Effects of non-normal quality data on the integrated model of imperfect maintenance, early replacement, and economic des
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Effects of non‑normal quality data on the integrated model of imperfect maintenance, early replacement, and economic design of X̄ ‑control charts M. A. Pasha1 · M. Bameni Moghadam1 · M. A. Rahim2 Received: 7 May 2017 / Revised: 23 June 2018 / Accepted: 7 September 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract The quality characteristic of a product for designing a control chart is commonly assumed to be normally distributed. However, this may not be reasonable in many practical applications. This study investigates the effects of non-normality data on the economic design of X̄ -control charts for systems under imperfect maintenance and the possibility of age-dependent repair before failure. These preventive maintenance policies increase the reliability of a system by reducing the shift rate to the out-of-control state of the process. A generalized economic model of the joint optimization problem is adopted for the Burr distributed quality data to derive the optimal design parameters of the integrated model under non-normality; i.e., the maintenance level, the replacement time, the sample size, the sampling intervals, and the control limits coefficient. Numerical examples reveal that the choice of quality characteristic distribution significantly affects the optimal design parameters of the integrated model. Furthermore, the higher maintenance levels reduce the quality control costs in non-normal cases similar to normal traditional approach. Keywords Non-normal distributed data · Imperfect maintenance · Truncated production cycle · Deteriorating process · Integrated hazard over sampling intervals
* M. A. Pasha [email protected] M. Bameni Moghadam [email protected] M. A. Rahim [email protected] 1
Department of Statistics, Allameh Tabataba’i University, Beheshti‑Ghasir Ave., Tehran 1513615411, Iran
2
Faculty of Business Administration, University of New Brunswick, Fredericton, NB E3B 5A3, Canada
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1 Introduction Control chart is the most popular instrument of statistical process control for decreasing the variation and increasing the efficiency of the production process. To implement any control chart, its design parameters, namely the sample size, the sampling intervals and the control limit coefficient, must be determined. The statistical optimization of the design can be attained by considering the distribution of the quality characteristic and assigning specific values to statistical criteria (e.g., the average run length). However, this kind of design does not pay any attention to the economic aspects of the design. Duncan (1956) firsts introduced the economic design (ED) of X̄ -chart to control process mean. Alongside the output characteristic distribution, the ED needs a distribution for the in-control time of the process, which is called the shock model or the process failure mechanism (PFM). The common approach in an ED problem is to define a quality cycle as the consequent periods starting from the in-control state to the
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