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Extra info for Statistical Process Monitoring and Optimization (Statistics: a Series of Textbooks and Monographs)
Sample text
Under these circumstances they are usually unaware of theconsequencesofpoorquality in theworkthey themselves do. By bringingpeopletogether in terms with a common goal, quality improvement becomes easier to communicate over departmental or func- QualityImprovementandStatisticalReasoning 41 tional walls. In this way the slow breaking down of barriers acts as a platform for change. ” Thischange implies significant personal change in the way people react and in their attitudes. A benchmarkingapproachcanalsohelptochangethe waythey do things.
Equations (18) and (20) may be approximately applied with satisfaction regardless of the distribution of the production quantity before the problem and despite variations in the fraction defective during the problem period. These statements are proved in Sections 5 and 6. 5. PROOFOFEQUATIONSFORNONSPECIFIC DISTRIBUTION Parameters A , B, C, U, e, and n in the previous section are used similarly in this section. Let P, (i = I , 2, . ) be the probability of causing trouble for the first time after the production was started at the ith unit.
Then our hypothesis may be written =0 From this it is seen that the T' statistic is equal to If the hypothesis is true, then F= N-n T2 (N - 1 ) ~ has an F-distribution with n and N - IZ degrees of freedom. The hypothesis is rejected if the computed F-statistic exceeds the critical value F a : l r , ~ - l r . Let + S(, = s,. - s,',. , . . , f l l ) : 1 ( N - I)/? /'(? N-~~ Now assume that the hypothesis is true, and let I' = (0, . . , 0, 1,0, . . , 0) TotalQualityManagement 31 Then we may write or To simplify.
