Chi-square
The chi-square test is used to compare the theoretical and observed frequencies. The chi-square distribution is not symmetrical, as normal or t-distribution. The mean and standard deviation can be calculated for the normal, t-, and Poisson distribution. However, there is no need for these parameters in chi-square distribution. The significance levels are applied the same way as in other distributions. However, for chi-squared tests only one-tailed tests are applicable. Therefore, the calculated value is compared to the critical value for the right tail of the chi-distribution.
The normal and t-distributions are applied only to numeric data, whereas the chi-squared distribution can be applied both to the numeric and categorical data. For the numeric data, the direct calculations of the theoretical and observed values are calculated; for the categorical data, the calculations of frequencies are performed.
The goodness-of-fit test checks if the observed values fit the predicted structure. In other words, if the observed frequencies (numbers) are well fit with the theoretically observed pattern. For example, the owner expects that the ice-cream sales will be as follow: 50% vanilla ice cream, 35% chocolate ice cream, 15% banana ice cream. These numbers are the expected frequencies. For 100 kg sales, the expected weights of the ice creams are calculated. As the real sales are obtained, the chi-square value is calculated. It is compared with the critical tabulated value: if the calculated value is greater than the critical, the real distribution does not fit well the theoretically expected; if the critical value is greater than the calculated, then the real distribution presents a good fit of the theoretically expected.
Pareto Charts
The company might struggle with difficulties at various areas of their activities. Trying to address all the issues is time- and efforts-consuming, as well as ineffective. Therefore, the managers need tools that will enable them to address the most challenging areas.
Pareto charts are used to find the most significant influences on the process and effectively address the issues. The Pareto chart helps to identify the areas that bring the maximal contribution in the process. For example, for a grocery store a Pareto chart shows which products are responsible for the maximal profit. Basing on this, the manager can decide which products to order, where to improve service or delivery system, and which products should be excluded from the order list. Concentration on the issues that significantly contribute to the company success will help to improve the company performance and save time and efforts.
Fishbone Diagrams
When a company has some problems, the actions required to improve the situation are typically written down. The fishbone diagram is a tool used to organize the ideas generated for addressing the problem. Fig. 1 illustrates the fishbone diagram.
The central line (“spine”) is a problem or an issue; the side blocks propose the areas or ideas for improvement. The areas improvement are linked to the “spine” by the “bones” which are used to write down the ideas, stages or steps to improve the situation.
The control charts are good for identifying seasonal trends in the industry. When sales are plotted as a function of time, the minimum and maximum points can be found, and the corresponding periods of low or busy activity determined. This helps to adjust inventory and staff workload.
Generally, the diagnostic techniques for quality goal are powerful tools to identify the problem and determine the ways of its solution.
