Variable Control Charts Based on Percentiles of the New Weibull-Pareto Distribution

Rao, B. Srinivasa; Nasiru, Suleman; K.N.V.R, Lakshmi

doi:10.18187/pjsor.v11i4.1017

Cited by 3 publications

(6 citation statements)

References 4 publications

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“…e control limits of the skewness correction method and the Gompertz Shewhart approach, Gompertz skewness correction method, and Gompertz exact method using equations (10), (15), and (20), respectively, are computed and presented in Table 1. To measure the performance of the charts, the coverage probability was computed for the four methods.…”

Section: Resultsmentioning

confidence: 99%

“…It is well known that 3σ limits of normal distribution include 99.73% of probability. Hence, we have to search for two limits of the sampling distribution of sample mean in Gompertz exponential distribution such that the probability content of those limits is 0.9973 (see Srinivasa Rao et al [14] and Srinivasa et al [15]). Symbolically, we have to find L and U such that…”

Section: Using Exact Control Limitsmentioning

confidence: 99%

“…(1) Generate n independent Gompertz (2.2, 4.7) variates for n � 2, 3, 4, 5, 7, 10 (2) Repeat Step (1) 30 times (r � 30) (3) Compute the control limits for the X chart using equation (10) for the Shewhart approach, equation (15) for the skewness correction approach, and equation (20) for the exact approach…”

Section: Simulation Studymentioning

confidence: 99%

“…Kantam et al [8] developed control charts for log-logistic distribution, Kan and Yazici [9] developed individual control charts for Burr distributed and Weibull distributed data, Subba Rao and Kantam [10] introduced control charts for double exponential distribution, Yazici and Kan [11] developed asymmetric control limits for small samples, Srinivasa Rao and Sarath Babu [12] proposed control charts for linear failure rate distribution, and Srinivasa Rao and Kantam [13] developed control charts for half-logistic distribution percentiles. Srinivasa Rao et al [14] developed control charts for a variable quality characteristic that is assumed to follow size-biased Lomax distribution based on the evaluated percentiles of sample statistics like mean, median, midrange, range, and standard deviation, Srinivasa Rao et al [15] developed control charts for a variable quality characteristic that is assumed to follow new Weibull-Pareto distribution based on the evaluated percentiles of sample statistics like mean, median, midrange, range, and standard deviation, Wang et al [16] proposed control charts for monitoring the lower Weibull percentiles under complete data and Type-II censoring, and Rao [17] considered an exponentiated halflogistic distribution to develop an attribute control chart for time-truncated life tests with a known or unknown shape parameter and references therein.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

Adewara

Adekeye

Aako

2020

Journal of Probability and Statistics

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In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. The proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. The coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based X¯ charts.

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Section: Resultsmentioning

confidence: 99%

Section: Using Exact Control Limitsmentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

Adewara

Adekeye

Aako

2020

Journal of Probability and Statistics

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“…In turn, Special Charts were divided into: Short Series, Multivariate, for monitoring the Time Between Events, distributions other than normal and for autocorrelated data. Boyapati, Nasiru & Lakshmi (2015) note in the case of short production runs, data for determining Control Limits is usually lacking, because the process is completed before they are estimated, leading to a situation in which stability assessment occurs afterwards. Boyapati, Nasiru & Lakshmi (2015) also indicate that in cases when it is possible to collect the appropriate amount of data, it is followed by conversion of machines and changing assortment, which is connected to the establishment of a new chart.…”

Section: Modern Control Chartsmentioning

confidence: 99%

The Classification and Characteristics of Control Charts

Czabak-Górska

2017

CBUP

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Control Charts are the basic tool for quality control. They were developed in the 1920s when the dominant type of production was mass production. In order to properly use classic Control Charts, the data from the manufacturing process should meet the following assumptions: an empirical distribution of measurement data should be normally distributed or close to a normal distribution, measurement data should be independent, the manufacturing process should be capable of quality depending on the type of Control Chart, a sample that is large enough (sometimes made of several elements) must be taken. Currently, a shift can be observed from mass production towards short production runs, which causes the proper use of the traditional approach to be impossible. In recent years, control charts are once again in the spotlight, and consequently many scientists, i.e. Reynolds, Zimmer, Costa, Calvin and Chan have undertaken the task to adapt the classic idea of keeping Control Charts to modern conditions of production. The development of science in this area allows for the avoidance of making major mistakes in the conduct of Control Charts and for making the wrong decisions based on erroneous analysis. However, the appearance of new literature pieces implies the need to classify Control Charts, therefore, this article describes the idea of conduct, the most important assumptions and distribution of classical Shewhart's Control Charts, as well as a suggestion for the distribution of advanced Control Charts that meet the needs of the currently used production types. The work also contains a concise description of the chosen control charts as well as the threats resulting from their inappropriate selection. This elaboration is an extension to the article of Czabak-Górska (2017).

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X̅ and R control charts based on marshall-olkin inverse log-logistic distribution for positive skewed data

Aako

Adewara

Adekeye

et al. 2020

AJPAS

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The fundamental assumption of variable control charts is that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of the MOILLD control chart. The results obtained were compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Distribution based control chart will be more appropriate.

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Variable Control Charts Based on Percentiles of the New Weibull-Pareto Distribution

Cited by 3 publications

References 4 publications

On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

The Classification and Characteristics of Control Charts

X̅ and R control charts based on marshall-olkin inverse log-logistic distribution for positive skewed data

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