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Simple statistical tools for product quality monitoring and improvement

Source:FoodPacific Manufacturing Journ     Date:2021-09-10
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CEO, Quality Partners Company, Ltd.

Academician Emeritus International Academy for Quality (IAQ)



RETENTION of product quality leadership in the marketplace rests heavily on the manufacturer’s capability to sustain timely implementation of approaches to monitoring of their product’s comparative consumer acceptability and their continuous improvement activities. If a company’s product is observed to have significantly declined in consumer acceptability level relative to its closest competitor, this should be promptly evaluated, and approaches to its improvement immediately initiated. To determine if a positive change had taken place as a result of the improvement process, effective statistically-based monitoring tools should be utilised to gauge product performance through time. For such activities, proper quantitative measurements are required and collected data subsequently analysed and interpreted using simple statistical tools. These practices are commonly employed by successful companies because they appreciate the importance of measurements coupled with the capability to analyse and interpret collected data using simple but effective statistical tools.


Basic statistical terms, symbols and formula

The use of statistics implies numbers obtained from measurements of desired information from the different target sample or population. It relies on certain basic concepts that quantitatively describe the data collected from a representative sample drawn at random from a population. Table 1 shows the basic terms and symbols used to examine data for analysis and interpretation so that reliable information and conclusions about the population under study can be drawn.  Basic statistical terms start with Sample represented by small “n” which estimates the value of the Population symbolized by big “N” where every member is represented by Xi (read X-sub i). Thus, “n” is the sample size drawn at random from the Population of finite size “N”. The central tendency or average ( X bar), is obtained by adding all values of each Xi in the sample “n” divided by “n”. The same is done for all Xi in the whole population to obtain the population Mean U (mu). Since there is an average or mean, then each Xi of the sample or population can vary in amount from their respective means. This is measured through the use of the population variance s2 (Sigma squared), the square-root of which is known as the population standard deviation (s) which is estimated respectively by the sample variance S2 and standard deviation S. These are the major considerations when it is desired to determine if there is a significant difference between two means utilising a “test statistic” at a chosen level of significance and the process is known as Test of Hypothesis. From results of the test, conclusions about the population being studied can be made with usually between 95% and 99% level of confidence with a probable error of respectively 5% and 1% called level of significance (Gatchalian and Brannan, 2011).                   

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Comparative product acceptability in the marketplace

The food industry is the world’s largest business since people need to consume food several times a day. Survival in a highly competitive market is a big challenge for those engaged in food manufacturing. It is smart company leaders who can achieve success, because they pay close attention to their consumer requirements and ensure these are fulfilled. In food manufacturing, measures of customer satisfaction compared with competitors provide a good indicator of their relative position in the marketplace. This can be achieved through determination of comparative levels of product acceptability through consumer tests. Sensory evaluation methods provide the major tools in the measurement of customer acceptability or preference, as well as, in understanding the causes for observed significant product variations.

When there is a noticeable decline in sales through time, the implication could be a shift in consumer’s choice of products or the competitors have developed a much better item. The use of the “9-point hedonic rating scale” (score of 9 =like extremely and 1= dislike extremely) to determine consumer acceptability for a given product manufactured by different companies, gives a good measure of product acceptability (Gatchalian, M.M. and Brannan, G.D. 2011). Average “hedonic ratings” from a representative sample of the consumer population can provide information whether a significant difference between the company product and the competitors actually exists. Table 2 shows the Z-test to determine if there is a significant difference between the closest competitor (A) and the company product (B) based on their respective hedonic rating means ( A and B) and variances (S2A and S2B). Consumer test for acceptability requires a sample size of 50 or more for the Z-test to be reliable with the assumption that random sampling was employed in the selection of sample consumer respondents.

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Company product quality versus competitor

The company product with average hedonic rating of 6.69 ( B) is significantly lower in average “hedonic rating” than the closest competitor’s product rating of 7.54 (A) since Zc = 2.196 is greater than Z tab = 1.96 at 5% level of significance. The next move would be to identify the quality characteristic(s) that caused the difference. Quantitative Descriptive Analysis (Sullivan, M.G. 2017) is a sensory evaluation method which enables the identification of specific product attributes, as well as, their intensities for use in comparisons. A simple “t-test for difference” will help identify characteristics which are seen to be significantly different between the products of the two companies. These findings provide the occasion to adequately plan for quality improvement directions especially when specific attributes had been identified to require change to improve the product. Table 3 shows the formula for “t-test for difference”, a simple statistical tool appropriate for proper identification of the starting point for change. The test can be used even when the respondents are just 5 or more, or less than 50 since this time trained panelists within the company do the evaluation instead of the target consumers.

