Fraction nonconforming control charts with m-of-m runs rules

In this article, we proposed m-of-m control chart for fraction nonconforming to increase sensitivity of the standard p-chart. The m-of-m control chart for fraction nonconforming is described, and the 3-of-3 control chart is discussed in detail as an illustration of the m-of-m control chart. The performance of proposed control charts is measured in terms of average run length, standard deviation of run length and quartiles under zero-state and steady-state modes. The Markov chain approach is used to compute average run length, standard deviation of run length and quartiles. Comparison study revealed that the performance proposed m-of-m control chart with m = 2, 3 is significantly better than the standard p-chart. Average run length values of the proposed control charts are at least 15 % less than that of the standard p-chart values for small to moderate shifts. Standard deviation of run length values of the proposed control charts is also at least 18 % less than the standard p-chart. An example is given to illustrate an application of procedures discussed.

[1]  Morton Klein,et al.  Two Alternatives to the Shewhart X̄ Control Chart , 2000 .

[2]  Michael B. C. Khoo,et al.  Two Improved Runs Rules for the Shewhart X¯ Control Chart , 2006 .

[3]  Arnonm Hurwitz,et al.  A VERY SIMPLE SET OF PROCESS CONTROL RULES , 1992 .

[4]  Sheng Zhang,et al.  Designs of control charts with supplementary runs rules , 2005, Comput. Ind. Eng..

[5]  E. S. Page.  CONTROL CHARTS WITH WARNING LINES , 1955 .

[6]  Douglas C. Montgomery,et al.  Introduction to Statistical Quality Control , 1986 .

[7]  A. Bissell,et al.  An attempt to unify the theory of quality control procedures , 1978 .

[8]  Ronald B. Crosier,et al.  A new two-sided cumulative sum quality control scheme , 1986 .

[9]  Charles W. Champ,et al.  Exact results for shewhart control charts with supplementary runs rules , 1987 .

[10]  Donald J. Wheeler,et al.  Detecting a Shift in Process Average: Tables of the Power Function for X Charts , 1983 .

[11]  Galit Shmueli,et al.  Run-Length Distribution for Control Charts with Runs and Scans Rules , 2003 .

[12]  C. A. Acosta-Mejia,et al.  Two Sets of Runs Rules for the Chart , 2007 .

[13]  Tae-Jin Lim,et al.  Design of control charts with m‐of‐m runs rules , 2009, Qual. Reliab. Eng. Int..

[14]  S. W. Roberts.  Properties of control chart zone tests , 1958 .

[15]  Michael B. C. Khoo,et al.  Design of Runs Rules Schemes , 2003 .

[16]  Athanasios C. Rakitzis,et al.  The Modified r Out of m Control Chart , 2008, Commun. Stat. Simul. Comput..

[17]  Michael B. C. Khoo.  Increasing the Sensitivity of Control Chart for Fraction Nonconforming , 2003 .