Study of the Rate of Occurrence

Under construction…

Under construction…

Scope: Quality metric (Y) for counting according to a Poisson distribution. For example: number of defects per PC, number of hold times per phone call, number of errors per document, etc.

Here we determine the target for reducing the occurrence rate required to achieve the target for reducing the defective rate.

Enter the following data:

Summary calculation (if you already know the initial defect rate):

• Di: initial defect rate
• DC: Target Defective Rate

Detailed calculation:

• λi: initial (current) occurrence rate
• τred.(%): desired reduction rate of the defective rate

Scope: Quality metric (Y) for counting according to a Poisson distribution. For example: number of defects per PC, number of hold times per phone call, number of errors per document, etc.

Here we determine the minimum sample size needed to detect the effect of reducing the occurrence rate that would allow us to achieve the objective of reducing the defective rate.

Enter the following data:

• α: risk of falsely concluding that the required effect exists
• β: risk of not detecting the required effect
• Di: initial defect rate
• DC: Target Defective Rate

Scope: Quality metric (Y) for counting according to a Poisson distribution. For example: number of defects per PC, number of hold times per phone call, number of errors per document, etc.

Here, we determine whether we can conclude that there is a decrease or increase in the occurrence rate, below or above a given threshold, based on the differences in occurrence rates observed in two samples. We typically test the effect associated with two different operating conditions (effect of an X, effect of a solution, etc.). The test implemented here is the two-sample Poisson test.

Enter the following data:

• n1 and n2: the sizes of each sample
• d1 and d2: the number of defects counted in each sample
• α: risk that the actual effect lies outside the calculated confidence interval; indicate 5% for a 95% confidence interval
• Emin: the threshold of the desired effect λ2 – λ1

Scope: Quality metric (Y) for counting according to a Poisson distribution. For example: number of defects per PC, number of hold times per phone call, number of errors per document, etc.

We determine here, within the framework of implementing a two-sample Poisson test:

• The minimum sample size required to detect a reduction or increase in the occurrence rate exceeding a given threshold
• The smallest detectable effect of reducing or increasing the rate of occurrence using given samples
• The power to detect an effect of reducing or increasing the rate of occurrence below or above a given threshold, using given samples

Enter the following data:

1/ For determining the sample size:

• α: risk of falsely detecting an effect
• β: risk of not detecting the effect
• λ1: the reference occurrence rate
• λ2: the rate of comparison occurrences corresponding to the effect threshold to be detected E _min = λ2 – λ1

2/ For determining the minimum detectable effect:

• α: risk of falsely detecting an effect
• β: risk of not detecting the effect
• n1 and n2: the sizes of each sample
• λ1: the reference occurrence rate

3/ For determining the power:

• n1 and n2: the sizes of each sample
• λ1: the reference occurrence rate
• λ2: the rate of comparison occurrences corresponding to the effect threshold to be detected E _min = λ2 – λ1

Scope: Counting metric (Y) following a Poisson distribution. For example: number of faults per PC, number of hold times per phone call, number of errors per document, etc.

Here we determine whether an occurrence rate differs from its hypothesized value, based on the observed occurrence rate in a sample. The test used here is the one-sample Poisson test.

Enter the following data:

• λ0: value of the hypothesized occurrence rate
• n: the sample size
• d: the number of defects counted in the sample
• α: risk that the true mean lies outside the calculated confidence interval; enter 5% if a 95% confidence interval is desired.

Scope: Counting metric (Y) following a Poisson distribution. For example: number of faults per PC, number of hold times per phone call, number of errors per document, etc.

Here, we determine, within the framework of implementing a one-sample Poisson test:

• The minimum sample size required to detect whether the occurrence rate is higher or lower than its hypothesized value.
• The smallest detectable difference between the occurrence rate and its hypothesized value using given samples
• The power to detect a discrepancy between the occurrence rate and its hypothesized value, using given samples

Enter the following data:

1/ For determining the sample size:

• α: risk of falsely detecting a discrepancy
• β: risk of not detecting the discrepancy
• λ0: the hypothesized occurrence rate
• λ: the rate of comparison occurrences such that ε _min = λ – λ0

2/ For determining the minimum detectable deviation:

• α: risk of falsely detecting a discrepancy
• β: risk of not detecting the discrepancy
• n: the sample size
• λ0: the hypothesized occurrence rate

3/ For determining the power:

• n: the sample size
• λ0: the hypothesized occurrence rate
• λ: the rate of comparison occurrences such that ε _min = λ – λ0