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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Other charts for nonconforming items are simple variations of the p chart. In the case of the 100p chart, all values of the p chart are expressed as percentages. In the case of the np chart, instead of plotting fraction or percent defectives, actual counts of nonconforming or defective items are plotted. See Banks [1989], De Vor et al. [1992], Grant and Leavenworth [1988], and Montgomery [1991] for greater detail. The formulas for the central line and the control limits for an np chart are given below. It is assumed that the revised value for universe fraction defective, p, is known. If p is not known, then the procedure for the p chart must be carried out to determine the revised value for the universe fraction defective: Central line =npo Control limits =npo±3npo1-po
X̄ and R Charts
Published in Roger W. Berger, Thomas Hart, Statistical Process Control, 2020
There are four primary ways to chart attribute data. First, for samples of not necessarily equal size the p chart is used to track the proportion of units nonconforming. Second, for samples of constant size the np chart is used to indicate the number of units nonconforming per sample. Next, for samples of constant size the c chart can be used to follow the number of defects per lot. Finally, the u chart is used to note the number of defects per unit from samples not necessarily of constant size. The next section will introduce and briefly cover the application of each of these charts.
Control Charts
Published in Lawrence S. Aft, Fundamentals of Industrial Quality Control, 2018
The np chart, also known as the number of nonconforming, is closely related to the p chart. The additional constraint of using an np chart is that the sample size must be uniform; np is the direct count or actual number of nonconforming units in each subgroup or sample.
Robust economic design of NP-chart under different process and economic parameters scenarios
Published in Quality Technology & Quantitative Management, 2023
Ahmed M. Attia, Mohammad A. M. Abdel-Aal
(Lee & Khoo, 2017; Lee et al., 2020) proposed a synthetic np-chart based on minimum out-of-control median run length (MRL) as a performance measure. (Chong et al., 2019) designed a multi-attribute np-chart and integrated it with a binomial multi-attribute cumulative sum (MCUSUM) chart to improve the detection efficiency of upward shifts. (Shu et al., 2019) combined the variable sample size (VSS) scheme with the np-chart design and assessed the new chart’s performance by measuring the ATS. (Lee & Khoo, 2019) evaluated the performance of the np-chart with a double sampling scheme by measuring ARL. They indicated that a large sample size is required in phase I, which is not practical in the industry. (Muhammad et al., 2020) introduced the neutrosophic exponentially weighted moving average statistic to design the np-chart. Monte Carlo simulation was used to find the neutrosophic ARL.
An improved design of exponentially weighted moving average scheme for monitoring attributes
Published in International Journal of Production Research, 2020
Salah Haridy, Mohammad Shamsuzzaman, Imad Alsyouf, Amitava Mukherjee
In this article, we mainly emphasise on the EWMA scheme for monitoring attributes. Several scholars have studied various aspects of attribute control charts. For example, Acosta-Mejia (1999) conducted a study to analyse the performance of several charts for monitoring increases and decreases in p based on their Run Length (RL) distribution. The results showed that replacing the lower control limit by a simple runs rule could increase in the overall chart performance. Rocke (1990) provided a simple procedure for constructing a control chart for fraction nonconforming p or number of nonconformities with varying sample sizes. Gan (1993) proposed an optimal design of the binomial Cumulative Sum (CUSUM) chart to considerably improve its performance for detecting a particular p shift value. Schwertman and Ryan (1999) published a study in which a dual np charts were suggested to detect changes; one chart is providing an early warning of quality deterioration and the other chart is a cumulative chart. Chang and Gan (2001) developed a binomial CUSUM chart for monitoring processes with a very low fraction nonconforming. Wu and Luo (2003) presented an algorithm for designing a three-triplet binomial np charts with an optimal combination of the sample size and the control limits, which made the operating characteristics of the np chart highly specifiable by providing more control in the design and operation of the np charts. Wu and Luo (2004) later on developed an optimisation algorithm to design adaptive np control chart for monitoring p and the results indicated that adaptive np chart could improve the effectiveness significantly, especially for detecting small and moderate shifts.
Optimal double sampling control chart based on gauges
Published in Quality Engineering, 2020
Jaime Mosquera, Francisco Aparisi
The DS strategy was later adapted to other variable control charts, such as the S (He and Grigoryan 2002, 2003), the S2 chart (Khoo 2004), the scheme (He and Grigoryan 2006), the multivariate |S| chart (Grigoryan and He 2005) and T2 Hotelling’s chart (Champ and Aparisi 2008), among others. For attributes control chart, the adaptation was developed for the U chart (Pérez et al. 2010), for the np chart (De Araújo Rodrigues, Epprecht, and De Magalhães 2011) and, recently, for the C control chart (Inghilleri, Lupo, and Passannanti 2015; Campuzano, Carrion, and Mosquera 2020).