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Product quality monitoring and improvement

Once product characteristics (i.e. flavour in beverage) requiring improvement have been identified, some changes can be initiated to make the product better than that of the closest competitor (Gatchalian, M.M. 2018). This would require some adjustments either on the formulation or on the process or both and changes continued until the desired product improvement had been achieved. To monitor performance of the improvement approaches, a simple control chart (Kubiak, T.M. 2012) can determine extent of variation of the critical product characteristics. Fig. 1 shows a model control chart (C.C.) for a measurable critical product characteristic like brix to acid (B/A) ratio for critical flavour of the company’s beverage. For the C.C. model in Fig. 1, the y-axis is the mean of B/A of samples in each subgroup being monitored through time in x-axis which are subgroup means per production day 1 up to day 20 at least. The bold central line (CL) is the mean of means obtained from the average of all subgroup (3 or more samples per subgroup) means divided by the number of subgroups.  At least 20 subgroups are required before the mean for the CL is computed to ensure a reliable result.

Fig 1.jpg


The Lower Control limit (LCL) and the Upper Control Limit (UCL) represented by broken lines in Fig. 1 show the limits for which the values of the critical characteristic would most likely fall when means of each subgroup is plotted from Day 1 production period to Day 2 up to the 20th subgroup on 20th production day. If only natural causes of variation occurred at each production period, no subgroup mean will be bigger than the UCL or lower than the LCL. This situation implies that the process had successfully controlled the variation of the means of the critical characteristic being monitored per production period. If the observed distance between the LCL and UCL appears larger than desired, this could imply the need to review the process to determine if variation reduction can still be done. Fig. 2 shows “Maintaining 1” or the current level of variation.  If reduction of variation was done through process improvement, this could be labeled as “Improvement 1” as seen in Fig. 2.

Fig 2.jpg

Improvement 1 showed no point either above UCL or below LCL indicating absence of any “outlier”. The improved process was repeated for another period of 20 observations and this was labeled “maintaining 2” where again no “outlier” was noted indicating that farther variation reduction could still be possible. This led to another improvement and control 3.

The C.C. approach is one of the most useful statistical tools for quality monitoring and improvement. There are at least seven different types of C.C. from which manufacturers can choose. The major advantage of C.C. especially for monitoring change, is that it allows the operators to immediately see the progress of their operations through time. Also, should an “outlier” occur in day 5 production for instance, immediate action on the situation can be made, thus avoiding more production of defective goods.


Summary and conclusions

Simple statistical tools are readily available and are easy to use in various situations or needs in the organisation. Significant difference between means of quantified measures can be obtained through the use of either the z-test or t- test for difference. Product and process quality maintenance and or improvement can be monitored using a simple control chart. These statistical tools are important in product quality monitoring and improvement activities, which are necessary for business success especially by manufacturing enterprises. Early appreciation by company leaders of the importance of statistical methods and their applications can generate and/or enhance interest in statistical approaches necessary for product quality development, monitoring and improvement. All these tools when effectively utilised and sustained through time will provide assurance of the Company’s profitability.


Literature cited

Gatchalian, Miflora M. 2018. Innovation management in food product development. Food Pacific Manufacturing Journal. Vol. XVIII NO. 2, (March) ISSN 1608-7100. Ringier Trade Media Ltd. Hongkong

Gatchalian, Miflora M. and Brannan, Grace D. 2011. Sensory Quality Measurement: Statistical Analysis of Human Responses, 3rd edition. Quality Partners Company, Ltd. Quezon City Philippines. 283pp. ISBN 978-971-691-921-9.  

Juran, Joseph and De Feo. Joseph. 2010. Juran’s Quality Handbook: The Complete Guide to Performance, 6th ed. New York, McGraw-Hill. 1111 pp. ISBN 978-0-07-162973-7       

Kubiak, T.M. 2012. The Certified Six Sigma Master Blackbelt Handbook. ASQ Quality Press , Milwaukee Wisconsin USA. 645pp.  ISBN 978-0-87389-805-8.

O’Sullivan, Maurice G. 2017. A Handbook for Sensory and Consumer-Driven New Product Development. Innovative Technologies for the Food and Beverage Industry. ELSEVER Imprint Woodland Publishing, UK. 337pp. ISBN 978-0-08-100352-7



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