METODOLOGI SIX SIGMA PERTEMUAN 9 ( Perhitungan Statistik) OLEH: EMELIA SARI

The Most Common Six Sigma Tools Used During the Measure Phase Process maps Check sheets Pareto charts Cause-and-effect Histograms Control charts Statistical techniques

Collecting Data Define the target population. Select a sampling scheme, which is a detailed description of what data will be collected and how. Determine sample size.

Measurement Data Types Measurement data are categorized as either continuous or discrete Continuous data, also called variable data, are based on a continuum of numbers, such as heights, weights, times, and dollars Discrete data, also called attribute data, are based on counts or classes, such as proportions, defects, yes/no or pass/fail, A, B, C, D Grades or a 5-point survey scale

Determining Sample Size for Continuous Data where Z = the standardized Z score at a specified confidence interval (e.g., a 95% confidence level = 1.96 Z score) S = sample standard deviation, or an estimate of the population standard deviation E = acceptable measurement error, expressed as a number.

Example Imagine that a Six Sigma team wants to estimate the sample size required to determine the mean time to process an insurance claim with a 95% confidence interval. The standard deviation is estimated at 29 min. The acceptable measurement error (E) is ±4 min from the mean. The calculation is:

Determining Sample Size for Discrete Data where Z2 = square of the standardized Z score at a specified confidence interval [e.g., a 95% confidence level = (1.96)2] p = estimated proportion of correct observations (successes) q = (p – 1) = estimated proportion of defects (failures) E2 = square of the acceptable measurement error.

Example If a Black Belt wants to determine the sample size required to estimate the proportion of defective billing statements (one or more errors on a statement) with 95% confidence and with a measurement error of no more than ±5% between the true proportion and the sample proportion, a sample size of 227 is required, as illustrated in Equation. The Black Belt estimates the proportion of defective billing statements at 18%, based on preliminary sampling:

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