the estimated parameters on the performance of control charts with economic–statistical design.

The purpose of this paper is to develop an extensive economic production quantity (EPQ) model on the basis of previous research. Considering an imperfect three‐state production process, this paper makes contributions to an integrated model combining conceptions of quality loss and design of control chart based on EPQ model. The objective is to minimize the total production cost with the determination of EPQ and design parameters of control chart subjected to quality loss and other process costs.

In this paper, imperfect process is defined as a three‐state process, and the quality cost corresponding to each state contributes to the eventual total expected cost formulation. Control chart is used to monitor the shift from the target value within whole process and its control limits are set to be related to the quality cost.

The proposed integrated model conforms more closely to the real situation of production process considering the process shift as a random variable.

Numerical computation and sensitivity analysis through a case study are presented to demonstrate the applications of the model.

Few research efforts investigate an integrated model considering EPQ, control chart and quality loss simultaneously. In particular, compared with the former researches, the process shift, due to which the quality cost incurs, is considered as a random variable in this paper.

The purpose of this paper is to compare the performances of np-VP control chart with estimated parameter to the np-VP control chart with known parameter using average time-to-signal (ATS), standard deviation of the time-to-signal (SDTS), and average number of observations to signal (ANOS) as performance measures.

The approach used in this study is probabilistic in which the expected values of performance measures are calculated using probabilities of different estimators used to estimate process parameter.

Numerical results indicate different performances for the np-VP control chart in known and estimated parameter cases. It is obvious that when process parameter is not known and is estimated using Phase I data, the chart does not perform as user expects. To tackle this issue, optimal Phase I estimation scenarios are recommended to obtain the best performance from the chart in the parameter estimation case in terms of performance measures.

This research adds to the body of knowledge in quality control of process monitoring systems. This paper may be of particular interest to practitioners of quality systems in factories where products are monitored to reduce the number of defectives and np chart parameter needs to be estimated.

The originality of this paper lies within the context in which an adaptive np control chart is studied and the process parameter unlike previous studies is assumed unknown. Although other types of control charts have been studied when process parameter is unknown but this is the first time that adaptive np chart performance with estimated process parameter is studied.

It is found that the process outputs from most of the industries are correlated and the performance of X-bar chart deteriorates when the level of correlation increases. The purpose of this paper is to compute the level of correlation among the observations of the weights of tablets of a pharmaceutical industry by using modified X-bar chart.

The design of the modified X-bar chart is based upon the sum of χ2s, using warning limits and the performance of the chart is measured in terms of average run lengths (ARLs). The ARLs at various sets of parameters of the modified X-bar chart are computed; using MATLAB software at the given mean and standard deviation.

The performance of the modified X-bar chart is computed for sample sizes of four. ARLs of optimal schemes of X-bar chart for sample size of four are computed. Various optimal schemes of modified X-bar chart for sample size (n) of four at the levels of correlation (Φ) of 0.00, 0.25, 0.50, 0.75 and 1.00 are presented in this paper. Samples of weights of the tablets are taken from a pharmaceutical industry and computed the level of correlation among the observations of the weights of the tablets. It is found that the observations are closely resembled with the simulated observations for the level of correlation of 0.75 in this case study. The performance of modified X-bar chart for sample size (n) of four at the levels of correlation (Φ) of 0.50 and 0.75 is also compared with the conventional (Shewhart) X-bar chart and it is concluded that the modified X-bar chart performs better than Shewhart X-bar chart.

All 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 modified X-bar chart can also be used for other industries; where the manufacturing time of products is small. This scheme may also be used for any sample sizes suitable for the industries

The optimal scheme of modified X-bar chart for sample size (n) of four is used according to the computed level of correlation in the observations. The simple design of modified X-bar chart makes it more useful at the shop floor level for many industries where correlation exists. 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 used.

The design of modified X-bar chart uses very less numbers of parameters so it can be used at the shop floor level with ease. 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 and service industries; where the data are correlated and normally distributed.

The purpose of this paper is to re‐evaluate the performance of the adaptive control charts which allow some of their design parameters to change during production depending on the collected information from samples over time. Instead of employing a single performance measure (average time to signal process changes), a set of measures, associated with the inspection efficiency and effort, is taken into account in the evaluation process.

A multivariate analysis of variation (MANOVA) approach along with the post hoc analysis are applied to investigate the performance of different adaptive control charts based on different measures.

The findings indicate that different adaptive control charts may have different performance, depending on the measure regarded and the value of shift in process mean. In general, the VSSC, VSSI, and VSI control charts would be recommended for a process with a small, moderate, and large shift, respectively. The SS chart is still the best choice for a process with an extremely large shift.

Up to now, the proposed procedure has been developed for the comparative analyses of adaptive X¯ charts, but it could be adjusted for other adaptive charts as well.

This paper provides a review of the performance of adaptive control charts from a novel perspective.